VOLUME 1, PAGES 1--126, FEBRUARY 1974 Congratulations to the thousand (editorial) ............................... 1--2 A letter of Al-Biruni: Habash al-Hasib's analemma for the qibla E. S. Kennedy and Y. `Id ........................................... 3--11 An Archimedean tract of Immanuel Tov-elem (14th cent.) N. L. Rabinovitch ................................................. 13--27 Hereditary stress as a cultural force in mathematics R. L. Wilder ...................................................... 29--46 Yang Hui's commentary on the ying nu chapter of the Chiu chang suan shu Lam L.-Y. ......................................................... 47--64 šbersiedlung eines deutschen Mathematikers von Braunschweig nach Kazan im Jahre 1807/08. Zur Biographie von M. Bartels, des Lehrers von Gauss und Lobachevskij K.-R. Biermann .................................................... 65--77 The earliest known record of California Indian numbers B. B. Hughes, OFM ................................................. 79--82 Henry Wilbraham and Gibbs Phenomenon in 1848 F. Ustina ......................................................... 83--84 SOURCES ................................................................. 85--86, 90 A note on mathematical papers in the archives of the Royal Institution of Great Britain J. R. Friday ...................................................... 85--86 BOOK REVIEWS ........................................................... 95--112 Abriss der Geschichte der Mathematik, by D. J. Struik (C. Lemaire) ...................................................... 95--96 Diofant i diofantovy uravneniya (Diophantus and diophantine equations) by I. G. Bashmakova (A. P. Gittleman) ................................................. 96--97 Razvitie teorii chisel v Rossii (The development of number theory in Russia) by E. P. Ozhigova (Clas-Olof Selenius) .................................................. 97 Classical and modern integration theories by Ivan N. Pesin (E. J. Barbeau) ................................................... 97--98 A computer perspective by the office of Charles and Ray Eames (Henry S. Tropp) ................................................. 99--100 Differential equations: with applications and historical notes by George F. Simmons (Carl B. Boyer) ................................................. 100--102 Mathematics in civilization by H. L. Resnikoff and R. O. Wells, Jr. (J. L. Berggren) ................................................ 102--106 A history of set theory by Philip E. Johnson (Robert McGuigan) ............................................... 106--108 Arabic arithmetic. The arithmetic of Aba al-Wafa' al-Buzajani, 10th century by A. S. Saidan (G. P. Matvievskaya) ............................................ 108--112 ABSTRACTS ......................................................... 113--126, 28 VOLUME 1, PAGES 127--252, MAY 1974 Should we be mathematicians, historians of science, historians, or generalists? (editorial) ..................................... 127--128 Mathematics and discovery in Galileo's physics S. Drake ........................................................ 129--150 The beginnings of mathematics in a howling wilderness E. R. Hogan ..................................................... 151--166 The introduction of mathematics in higher education in China, 1865--1887 F. J. Swetz ..................................................... 167--179 BOOK REVIEWS Creative Teaching: Heritage of R. L. Moore by Reginald D. Traylor with William Bane and Madeline Jones (P. R. Halmos) .................................................. 188--192 Bibliography and Research Manual of the History of Mathematics by Kenneth O. May (I. Grattan-Guinness) ........................................... 192--194 Bolyai, Sau Aventura Geometriilor Neeuclidiene by Florica T.Campan (H. Guggenheimer) .................................................... 194 Demotic Mathematical Papyri by Richard A. Parker (K. Vogel) ...................................................... 195--199 O R -> C. J. The Foundations and Mathematical Models of Operations Research with Extensions to the Criminal Justice System by Haig Edward Bohigan (P. J. Schellengerg) ............................................ 199--200 The Euler-Mayer Correspondence (1751--1755): A New Perspective on Eighteenth-Century Advances in the Lunar Theory by Eric C. Forbes (R. Calinger) ................................................... 200--202 G”ttingen and New York Film produced by the Mathematical Association of America (B. B. Hughes) ....................................................... 202 Development of Modern Mathematics by J. M. Dubbey (J. V. Grabiner) ................................................ 202--204 The Origins of Digital Computers: Selected Papers by Brian Randell (D. E. Knuth) ................................................... 204--207 Die Hilbertische Probleme by P. S. Alexandrov (I. Kaplansky) .................................................. 207--208 A Concise History of Science in India by D. M. Bose, S. N. Sen, and B. V. Subbarayappa (A. Volodarsky) ............................... ................. 208-212 Development of Mathematical Logic by R. L. Goodstein (A. Urquhart) ................................................... 212--214 A Handbook of Terms Used in Algebra and Analysis by A. G. Howson (J. H. Baumwell) ..................................................... 214 The Paradox of the Liar by R. L. Martin (E. J. Ashworth) ................................................ 215--218 ABSTRACTS .............................................................. 219--252 VOLUME 1, PAGES 253--386, AUGUST 1974 The Canadian connection (editorial) ........................................ 253 Sur l'histoire des d‚monstrations analytiques du th‚orŠme fondamental de l'alg‚bre S.S. Petrova .................................................... 255--261 Mathematicians in the history of meteorology: the pressure-height problem from Pascal to Laplace H.H. Frisinger ...................................................263--286 An Indian form of third order Taylor series approximation of the sine R. C. Gupta ..................................................... 287--289 ``Die Muse der Pythagoreer'' zur Fruhgeschichte der Geometrie Arp˜d Szabo ......................................................291--316 On medieval Islamic multiplication tables D. A. King ...................................................... 317--323 SOURCES .................................................................... 324 BOOK REVIEWS ........................................................... 333--350 Origins of Modern Algebra by Lubos Novy (Garrett Birkhoff) ............................................... 333-337 Mathematicians from Antiquity to Today by J. Fang (K. R. Biermann) ................................................ 337--339 Akademik V. A. Steklov by V. S. Vladimirov and I. I. Markush (V. Linis) ...................................................... 339--341 The IBM Watson Laboratory at Columbia University by J. F. Brennan (Saul Rosen) .................................................... 341--342 The Mathematical Association of America: Its First Fifty Years ed. by K. O. May (James K. Bidwell) .............................................. 342--344 Chinese Science: Exploration of an Ancient Tradition by S. Nakayama and N. Sivin (Hideo Hirose) .................................................. 344--346 Al-Bahir in Algebra by as-Samaw'al, ed. by S. Ahmad and R. Rashed (A. S. Saidan) .................................................. 346--347 Humanism and the Rise of Science in Tudor England by A. McLean (R. C. H. Tanner) ............................................... 348--350 Philosophy and Mathematics: From Plato to the Present by R. J. Baum (Mario Bunge) ........................................................ 350 ABSTRACTS .............................................................. 351--386 VOLUME 1, PAGES 387--516, NOVEMBER 1974 Peano's concept of number H. C. Kennedy ................................................... 387--408 The mathematical studies of G. W. Leibniz on combinatorics Eberhard Knobloch ............................................... 409--430 Gergonne's 1815 paper on the design and analysis of polynomial regression experiments (S. M. Stigler) ................................................. 431--447 SOURCES ..................................................................... 448 BOOK REVIEWS ........................................................... 464--480 Mathematics in the Time of the Pharaohs by Richard J. Gillings (A. E. Raid) .................................................... 464--468 Carl Friedrich Gauss: Werke by the K”nigliche Gesellschaft der Wissenschaften zu G”ttingen (C.J. Scriba) .................................................... 468-470 The Mathematical Career of Pierre de Fermat 1601-1665 by Michael S. Mahoney (Jean Itard) .................................................... 470--476 Scientific Instruments of the Seventeenth Century by Maurice Daumas (S. Drake) ...................................................... 476--477 Invisible Colleges. Diffusion of Knowledge in Scientific Communities by Diana Crane (W.R. Scott) .................................................... 477--479 Time and Method: An Essay on the Methodology of Research by F. Gonseth (G. J. Whitrow) ................................................. 479--480 ABSTRACTS .............................................................. 481--510 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME I........................................................... 511 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME I....................................... 512--516 VOLUME 2, PAGES 1--126, FEBRUARY 1975 Cauchy and the spectral theory of matrices Thomas Hawkins ..................................................... 1--29 On the sources of my book Moderne Algebra B. L. Van der Waerden ............................................. 31--40 Reports on mathematics in Viet Nam Le Van Thiem ...................................................... 41--42 Mathematical bibliography for W. H. and G. C. Young I. Grattan-Guinness ............................................... 43--58 SOURCES ................................................................. 67--73 A medieval physico-mathematical manuscript newly discovered in the Kuibyshev Regional Library Boris A. Rosenfeld ..................................................7--69 The Leonard J. Savage papers Andrew M. Patterson ............................................... 70--72 A renewed appeal for the preservation of archival materials by the CBMS Advisory Committee on History ..................................... 72--73 BOOK REVIEWS ............................................................ 86--101 Iz istorii tochnykh nauk na srednevekovom blizhnem i srednem vostoke [From the History of the Exact Sciences in the Medieval Near and Middle East] by S. K. Sirazhdinov (E. S. Kennedy) ................................................... 86--90 Giuseppe Peano by Hubert C. Kennedy (A. F. Monna) ..................................................... 90--92 Goethe kak estestvoispytatel [Goethe as a Natural Scientist] by I. I. Kanaev (Martin Dyck) ..................................................... 92--95 The Vortex Theory of Planetary Motions by E. J. Aiton (Laszlo Vekerdi) .................................................. 95--97 Casuality and Scientific Explanation by William A. Wallace (P. E. Hodgson) .................................................. 97--100 The Origins of Feedback Control by Otto Mayr (Colin A. Russell) ................................................... 100 Probability and Statistical Inference in Ancient and Medieval Jewish Literature. by N. L. Rabinovitch (F. N. David) ........................................................ 101 ABSTRACTS .............................................................. 102--126 VOLUME 2, PAGES 127--252, MAY 1975 Did Newton renounce infinitesimals? Tyrone Lai ...................................................... 127--136 Address on the 65th birthday of J. E. Hofmann at Oberwolfach (portrait) Johann Jakob Burckhardt ......................................... 137--146 Chronology of J. E. Hofmann, biobibliographic note, and supplementary bibliography of his publications C. J. Scriba .................................................... 147--152 Notice sur les travaux scientifiques Gustave Choquet ................................................. 153--160 Ten ``laws'' concerning patterns of change in the history of mathematics Michael J. Crowe ................................................ 161--166 Rationale of the Chakravala process of Jayadeva and Bhaskara II Clas-Olof Selenius .............................................. 167--184 Historiographic vices I. Logical attribution Kenneth O. May .................................................. 185--187 Euclid and the fundamental theorem of arithmetic M. D. Hendy ..................................................... 189--191 SOURCES ............................................................... 200--202 The mathematical papers and library of Sir Edward Collingwood in the University of Durham I. Grattan-Guinness ............................................. 200--202 Archives of mathematical journals J. D. Gray ........................................................... 202 BOOK REVIEWS .......................................................... 204--223 Lazare Carnot Savant by Charles Coulston Gillispie (Ren‚ Taton) ......................................................... 204--207 Africa Counts by Claudia Zaslavsky (R. W. Wilder) ................................................... 207-210 Statistical Papers in Honor of George W. Snedecor by T. A. Bancroft (Churchill Eisenhart) ........................................... 211--218 Ming Kan No Syuzan Syo [Chinese Abacus Books Published in the Ming Age] by Akihito Kodama (Shin-ichi Oya) ................................................. 218--219 Euclid and his modern rivals by Lewis Carroll (Daniel Pedoe) .................................................. 219--222 Joseph Fourier 1768--1830 by I. Grattan-Guinness (J. W. Herivel) ................................................. 222--223 ABSTRACTS ............................................................. 224--252 VOLUME 2, PAGES 253--424, AUGUST 1975 The geometry of African art II. A catalog of Benin patterns Donald W. Crowe ................................................. 253--271 The invariance of dimension: Problems in the early development of set theory and topology Joseph W. Dauben ................................................ 273--288 The space-time continuum H. S. M. Coxeter ................................................ 289--298 The earliest reckoning books existing in the Persian language Heinrich Hermelink .............................................. 299--303 Some historical aspects of the development of mathematical analysis in Hungary M. Mikol˜s ...................................................... 304--308 D'Alembert's letter to Euler of 3 March 1766 Peeter Mrsepp ................................................. 309--311 Ausz disem wirdt vil dings gemacht: A Drer construction of tangent circles Dan Pedoe ....................................................... 312--314 Historiographic vices II. Priority chasing Kenneth O. May .................................................. 315--317 REVIEWS ............................................................... 339--375 `Boethius' Geometrie II by Menso Folkerts (G. P. Matvievskaya) ............................................ 339--341 Diderot by Arthur M. Wilson (Charles C. Gillispie) .......................................... 342--344 Einstein. Zhizn, Smert, Bessmertie by B. G. Kuznetsov (Martin Dyck) ................................................... 344--347 Women in Mathematics by Lynn M. Osen (Mary E. Williams) .............................................. 348--349 Georgii Nikolaevich Nikoladze by A. N. Bogolyubov (Esther Portnoy) ..................................................... 349 Babbage, La Macchina Analitica by Mario G. Losano (Umberto Forti) ................................................. 350--353 Chinese Mathematics in the Thirteenth Century: The Shu-Shu Chiu-Chang of Ch'in Chiu-Shao by Ulrich Libbrecht (Lam Lay Yong) .................................................. 353--355 English-Greek Mathematical Dictionary by C. P. Tzelekis (S. P. Zervos) ....................................................... 355 Matematica Si Viata by Simion Stoilow (George St. Andonie) ............................................ 356--358 Men and Discoveries in Mathematics by Bryan Morgan (Gregory H. Moore) .............................................. 358--359 Leibniz and Dynamics by Pierre Costabel (C. Truesdell) .................................................. 360--361 History of Mathematical Logic from Leibniz to Peano by N.I. Styazhkin (Evandro Agazzi) ................................................ 361--365 Mathematical Education in China: Its Growth and Development by Frank Swetz (Ho Peng Yoke) .................................................. 365--366 Die Mathematik und Ihre Dozenten an Der Berliner Universit„t 1810--1920 by Kurt-R. Biermann (Ronald Calinger) ............................................... 367--369 The History of Quantum Theory by Friedrich Hund (Lewis Pyenson) ................................................. 370--375 ABSTRACTS VOLUME 2, PAGES 425--624, NOVEMBER 1975 Proceedings of the American Academy Workshop on the Evolution of Modern Mathematics held at the American Academy of Arts and Sciences in Boston, Massachusetts, August 7--9, 1974. Edited by Garrett Birkhoff with the assistance of Sue Ann Garwood ......................................................... 425--615 Forward John Voss ....................................................... 425--427 Preface Garrett Birkhoff and Sue Ann Garwood ............................ 429--430 Participants in the Workshop .......................................... 431--432 Opening Remarks for the Conference Garrett Birkhoff and I. B. Cohen ................................ 433--436 Part A: Historiography Introduction Garrett Birkhoff ........................................... 437--438 The mathematician, the historian and the history of mathematics J. V. Grabiner ............................................. 439--447 What is good history and who should do it? Kenneth O. May ............................................. 449--455 Progress in mathematics Elaine Koppelman ........................................... 457--463 The role of oral communication Henry Tropp ................................................ 465--468 Ten ``laws'' concerning conceptual change in mathematics Michael J. Crowe ........................................... 469--470 A role for the history of mathematics Phillip S. Jones ........................................... 471--472 Part B: History of Foundations Introduction Garrett Birkhoff ........................................... 473--474 Preliminary notes on the historical significance of quantification and of the axioms of choice in the development of mathematical analysis I. Grattan-Guinness ........................................ 475--488 Russell's logical progress: some new light from manuscript sources I. Grattan-Guinness ........................................ 489--495 The cradle of modern topology, according to Brouwer's inedita Hans Freudenthall .......................................... 495--502 Part C: Foundations of Mathematics Introduction Garrett Birkhoff ........................................... 503--505 The crisis in contemporary mathematics Errett Bishop .............................................. 507--517 Commentary on Bishop's talk Nancy Kopell and Gabriel Stolzenberg ....................... 519--521 Remarks against foundational activity Gerald Sacks ............................................... 523--528 What is mathematical truth? Hilary Putnam .............................................. 529--533 Part D: Algebra Introduction Garrett Birkhoff ........................................... 535--536 Introductory remarks on algebra, topology and analysis Jean Dieudonn‚ ............................................. 537--548 Some historical remarks on number theory Alan Baker ................................................. 549--553 Some remarks on harmonic analysis George Mackey .............................................. 555--562 Mathematical progress without fusion Thomas Hawkins ............................................. 563--566 High-school algebra in algebraic geometry Shreeram S. Abhyankar ...................................... 567--572 Part E: Analysis Introduction Garrett Birkhoff ........................................... 573--574 Opening remarks Morris Kline .................................................... 575 The relation of functional analysis to concrete analysis in 20th century mathematics Felix E. Browder ........................................... 577--590 The role of Fourier series in the development of analysis Antoni Zygmund ............................................. 591--594 A central object in mathematics: the Brownian motion J. P. Kahane ............................................... 595--600 How mathematics progresses Joaquin B. Diaz ............................................ 601--602 Appendices Additional discussion questions Sue Ann Garwood ........................................... 603--604 Bibliographies Garrett Birkhoff and Sue Ann Garwood ...................... 605--615 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME II........................................................ 619 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED OR ABSTRACTED IN VOLUME II..................................... 620--624 VOLUME 3, PAGES 1--132, FEBRUARY 1976 Questions of Policy (editorial) ..................................... 1--4 Probl‚mes d'histoire de l'analyse math‚matique au XIX‚me si‚cle. Cas de Karl Weierstrass et de Richard Dedekind Pierre Dugac ....................................................... 5--19 Shifting the foundations: Descartes's transformation of ancient geometry A. G. Molland ..................................................... 21--49 Quantitative growth of modern mathematics in Japan prior to 1930 Katsuhiko Yoshida ................................................. 51--54 D‚veloppements r‚cents de la th‚orie des graphes Jean Mayer ........................................................ 55--62 Oronce Fine's De speculo ustorio: A heretofore ignored early French Renaissance printed treatise on mathematical optics Richard P. Ross ................................................... 63--70 The anonymous Professor Gergonne Stephen M. Stigler ................................................ 71--74 BOOK REVIEWS ........................................................... 87--109 Istoriya Matematiki s Drevneishikh Vremen do Nachala XIX Stoletiya by A. P. Yushevich et al. (Hubert C.Kennedy) ............................................... 87--109 Science Awakening II. The Birth of Astronomy by Bartel L. van der Waerden (David Pingree) ................................................... 90--91 L'arithm‚tique Amusante by Edouard Lucas (William L. Schaaf) ............................................... 91--93 Functional Analysis in Historical Perspective by A. F. Monna (Bernard Aupetit) ................................................. 93--95 The Heritage of Copernicus: Theories ``Pleasing to the Mind'' edited by Jerzy Neyman (maurice Kendall) ................................................. 95--96 Physics at Seventeenth and Eighteenth Century Leiden by Edward G. Ruestow (Lewis Pyenson) .................................................. 96--100 From Mathematics to Philosophy by Hao Wang (Mario Bunge) ................................................... 100--102 A Boolean Anthology by D. G. Tahta (N. T. Gridgeman) ............................................... 102--103 Galileo's Intellectual Revolution: Middle Period, 1610--1632 by William R. Shea (Winifred L. Wisan) ............................................. 103--109 ABSTRACTS ............................................................. 110--132 VOLUME 3, PAGES 133--258, MAY 1976 This issue is dedicated to Dirk J. Struik with best wishes for his eighty-second birthday on September 30 and for many more years of the vigour he continues to share with the scholarly community. To Dirk J. Struik at eighty-two (editorial) ................................ 133 The introduction of probability into mathematics Ivo Schneider ................................................... 135--140 Euler's 1760 paper on divergent series E. J. Barbeau and P. J. Leah .................................... 141--160 The work of Indalecio Li‚vano on the foundations of real numbers Victor S. Albis-Gonz˜lez ........................................ 161--166 The origins and history of the Fields Medal Henry S. Tropp .................................................. 167--181 Multiplication in changing bases: A note on Lewis Carroll Francine Abeles ................................................. 183--184 Louis Charles Karpinski, historian of mathematics and cartography Phillip S. Jones ................................................ 185--202 BOOK REVIEWS .......................................................... 221--243 Ocherki razvitiya analiticheskoi teorii differenzialnykh uravnenii by V. A. Dobrovolskii (L.Reizins) ..................................................... 221--223 Les nouvelles pens‚es de Galilee. Par Marin Mersenne by Pierre Costabel and Michel-Paul Lerner (James MacLachlan) .............................................. 223--224 Entwicklung der Mathematik in der DDR edited by Horst Sachs (Sanford L. Segal) .............................................. 225--226 On a research program in early modern physics by Aant Elzinga (Norman L. Thomas) .............................................. 226--230 Selected works of Giuseppe Peano translated and edited by H.C.Kennedy (Maria Cinquini Cibrario) ....................................... 230--232 Probability theory: A historical sketch by L. E. Maistrov (Mario Bunge) ........................................................ 235 La math‚matisation des doctrines informes Proceedings of a colloquium directed by George Canguilhem (Mario Bunge) ........................................................ 235 Razvitie matematiki v Moldavskoi SSR. Kratkii ocherk by V. P. Bychkov and K. S. Sibirskii (Chandler Davis) ................................................ 235--236 The Einstein decade by Cornelius Lanczos (John T. Blackmore) .................................................. 236 Isaac Newton's Philosophiae Naturalis Principia Mathematica edited by Alexander Koyre and I. B. Cohen (W. Allan Gabbey) ............................................... 237--243 ABSTRACTS ............................................................. 244--258 VOLUME 3, PAGES 259--384, AUGUST 1976 This issue is dedicated to A. P. Yushkevich on the occasion of his seventieth birthday with best wishes for many more years of leadership of the history of mathematics community. Adolphe Pavlovich Yushkevich (On the occasion of his seventieth anniversary) Isabella G. Bashmakova, A. T. Grigoryan, A. I. Markushevich, F. A. Medvedev, and B. A. Rozenfeld ............................. 259--278 šber die šberlieferung der Elemente Euklids ber die L„nder des Nahen Ostens nach West-Europe H. L. L. Busard ................................................. 279--290 On approximation methods of Leonardo Fibonacci Stanislaw Glushkov .............................................. 291--296 T. S. Kuhn's theories and mathematics: A discussion paper on the ``new historiography'' of mathematics Herbert Mehrtens ................................................ 297--320 Person index for Delambre's Rapport Historique of 1810 Philip C. Enros ................................................. 321--324 History of mathematics and histories of other sciences I. Grattan-Guinness ............................................. 325--327 SOURCES ................................................................. 331 BOOK REVIEWS .......................................................... 341--361 Guiseppe Peano by Hubert C. Kennedy (Toshio Umezawa) ................................................ 341--342 Rapport historique sur les progr‚s des sciences math‚matiques depuis 1789, et sur leur ‚tat actuel, etc. by J. B. J. Delambre (Philip C. Enros) ............................................... 342--344 Vzaimosvyaz filosofii i matematiki v protesse istoricheskogo razvitiya ot epokhi vosrozhdeniya do nachala XX veka by O. I. Kerovskii (Ernest Stipanic) ............................................... 344--350 La topologie alg‚brique des origins … Poincar‚ by Jean-Clause Pont (H. Freudenthal) ................................................ 350--352 The life and times of the central limit theorem by William J. Adams (Wei-Ching Chang) ............................................... 353--354 The mathematical preface to the Elements of Geometrie of Euclide of Megara (1570) by John Dee (Nicoholas H.Clulee) ............................................ 355--357 Mathematics and mathematicians by P. Dedron and J. Itard (Phillip S. Jones) .............................................. 357--359 History of mathematics by Arthur Gittleman (Barnabus Hughes) ............................................... 359--361 ABSTRACTS ............................................................. 362--384 VOLUME 3, PAGES 385--514, NOVEMBER 1976 This issue is dedicated to C. B. Boyer, on what was to have been the occasion of his seventieth birthday on November 3, but is now a tribute to his services to scholarship and the wider community that were terminated by his sudden death on April 26, 1976. Reorganization (editorial) ................................................. 385 Carl B. Boyer---In Memoriam Morris Kline .................................................... 387--394 Chronology of Carl B. Boyer ........................................... 395--396 Bibliography of the writings of Carl B. Boyer Michael J. Crowe ................................................ 397--401 George Baron and the Mathematical Correspondent Edward R. Hogan ................................................. 403--415 The antecedents of Old Babylonian place notation and the early history of Babylonian mathematics Marvin A. Powell, Jr. ........................................... 417--439 SOURCES ............................................................... 472, 440 BOOK REVIEWS .......................................................... 481--499 Oeuvres compl‚tes d'Augustin Cauchy. II-e S‚rie---Tome XI edited under the direction of the Paris Academy of Sciences (I. Grattan-Guinness) ........................................... 481--485 Thomas Reid's Inquiry: The geometry of visibles and the case for realism by Norman Daniels (Richard G. Olson) .............................................. 486--487 Der Almagest: Die syntaxis mathematica des Claudius Ptolem„us in Arabisch-Lateinscher šberlieferung by Paul Kunitzsch (Bernard R. Goldstein) .......................................... 488--489 Karl Marx. Mathematische manuskripte edited by Wolfgang Endemann. Karl Marx. Manoscritti matematici translated and edited by Francesco Matarrese and Augusto Ponzio (H. C. Kennedy) ................................................. 490--494 History of mathematics: Topics for schools by Walter Popp (Howard Eves) ................................................... 495--496 Condorcet math‚matique et soci‚t‚ by Roshdi Rashed (Gilles Gaston Granger) ......................................... 496--497 The evolution of the Euclidean Elements by Wilbur Richard Knorr (B. L. van der Waerden) ......................................... 497--499 ABSTRACTS ............................................................. 500--508 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME III......................................................... 509 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME III..................................... 510--514 VOLUME 4, PAGES 1--126, FEBRUARY 1977 This volume is dedicated to Carl Friedrich Gauss in the year of the two hundredth anniversary of his birth, 30 April 1977. A Lacuna in Book I of Archimedes' Sphere and Cylinder J. L. Berggren ...................................................... 1--5 The interactions of mathematics and society in history. Some exploratory remarks H. J. M. Bos and H. Mehrtens ....................................... 7--30 An attack on Gauss, published by Legendre in 1820 Stephen M. Stigler ................................................ 31--35 Gauss' letter to Fuss of 4 April 1803 Peeter Mrsepp ................................................... 37--41 The Borel Law of Normal Numbers, the Borel Zero-One Law, and the work of Van Vleck Albert Novikoff and Jack Barone ................................... 43--65 BOOK REVIEWS ........................................................... 97--114 Leonard Euler Briefwechsel. Opera Omnia. Series Quarta Q: Commercium Epistolicum, Vol. I by A. P. Yushkevich et al. (E. J. Barbeau) .................................................. 97--100 Message d'un math‚maticien: Henri Lebesgue by Lucienne F‚lix (Burnett Meyer) ................................................. 100--102 Stability of motion by A. T. Fuller (C. W. Kilmister) ............................................... 102--103 Sets and integration. An outline of the development by D. van Dalen and A. F. Monna (Thomas Hawkins) ..................................................... 103 G. W. Leibniz marginalia in Newtoni Principia Mathematica by E. A. Fellmann (H. J. M. Bos) .................................................. 104--105 Histoire des math‚matiques by Jean-Paul Collette (Guy A. R. Guillotte) ........................................... 105--106 The Italian Renaissance of mathematics by Paul Lawrence Rose (Stillman Drake) ................................................ 106--107 Istoriya matematiki s drevneishikh vremen do nachala XIX stoletiya. Tom Pervyi: s drevneishikh vremen do nachala novogo vremeni edited by A. P. Yushkevich (Kurt Vogel) .................................................... 108--109 A survey of the Almagest. Acta historica scientiarum naturalium et medicinalium, Vol. 30 by Olaf Pedersen (N. M. Swerdlow) ................................................ 110--113 Die hauptschriften zur dyadik von G. W. Leibniz by Hans J. Zacher (Eberhard Knobloch) .................................................. 114 ABSTRACTS ............................................................. 115--126 VOLUME 4, PAGES 127--252, MAY 1977 An interpretation of Vi‚te's ``Calculus of Triangles'' as a precursor of the algebra of complex numbers Stanislav Glushkov .............................................. 127--136 Quadrature of the circle in ancient Egypt Hermann Engels .................................................. 137--140 Descartes and the birth of analytic geometry Eric G. Forbes .................................................. 141--151 The kinship of E. H. Moore and R. L. Moore Robert E. Greenwood ............................................. 153--155 Robert Adrain: American mathematician Edward R. Hogan ................................................. 157--172 Mersenne's solution for Galileo's problem of the rotating earth James MacLachlan ................................................ 173--182 The initial development of the WKB solutions of linear second order ordinary differerential equations and their use in the connection problem Arthur Schlissel ................................................ 183--204 On ``The Tantalizer'' and ``Instant Insanity'' Frank Harary .................................................... 205--206 SOURCES ............................................................... 207--210 The mathematical papers of Enrico Betti in the Scuola Normale Superiore of Pisa Umberto Bottazzini .............................................. 207--209 The correspondence of Camille Jordan Dale M. Johnson ...................................................... 210 BOOK REVIEWS .......................................................... 217--239 Condorcet. From natural philosophy to social mathematics by Keith Michael Baker (Maurice P. Crosland) ........................................... 217--218 Notice sur les travaux scientifiques, suivi de le parallelisme absolu et la th‚orie unitaire du champ by Elie Cartan (Hans Freudenthal) ................................................... 218 Joseph Fourier: The man and the physicist by John Herivel (Stephen G. Brush) .............................................. 219--221 Leonhardi Euleri opera omnia. Commentationes mechanicae et astronomicae ad scientiam navalem pertinentes edited by Walter Habicht (E. J. Barbeau) ...................................................... 221 Dirichlet's principle. A mathematical comedy of errors and its influence on the development of analysis by A. F. Monna (Ivor Grattan-Guinness) ......................................... 222--225 Census of the exact sciences in Sanskrit by David Pingree (Alexander Volodarsky) .......................................... 226--227 Arts and sciences at Padua: The Studium of Padua before 1350 by Nancy G. Sirasi (Edward A. Maziarz) .................................................. 227 Ricci and Levi-Civita's tensor analysis paper translated and edited by Robert Hermann (Judith R. Goodstein) ................................................ 228 Sophus Lie's 1880 transformation group paper by Robert Hermann, Sophus Lie's 1884 differential invariant paper by Robert Hermann (Thomas Hawkins) ................................................ 229--230 On the history of statistics and probability edited by D. B. Owen (James H. Cassedy) .............................................. 231--232 George Green, Miller, Snienton by R. M. Bowley, L. J. Challis, F. W. Sheard, F. M. Wilkins Jones, and David Phillips (L. Pearce Williams) ................................................. 232 Adventures of a mathematician by S. M. Ulam (Garrett Birkhoff) .............................................. 233--236 Die principien der h”heren analysis in ihrer entwickelung von Leibniz bis auf Lagrange als ein historisch-kritischer beitrag zur geschichte der mathematik dargestellt by Hermann Weissenborn (H. J. M. Bos) .................................................. 236--239 ABSTRACTS ............................................................. 240--252 VOLUME 4, PAGES 253--378, AUGUST 1977 This issue is dedicated to Ren‚ Taton, distinguished historian of mathematics and a world leader of the wider history of science community, on the thirtieth anniversary of his first publication in the history of mathematics. Introduction, translation, and discussion of Chao Chun-Ch'ing's ``Notes to the Diagrams of Short Legs and Long Legs and of Squares and Circles'' Brendan S. Gillon ............................................... 253--293 Babbage, Peacock and modern algebra J. M. Dubbey .................................................... 295--302 Karl Marx and the foundations of differential calculus Hubert C. Kennedy ............................................... 303--318 Some examples of historical cryptanalysis Albert C. Leighton .............................................. 319--337 EDITORIAL .................................................................. 350 BOOK REVIEWS .......................................................... 355--369 The new elements of mathematics. Volume 1 edited by Carolyn Eisele (Charles V. Jones) .............................................. 355--360 Diocles on burning mirrors. The Arabic translation of the lost Greek original edited by G. J. Toomer (J. L. Berggren) ................................................ 360--363 A source book in classical analysis edited by Garrett Birkhoff with Uta Merzbach (Michael Bernkopf) .............................................. 364--365 The method of analysis. Its geometrical origin and its general significance by Hintikka J. and Remes U. (R. McKirahan) .................................................. 366--369 ABSTRACTS ............................................................. 370--378 VOLUME 4, PAGES 379--504, NOVEMBER 1977 Gauss as a geometer H. S. M. Coxeter ................................................ 379--396 Gauss and the eight queens problem: A study in miniature of the propagation of historical error Paul J. Campbell ................................................ 397--404 The Principia's theory of the motion of the lunar apse Philip P. Chandler .............................................. 405--410 Boris A. Rosenfeld on the 60th anniversary of his birth A. T. Grigoryan and A. P. Yushkevich ............................ 411--414 Babbage as a computer pioneer M. V. Wilkes .................................................... 415--440 A missing table in C. S. Peirce's New Elements of Mathematics, Vol. 1 Charles V. Jones ................................................ 441--442 Early support for mathematics from Rockefeller agencies Warren Weaver ................................................... 443--444 Some comments on R. J. Gillings' analysis of the 2/n table in the Rhind Papyrus M. Bruckheimer and Y. Salomon ....................................445--452 SOURCES .................................................................... 455 BOOK REVIEWS .......................................................... 461--481 Thinkers and tinkers: Early American men of science by Silvio A. Bedini (Elizabeth Hodes) ............................................... 461--463 Men and institutions in American mathematics edited by J. Daltan Tarwater, John T. White, and John D. Miller (Judith V. Grabiner) ............................................ 464--465 The kind of motion we call heat, a history of the kinetic theory of gases in the nineteenth century. Volume I by Stephen G. Brush (Jed Z. Buchwald) ............................................... 466--467 From Frege to G”del: A source book in mathematical logic, 1879--1931 edited by Jean van Heijenoort (Gregory H. Moore) .............................................. 468--471 Thomas Hobbes: De Homine. Trait‚ de L'Homme translation and commentary by Paul-Marie Maurin (Kurt Moller Pedersen) .......................................... 471--472 The Renaissance rediscovery of linear perspective by Samuel Y. Edgerton, Jr. (Phillip S. Jones) .............................................. 472--474 Ernst Eduard Kummer. Collected Papers. Volume I edited by Andr‚ Weil (Harold M. Edwards) ............................................. 475--478 Courant in G”ttingen and New York by Constance Reid (Harold M. Edwards) ............................................. 479--480 Graph Theory 1736--1936 by N. L. Biggs, E. K. Lloyd, and R. J. Wilson (Frank Harary) .................................................. 480--481 ABSTRACTS ............................................................. 482--498 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME IV ......................................................... 499 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME IV ..................................... 500--505 VOLUME 5, PAGES 1--126, FEBRUARY 1978 This issue is dedicated to Kenneth O. May. Kenneth O. May, 1915--1977 ................................................ 1--2 A Memorial Tribute to Kenneth O. May S. Drake, H. S. M. Coxeter, C. V. Jones, H. S. Tropp, C. J. Scriba, B. Sinclair, M. S. Mahoney, and D. J. Struik ......... 3--12 Johann Heinrich Lambert, mathematician and scientist, 1728--1777 J. J. Gray and Laura Tilling ...................................... 13--41 Archimedes and the spirals: The heuristic background Wilbur R. Knorr ................................................... 43--75 The origin of ``Zorn's Lemma'' Paul J. Campbell .................................................. 77--89 SOURCES ..................................................................... 93 BOOK REVIEWS ........................................................... 96--113 Seki takakazu zenshu edited and explained by A. Hirayama, K. Shimodaira and H. Hirose (Toshio Matsuzaki) ................................................ 96--98 Nihonjin no sugaku by S. Shimodaira (Toshio Matsuzaki) .................................................... 99 Evolution of mathematical concepts: An elementary study by Raymond L. Wilder (Michael J. Crowe) ............................................... 99--105 Grecheskaya logistika by A. M. Eganyan (Jacob Klein) ................................................... 105--107 Vorlesungen ber neuere geometrie by M. Pasch with an appendix by M. Dehn (B. L. van der Waerden) .............................................. 107 Galileo, two new sciences by Stillman Drake (D. Mangeron) ................................................... 107--108 Histoire compar‚e des num‚rations ‚crites, by Genevi‚ve Guitel (Evert M. Bruins) ABSTRACTS ............................................................. 114--126 VOLUME 5, PAGES 127--252, MAY 1978 How Bertrand Russell discovered his paradox I. Grattan-Guinness ............................................. 127--137 The Casorati-Weierstrass theorem (Studies in the history of complex function theory I) E. Neuenschwander ............................................... 139--166 The astronomical work of Carl Friedrich Gauss (1777--1855) Eric G. Forbes .................................................. 167--181 Gauss's contribution to statistics D. A. Sprott .................................................... 183--203 A thirteenth-century `proof' of the parallel postulate Sabetai Unguru .................................................. 205--210 Cayley's anticipation of a generalised Cayley-Hamilton theorem Tony Crilly ..................................................... 211--219 BOOK REVIEWS .......................................................... 234--245 Gottfried Wilhelm Leibniz. Mathematischer naturwissenschaftlicher und technischer briefwechsel edited by J. E. Hofmann and the Leibniz-Archiv der Nieders„chsichen Landesbibliothek, Hanover (Margaret E. Baron) ............................................. 234--237 La matematica come sistema ipotetico-deduttivo, profilo storico by Silvio Maracchia (Hubert C. Kennedy) ............................................ 237--239 Les syst‚mes d'‚quations polyn…omes dans le Siyuan Yujian (1303) by Jack Hoe (K. E. Pledger) ................................................ 239--241 Memoirs by P. Ya. Kochina (Esther R. Phillips and George W. Phillips) .................... 241--245 ABSTRACTS ............................................................. 246--251 VOLUME 5, PAGES 253--378, AUGUST 1978 Chinese interest in right-angled triangles Ang Tian-se .................................................... 253--266 šber eine bemerkung von G. W. Leibniz zu einem theorem in Newtons Principia Mathematica E. A. Fellmann ................................................. 267--273 Nicolai Nicolaevich Luzin and the Moscow school of the theory of functions Esther R. Phillips ............................................. 275--305 A bibliography of William Burnside (1852--1927) Ascher Wagner and Verity Mosenthal ............................. 307--312 Cauchy and the infinitely small Gordon M. Fisher ............................................... 313--331 SOURCES .......................................................... 274, 333--341 Der nachlass Axel Anthon Bj”rnbos M. Folkerts .................................................... 333--339 Establishment of ``The archives of American mathematics'' Albert C. Lewis ................................................ 340--341 BOOK REVIEWS .......................................................... 352--367 Briefwechsel zwischen Alexander von Humboldt und Carl Friedrich Gauss edited by K.-R. Biermann (D. J. Struik) ................................................. 352--353 The exhaustive treatise on shadows by Abu al-Rayhan Muhammad b. Ahmad al-Biruni translation and commentary by E. S. Kennedy (G. J. Tee) .................................................... 354--357 Bernard Bolzano: Gr”ssenlehre II. Reine zahlenlehre edited by Jan Berg (Philip Kitcher) ................................................ 358--363 Doctrine de l'angle solide by Florimond de Beaune edited by Pierre Costabel (Michael S. Mahoney) ............................................ 363--366 Ada, Countess of Lovelace: Byron's legitimate daughter by Doris Langley Moore (Anthony Hyman) ................................................. 366--367 ABSTRACTS ............................................................. 368--377 VOLUME 5, PAGES 379--500, NOVEMBER 1978 The origins of Cauchy's theory of the derivative Judith V. Grabiner .............................................. 379--409 Ricerche di P.~Tardy sui differenziali di indice qualunque, 1844--1868 Umberto Bottazzini .............................................. 411--418 On the Kronecker Nachlass Harold M. Edwards ............................................... 419--426 On the forgotten theorem of Mr. Vincent Alkiviadis G. Akritas and Stylianos D. Danielopoulos ............ 427--435 A history of the divergence theorem Charles H. Stolze ............................................... 437--442 Johann-Heinrich Rehbein: une voie philosophique vers la topologie Jean-Claude Pont ................................................ 443--454 Gauss and Tartu University Peeter Mrsepp ................................................. 455--459 SOURCES ............................................................... 470--472 BOOK REVIEWS .......................................................... 474--487 Gottfried Wilhelm Leibniz by R. Calinger (J. F. Peters) .................................................. 474--478 The Muslim contribution to mathematics by Ali Abdullah Al-Daffa' (George Saliba) ................................................. 478--479 A history of numerical analysis from the 16th through the 19th century by Herman H. Goldstine (Garrett Birkhoff) .............................................. 479--482 Gauss und die Nicht-Euklidische Geometrie by Hans Reichardt (Jeremy Gray) .................................................. 482--483 Biographien Bedeutender Mathematiker, Eine Sammlung von Biographien edited by Hans Wussing and Wolfgang Arnold (Eberhard Knobloch) ............................................. 483--485 About the theory of probability and mathematical statistics (correspondence of A. A. Markov and A. A. Tshuprov) edited by H. O. Ondar (Jerzy Neyman) .................................................. 485--486 Mathematisches Tagebuch, 1796--1814 von C. F. Gauss edited by K.-R. Biermann (Tord Hall) ..................................................... 486--487 ABSTRACTS ............................................................. 488--494 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 5 .......................................................... 496 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 5 ...................................... 497--500 VOLUME 6, PAGES 1--107, FEBRUARY 1979 This issue is dedicated to Laura Roebuck. A Message to Readers of Historia Mathematica from the Chairman of the International Commission on the History of Mathematics Christoph J. Scriba ................................................. 1--2 Note from the Editor Joseph W. Dauben .................................................... 3--4 The Contributions of Carl Friedrich Gauss to Geomagnetism G. D. Garland ...................................................... 5--29 The H. G. Wells Quote on Statistics: A Question of Accuracy James W. Tankard, Jr. ............................................. 30--33 šber Einen Gedanenstrich bei Frege: Eine Nachlese zur Edition Seines Wissenschaftlichen Nachlasses Gottfried Gabriel ................................................. 34--35 The Ladies' Diary or the Woman's Almanack, 1704--1841 Teri Perl ......................................................... 36--53 NOTE Beppo Levi and the Axiom of Choice Barbara Moss ...................................................... 54--56 SOURCES Contemporary Scientific Archives Centre, Oxford, England .................... 62 BOOK REVIEWS A history of ancient mathematical astronomy, by O. Neugebauer (N. M. Swerdlow) .................................................. 76--85 Razvitie ponyattiya integrala [The development of the concept of the integral], by F. A. Medvedev (Esther R. Phillips) .............................................. 85--91 Lobatchevski, by V. F. Kagan (Imre Toth) ....................................................... 91--97 ABSTRACTS .............................................................. 98--105 VOLUME 6, PAGES 109--231, MAY 1979 The Roots of Combinatorics N. L. Biggs ..................................................... 109--136 Karl M. Peterson: The Earliest Derivation of the Mainardi-Codazzi Equations and the Fundamental Theorem of Surface Theory Esther R. Phillips .............................................. 137--163 An Early Chinese Derivation of the Volume of a Pyramid: Liu Hui, Third Century A.D. Donald Blackmore Wagner ......................................... 164--188 SOURCES Archive for Linear Algebra and its Applications ............................ 206 Archive of the School Mathematics Study Group ......................... 206--207 Boncompagni Papers in the Library of Trinity College, Dublin .......... 207--208 BOOK REVIEWS An Annotated Bibliography of Cryptography, by David Shulman (Albert C. Leighton) ............................................ 209--212 Ocherki Istorii Teorii Funktsii Deistvitel'nogo Peremennogo [Essays on the history of the theory of functions of a real variable], by F. A. Medvedev (F. Smithies) ................................................... 213--218 Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China, by Frank J. Swetz and T. I. Kao (Lam Lay-Yong) .................................................. 218--220 ABSTRACTS ............................................................. 221--228 VOLUME 6, PAGES 233--349, AUGUST 1979 This issue is dedicated to Dr. Heinrich Hermelink. Heinrich Hermelink: In Memoriam Christoph J. Scriba ............................................. 233--235 Non-Euclidean Geometry---A Re-Interpretation Jeremy Gray ..................................................... 236--258 D'Alembert's Critique of Probability Theory L. J. Daston .................................................... 259--279 Zur Geschichte der Richardson-Extrapolation Hermann Engels .................................................. 280--293 In Memoriam Kurt G”del: His 1931 Correspondence with Zermelo on His Incompletability Theorem I. Grattan-Guinness ............................................. 294--304 "Class as One" and "Class as Many" before Modern Set Theory Ignacio Angelelli ............................................... 305--309 Ranking by Inversion: A Note on C. L. Dodgson Francine Abeles ................................................. 310--317 SOURCES Contemporary Scientific Archives Centre ............................... 326--327 BOOK REVIEWS Richard Dedekind et les Fondements des Math‚matiques, by Pierre Dugac (Thomas Hawkins) ................................................ 328--332 Girolamo Cardano (1501--1576), by Markus Fierz (Eberhard Knobloch) ............................................. 332--334 History of the Department of Mathematics of the University of Kansas, 1866--1970, by G. Baley Price (Albert C. Lewis) ............................................... 334--336 Les Math‚matiques Arabes (VIII-e - XV-e Siecles), by Adolf P. Youschkevitch (George Saliva) ...................................................... 337 ABSTRACTS ............................................................. 338--345 VOLUME 6, PAGES 351--490, NOVEMBER 1979 This issue is dedicated to Kurt-Reinhard Biermann on the occasion of his sixtieth birthday, with all best wishes for many years of continuing scholarship and leadership in the community of historians of mathematics. Kurt-Reinhard Biermann: Dedication .................................... 351--354 Descartes and the Geometrization of Thought: The Methodological Background of Descartes' G‚om‚trie Timothy Lenoir .................................................. 355--379 The First Example of a Recursive Function which is not Primitive Recursive C. Calude, S. Marcus, and I. Tevy ............................... 380--384 The Rejected Parts of Brouwer's Dissertation on the Foundations of Mathematics Walter P. Van Stigt ............................................. 385--404 Supplementary Notes on Medieval Islamic Multiplication Tables David A. King ................................................... 405--417 A Remark on Euclid II, ll Roger Fischler .................................................. 418--422 James Mills Peirce and the Cult of Quaternions Hubert Kennedy .................................................. 423--429 Gauss on Infinity William C. Waterhouse ........................................... 430--436 Ancient Portraits of Mathematicians Warren W. Esty .................................................. 437--441 BOOK REVIEWS History of Non-Euclidean Geometry. The Development of the Concept of Geometric Space, by B. A. Rozenfeld (Boris M. Schein) ............................................... 460--464 Dear Russell--Dear Jourdain. A Commentary on Russell's Logic, Based on his Correspondence with Philip Jourdain, by I. Grattan-Guinness (Ignacio Angelelli) ............................................. 464--466 A Critical Study of the Yang Hui Suan Fa A Thirteenth-Century Chinese Mathematical Treatise, by Lam Lay Yong (Joseph Needham) ................................................ 466--468 Felix Klein and Sophus Lie, by I. M. Yaglom (Samuel Kotz) ................................................... 468--469 Nikolai Ivanovich Fuss: 1755--1826, by V. I. Lysenko (Esther R. Phillips) ............................................ 469--472 ABSTRACTS ............................................................. 473--479 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 6 .......................................................... 486 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 6 ...................................... 487--490 VOLUME 7, PAGES 229--367, AUGUST 1980 This issue of Historia Mathematica is dedicated to Erwin N. Hiebert in honor of his 60th birthday. Because of the special nature of this Festschrift, the usual Departments, News, Notices, Reviews, and Abstracts do not appear. They will reappear as usual in the next issue of Historia Mathematica for this year (Volume 7, Number 4). Introduction Roger H. Stuewer ................................................ 229--233 Probabilistic Expectation and Rationality in Classical Probability Theory Lorraine J. Daston .............................................. 234--260 Mathematicians and World War I: The International Diplomacy of G. H. Hardy and G”sta Mittag-Leffler as Reflected in their Personal Correspondence Joseph W. Dauben ................................................ 261--288 Non-Euclidean Geometry and Weierstrassian Mathematics: The Background to Killing's Work on Lie Algebras Thomas Hawkins .................................................. 289--342 The Art and the Science of British Algebra: A Study in the Perception of Mathematical Truth Joan L. Richards ................................................ 343--365 VOLUME 7, PAGES 369--477, NOVEMBER 1980 Richard Courant and the Finite Element Method: A Further Look Frank Williamson, Jr. ........................................... 369--378 Thomas Bayes and Fluxions G. C. Smith ..................................................... 379--388 Woodhouse, Babbage, Peacock, and Modern Algebra Harvey W. Becher ................................................ 389--400 The Binomial Theorem: A Widespread Concept in Medieval Islamic Mathematics Mohammad Yadegari ............................................... 401--406 The Chinese Connection between the Pascal Triangle and the Solution of Numerical Equations of Any Degree Lam Lay-Yong .................................................... 407--424 Historique de la notion de compacit‚ Jean-Paul Pier .................................................. 425--443 SOURCES An Unpublished Manuscript of Hans Rademacher .................... 445--446 BOOK REVIEWS Piero dell Francesca's Mathematical Treatises: The "Trattato d'Abaco" and "Libellus de Quinque Corporibus Regularibus," by Margaret Daly Davis (Warren Van Egmond) ............................................. 449--451 Women and Mathematics, Science and Engineering. A Partially Annotated Bibliography with Emphasis on Mathematics and with References on Related Topics, by Else H#248yrup (Louis L. Bucciarelli) ............................................... 451 United States Diplomatic Codes and Ciphers 1775-1938, by Ralph E. Weber (David Shulman) ................................................. 452--454 Die Entstehung der Verbandsteorie, by Herbert Mehrtens (Garret Birkhoff) ............................................... 454--457 The Translation of the Elements of Euclid from the Arabic into Latin by Herman of Carinthia(?), edited by H. L. L. Busard (G. J. Toomer) .................................................. 457--458 ABSTRACTS.............................................................. 459--467 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 7........................................................... 473 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 7....................................... 474--477 VOLUME 7, PAGES 1--111, FEBRUARY 1980 This issue is dedicated to Professor Viggo Brun. Viggo Brun: In Memoriam Christoph J. Scriba ................................................. 1--6 LaGrange's Early Contributions to the Theory of First-Order Partial Differential Equations S. B. Engelsman .................................................... 7--23 Algebraische Untersuchungen in Italien, 1850--1863 Umberto Bottazzini ................................................ 24--37 The Trigonometric Tables of Al-Kashi in his Zij-I Khani Javad Hamadanizadeh ............................................... 38--45 Helmut Hasse in 1934 S. L. Segal ....................................................... 46--56 Female Philomaths Ruth and Peter Wallis ............................................. 57--64 NOTE: The History of the Concept of a Finite-Dimensional Vector Space Jeremy Gray ....................................................... 65--70 SOURCES Tardy's Letters and Library in Genoa Umberto Bottazzini ................................................ 84--85 BOOK REVIEWS Paradoks˜ Teorii Mnozhestb I Dialektika, by I. N. Burova (I. Grattan-Guinness) ............................................. 92--93 A History of the Mathematics Departments of the University of Colorado, by Burton W. Jones and Wolfgang Thron (G. Baley Price) .................................................. 93--95 Variationen uber ein Zahlentheoretisches Thema von C. F. Gauss, by H. Pieper (Harold M. Edwards) ............................................... 95--96 The Arithmetic of Al-Uqlidisi, by A. S. Saidan (David Pingree) ................................................... 97--98 The Mathematical Work of Charles Babbage by John Michael Dubbey (Philip C. Enros) ................................................ 98--100 ABSTRACTS ............................................................. 101--107 VOLUME 7, PAGES 113--228, MAY 1980 Huygens' Foundations of Probability Hans Freudenthal ................................................ 113--117 Gauss and Generalized Inverse Donald W. Robinson .............................................. 118--125 Bibhutibhusan Datta (1888--1958), Historian of Indian Mathematics R. C. Gupta ..................................................... 126--133 Solar and Lunar Velocities in the Alfonsine Tables Bernard R. Goldstein ............................................ 134--140 Discussions on Newton's Infinitesimals in Eighteenth-Century Anglo-America Roy N. Lokken ................................................... 141--155 A Translation of Bolzano's Paper on the Intermediate Value Theorem S. B. Russ ...................................................... 156--185 NOTE: The Egyptians and Pythagorean Triples Beatrice Lumpkin ................................................ 186--187 BOOK REVIEWS Witelonis Perspectivae Liber Primus, by Sabetai Unguru (Nicholas H. Steneck) ........................................... 199--200 Von Eudoxos zu Aristoteles. Das Fortwirken der Eudoxischen Proportionentheorie in der Aristotelischen Lehre vom Kontinuum, by Hans-Joachim Waschkies (Ian Mueller) ................................................... 200--210 The History of Statistics in the 17th and 18th Centuries against the Changing Background of Intellectual, Scientific and Religious Thought, edited by E. S. Pearson (James H. Cassedy) .............................................. 210--212 The Emergence of Probability, by Ian Hacking (Eberhard Knobloch) ............................................. 212--216 ABSTRACTS ............................................................. 217--224 VOLUME 8, PAGES 1--124, FEBRUARY 1981 A Marginal Note of Mersenne Concerning the "Galileian Spiral" Don Engelberg and Michael Gertner .................................. 1--14 Zermelo's Discovery of the "Russell Paradox" B. Rang and W. Thomas ............................................. 15--22 George Peacock and the British Origins of Symbolical Algebra Helena M. Pycior .................................................. 23--45 Tables Trigonometriques de Giovanni Bianchini Grazyna Rosinska .................................................. 46--55 NOTE The Solution of a Famous Two-Centuries-Old Problem. The Leonhard Euler-Latin Square Conjecture H. Howard Frisinger ............................................... 56--60 BOOK REVIEWS Didaktik der Mathematik, by Hans-Georg Steiner (Jens Hoyrup) ..................................................... 81--85 The Bicentennial Tribute to American Mathematics, 1776-1976, edited by Dalton Tarwater (Albert C. Lewis) ................................................. 85--90 Vito Vol'Terra (Vito Volterra), by E. M. Polishchuk (F. Smithies) ..................................................... 90--92 History of Analysis, edited by R. J. Stanton and R. O. Wells, Jr. (I. Grattan-Guinness) ............................................. 92--93 George E. Andrews: Partitions: Yesterday and Today, by New Zealand Mathematical Society (Elaine Koppelman) ................................................ 94--95 Proceedings of the First International Symposium for the History of Arabic Science, April 5--12, 1976. Volume II: Papers in European Languages, edited by A. Y. al-Hassan, G. Karmi, and N. Namnum (David Pingree) ................................................... 95--95 Chapters in the Recent History of Mathematics, Special issue of Nieuw Archief Voor Wiskunde (Paul P. Bockstaele) .............................................. 97--99 Imre Lakatos, Proofs and Refutations. The Logic of Mathematical Discovery, edited by John Worral and Elie Azhar (Timothy Lenoir) ................................................. 99--104 Storia Della Teoria delle Equazioni Algebrice, by Raffaela Franci and Laura Toti Rigetelli (Lubos Novy) .................................................... 104--105 Socialist Mathematics Education, edited by Frank J. Swetz (Hans Freudenthal) ................................................... 106 Geschichte der Elementarmathematik. BAND 1: Artihmetik und Algebra, by Johannes Tropke (Phillip S. Jones) .............................................. 106--109 ABSTRACTS.............................................................. 110--118 VOLUME 8, PAGES 125--234, MAY 1981 A. I. Markushevich as a Historian of Mathematics P. S. Alexandrov, A. N. Kolmogorov, and A. P. Youschkevitsch .... 125--132 John Ward's Method for the Calculation of Pi G. L. Cohen and A. G. Shannon ................................... 133--144 American Attempts to Solve Newton's Pasturage Problem Steven L. Jordan ................................................ 145--160 The History of Differential Forms from Clairaut to Poincar‚ Victor J. Katz .................................................. 161--188 SOURCES Centro studi per la mathematica medioevale ........................... 198 BOOK REVIEWS Da Cardano a Galois: Moment di storia dell'algebra, by Silvio Maracchia (Hubert Kennedy) ................................................ 199--200 La th‚orie g‚n‚rale de l'‚quilibre et du mouvement des syst‚mes, by Louis Poinsot (Craig Fraser) .................................................. 200--202 Die Berliner und die Petersburger Akademie der Wissenschaften im Briefwechsel Leonhard Eulers, Teil III (The Berlin and Petersburg Academies in the Correspondences of Leonhard Euler), edited by A. P. Juskevic and E. Winter, in cooperation with P. Hoffmann, T. N. Kladno, and Ju. Ch. Koplevic (Rdiger Thiele) ................................................ 202--205 Wittgenstein's Lectures on the Foundations of Mathematics, from the notes of R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smithies, edited by Cora Diamond (Ignacio Angelelli) ............................................. 205--207 Frantsuzskaya Shkola Teorii Funktsii i Mnozhestv, na Rubezhe XIX-XX VV (The French School of the Theory of Functions and Sets at the Turn of the XIX-XX Centuries), by F. A. Medvedev (Esther R. Phillips) ............................................ 208--211 Matematika XIX Veka. Matematicheskaya Logika. Algebra. Teoriya Chisel. Teoriya Veroyatnostei., edited by A. N. Kolmogorov (I. Grattan-Guinness) ........................................... 212--213 Histoire du theoreme des accroissements finis, by Pierre Dugac (Judith V. Grabiner) ............................................ 214--219 ABSTRACTS ....................................................... 220--228 VOLUME 8, PAGES 235--388, AUGUST 1981 Ettore Carruccio---The Man and the Scientist Bruno D'Amore ................................................... 235--242 An Outline of the Life and Work of E. B. Christoffel (1829-1900) Paul L. Butzer .................................................. 243--276 Methods and Traditions of Babylonian Mathematics: Plimpton 322, Pythagorean Triples, and the Babylonian Triangle Parameter Equations J”ran Friberg ................................................... 277--318 Burali-Forti's Paradox: A Reappraisal of its Origins Gregory H. Moore and Alejandro Garciadiego ...................... 319--350 BOOK REVIEWS Practical Geometry in the High Middle Ages: Artis Cuiuslibet Consummatio and the Pratike de Geometrie,} edited by Stephen K. Victor (Edith Sylla) ................................................... 368--375 Georg Cantor. His Mathematics and Philosophy of the Infinite, by Joseph Warren Dauben (Thomas Hawkins) ................................................ 368--375 Sadi Carnot et L'Essor de la Thermodynamique. Table Ronde du Centre National de la Recherche Scientifique (Erwin Hiebert) ................................................. 375--377 Die Pythagoreer: Religi”se Bruderschaft und Schule der Wissenschaft, by B. L. Van der Waerden (John Dillon) ................................................... 377--378 ABSTRACTS.............................................................. 379--383 VOLUME 8, PAGES 389--502, NOVEMBER 1981 Isabella Grigoryevna Bashmakova On the Occasion of Her 60th Birthday ................................................... 389--392 Arithmetic of Algebraic Curves from Diophantus to Poincar‚ Isabella G. Bashmakova .......................................... 393--416 How Trisections of the Angle Were Transmitted from Greek to Islamic Geometry Jan P. Hogendijk ................................................ 417--438 Theodore Strong and Ante-Bellum American Mathematics Edward R. Hogan ................................................. 439--455 NOTES The Egyptian Mathematical Leather Role---Line 8. How Did the Scribe Do It? Richard J. Gillings ............................................. 456--457 Wie kommt "Napoleons Satz" zu seinem Namen? Christoph J. Scriba ............................................. 458--459 BOOK REVIEWS Sur les Fondements de L'Analyse au XIX-e Si‚cle, by Pierre Dugac (Philip Kitcher) ................................................ 473--476 Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce: Essays by Carolyn Eisele, edited by R. M. Martin (Helena Pycior) ................................................. 477--481 Elwin Bruno Christoffel, Gedenkschrift (Dirk J. Struik) ................................................ 481--482 Greek Mathematics and the Architects to Justinian, by John Warren (Ivor Bulmer-Thomas) ............................................ 482--485 Briefwechsel zwischen Alexander von Humboldt und Heinrich Christian Schumacher,, by Kurt-R. Biermann (Otto Volk) ..................................................... 485--487 I. J. Bienayme. Statistical Theory Anticipated, by C. C. Heyde and E. Seneta (Lorraine J. Daston) ............................................ 487--488 ABSTRACTS ............................................................. 489--493 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 8 .......................................................... 498 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 8 ...................................... 499--502 VOLUME 9, PAGES 1--132, FEBRUARY 1982 Riemann's Contribution to Differential Geometry Esther Portnoy ..................................................... 1--18 Investigations of an Early Sumerian Division Problem, c. 2500 B.C. Jensoyrup .......................................................... 19--36 Anna Johnson Pell Wheeler: Her Life and Work Louise S. Grinstein and Paul J. Campbell .......................... 37--53 NOTE Minoan and Mycenaean Numerals Dirk J. Struik .................................................... 54--58 SOURCES The Manuscripts of Paul Charpit I. Grattan-Guinness and S. Engelsman .............................. 65--75 Unpublished Writings of Giuseppe S. Verzaglia Raffaella Franci and Laura Toti Rigatelli ......................... 76--77 A Manuscript by Teofilo Gallaccini in the Siena Municipal Library Rossella Vagaggini ................................................ 78--80 ESSAY REVIEW Geschichte der mechanischen Prinzipien und ihrer wichtigsten Anwendungen, by Istv˜n Szabo (Gunhard ’. Oravas) ............................................. 81--94 BOOK REVIEWS Ideas of Space, by Jeremy Gray (Joan L. Richards) ................................................ 95--97 Les instruments de la th‚orie des plan‚tes selon Ptol‚m‚e: Equatoires et horologerie plan‚taire du XIII$^e$ au XVI$^e$ si‚cle, by Emmanuel Poulle (Bernard R. Goldstein) ............................................ 97--99 Two Decades of Mathematics in the Netherlands 1920--1940. A Retrospection on the Occasion of the Bicentennial of the Wiskundig Genootschap, edited by E. M. J. Bertin, H. J. M. Bos, and A. W. Grootendors (Dirk J. Struik) ................................................. 99--100 Theon of Smyrna. Mathematics Useful for Understanding Plato, by J. Dupuis, translated by Robert and Deborah Lawlor and edited by Christos Toulis and others (Richard D. McKirahan, Jr.) ..................................... 100--104 R. A. Fisher. The Life of a Scientist, by Joan Fisher Box (N. T. Gridgeman) ............................................... 104--106 The Library of Isaac Newton, by John Harrison (I. Bernard Cohen) .............................................. 106--109 Die mathematischen Studien von G. W. Leibniz zur Kombinatorik: Studia Leibnitiana Supplementa, Vol. XI, by Eberhard Knobloch Die mathematischen Studien von G. W. Leibniz zur Kombinatorik: Textband: Studia Leibnitiana Supplementa, Vol. XVI, by Eberhard Knobloch Leibniz … Paris (1672--1676), edited by A. Heinekamp and D. Metter (J. F. Peters) .................................................. 113--123 ABSTRACTS........................................................ 124--127 VOLUME 9, PAGES 133--262, MAY 1982 Techniques of Fractions in Ancient Egypt and Greece Wilbur Knorr .................................................... 133--171 Matthew O'Brien's Anticipation of Vectorial Mathematics G. C. Smith ..................................................... 172--190 Bemerkungen zu einer Tagebuchnotiz von Carl Friedrich Gauss Karsten Johnsen ................................................. 191--194 NOTE Algebra and Pure Time: Hamilton's Affinity with Kant Anthony T. Winterbourne ......................................... 195--200 SOURCES Volterra Archive at the Accademia Nazionale dei Lincei Giorgio Israel .................................................. 229--238 BOOK REVIEWS Epistemological and Social Problems of the Sciences in the Early Nineteenth Century, edited by H. N. Jahnke and M. Otte (Joan L. Richards) .............................................. 239--245 It Seems I Am a Jew, by Grigori Freiman, translated and edited by Melvyn B. Nathanson (Yakov Rabkin) .................................................. 245--247 The Emergence of Number, by John N. Crossley (Raymond L. Wilder) ............................................. 247--251 Prolegomena alle ``Vite dei Matematici'' di Bernardino Baldi (1587--1596), by Bronislaw Bilinski ABSTRACTS....................................................... 253--259 VOLUME 9, PAGES 263--372, AUGUST 1982 Preface James B. Freeman ................................................ 263--264 Peirce's Place in American Life Max H. Fisch .................................................... 265--287 Peirce the Logician Hilary Putnam ................................................... 290--301 Charles Peirce's Place in Philosophy Ernest Nagel .................................................... 302--310 Peirce's Place in Mathematics Joseph W. Dauben ................................................ 311--325 Carolyn Eisele's Place in Peirce Studies Kenneth Laine Ketner ............................................ 326--332 Mathematical Methodology in the Thought of Charles S. Peirce Carolyn Eisele .................................................. 333--341 SOURCES Charles Babbage Materials in New Zealand and Australia Garry J. Tee .................................................... 344--345 ESSAY REVIEW Abr‚g‚ d'Histoire des Math‚matiques, 1700--1900, edited by J. Dieudonn‚ (Isabella G. Bashmakova, A. N. Kolmogorov, A. I. Markushevitch, A. N. Parshin, and A. P. Youshkevitch) .......... 346--360 ABSTRACTS........................................................ 361--367 VOLUME 9, PAGES 373--512, NOVEMBER 1982 Joseph Liouville's Contribution to the Theory of Integral Equations Jesper Ltzen ................................................... 373--391 Early Criticism of the Symbolical Approach to Algebra Helena M. Pycior ................................................ 392--412 Herbart's Influence on Bernhard Riemann Erhard Scholz ................................................... 413--440 Ans„tze zur Begrndung theoretischer Terme in der Mathematik---die Theorie des Unendlichen bei Johann Schultz Gert Schubring .................................................. 441--484 BOOK REVIEWS A Half Century of Polish Mathematics: Remembrances and Reflections, by Kazimierz Kuratowski Waclaw Sierpinski: Oeuvres Choisies, edited by Stanislaw Hartman, Kazimierz Kuratowski, Edward Marczewski, Andrezj Mostowski, Andrezj Schinzel, Roman Sikorski, and Marcelli Stark (Gregory H. Moore) .............................................. 489--495 Matematica: Un Profilo Storico, by Dirk J. Struik (Hubert Kennedy) ................................................ 495--496 ABSTRACTS ....................................................... 497--504 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 9........................................................... 508 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 9....................................... 509--512 VOLUME 10, PAGES 1--148, FEBRUARY 1983 Editorial Joseph W. Dauben .................................................... 1--2 Albertus Magnus and Mathematics: A Translation with Annotations of Those Portions of the Commentary on Euclid's Elements Published by Bernhard Geyer Anthony Lo Bello ................................................... 3--23 The Analytical Society (1812--1813): Precursor of the Renewal of Cambridge Mathematics Philip C. Enros ................................................... 24--47 The Mathematical Technique in Fermat's Deduction of the Law of Refraction Kirsti Andersen ................................................... 48--62 NOTES Euclid's Intended Interpretation of Superposition Robert J. Wagner .................................................. 63--70 On the Transmission of Geometry from Greek into Arabic Wilbur Knorr ...................................................... 71--78 Sixth-Century Intuitive Probability: The Statistical Significance of a Miracle Jensoyrup ......................................................... 80--84 Some Comments on Riemann's Contributions to Differential Geometry J. D. Zund ........................................................ 84--89 SOURCES Correspondence and Manuscripts Recovered at the Istituto Matematico ``G. Castelnuovo'' of the University of Rome Giorgio Israel and Laura Nurzia ................................... 93--97 ESSAY REVIEW Black Mathematicians and Their Works, edited by Virginia K. Newell, Joella H. Gipson, L. Waldo Rich, and Beauregard Stubblefield A Negro History Compendium, by Ethel M. Turner (Claudia Zaslavsky) ............................................. 105--115 REVIEWS Johannes Kepler---Mysterium Cosmographicum---The Secret of the Universe. Translation by A. M. Duncan (Owen Gingerich) ................................................ 116--117 Mathematical Discoveries: 1600--1750, by P. L. Griffiths (Jeremy Kilpatrick) ............................................. 117--118 A History of the Calculus of Variations from the 17th through the 19th Century , by Herman H. Goldstine (Ronald Calinger) ............................................... 118--121 The Mathematical Experience, by Philip J. Davis and Reuben Hersh (Peter Hilton) .................................................. 122--125 Jordanus de Nemore. De numeris datis, edited and translated by Barnabas Bernard Hughes Sir William Rowan Hamilton, by Thomas L. Hankins (Helena M. Pycior) .............................................. 129--132 Brouwer's Cambridge Lectures on Intuitionism, edited by D. van Dalen (William F. Aspray) ............................................. 132--135 ABSTRACTS......................................................... 136--143 VOLUME 10, PAGES 149--260, MAY 1983 Distributions: The Evolution of a Mathematical Theory John Synowiec ................................................... 149--183 Neo-Kantian Foundations of Geometry in the German Romantic Period Frederick Gregory ............................................... 184--201 Quantifier Problems Beyond Uniformity William C. Waterhouse ........................................... 202--207 REVIEWS From Eniac to Univac: An Appraisal of the Eckert-Mauchley Computers by Nancy Stern (William Aspray) ................................................ 228--233 A History of Computing in the Twentieth Century, edited by N. Metropolis, J. Howlett, and Gian-Carlo Rota .................. 233--236 History of Binary and Other Nondecimal Numeration by Anton Glaser (Donald E. Knuth) ............................................... 236--243 John von Neumann and Norbert Wiener by Steve Heims (Garrett Birkhoff) .............................................. 243--248 ABSTRACTS........................................................ 249--256 VOLUME 10, PAGES 261--382, AUGUST 1983 Kurt Vogel: Biographie und Bibliographie Menso Folkerts .................................................. 261--273 Gregory's Converging Double Sequence Christoph J. Scriba ............................................. 274--285 Potenzsummenformeln im 17. Jahrhundert Ivo Schneider ................................................... 286--296 Maestro Benedetto da Firenze e la Storia dell'Algebra Raffaella Franci and Laura Toti Rigatelli ....................... 297--317 Von Riemann zu Lebesgue---zur Entwicklung der Integrationstheorie Eberhard Knobloch ............................................... 318--343 Hibeh Papyrus i 27: An Early Example of Greek Arithmetical Notation D. H. Fowler and E. G. Turner ................................... 344--359 Ein Vermessungsproblem reist von China nach Paris Kurt Vogel ...................................................... 360--367 ABSTRACTS........................................................ 372--379 VOLUME 10, PAGES 383--499, NOVEMBER 1983 A. N. Kolmogorov: Historian and Philosopher of Mathematics. On the Occasion of his 80th Birthday A. P. Youschkevitch ............................................. 383--395 F. A. Medvedev et son apport … l'historie de la th‚orie des fonctions A. P. Youschkevitch, S. S. Demidov, and P. Dugac ................ 396--398 The Algebra of Master Dardi of Pisa Warren Van Egmond ............................................... 399--421 C. F. Gauss als Mathematik- und Astronomiehistoriker Kurt-R. Biermann ................................................ 422--434 Eine bisher unbekannte Abhandlung ber das Rechenbrett aus dem beginnenden 14. Jahrundert Menso Folkerts .................................................. 435--447 NOTES A Forgotten Chapter in the History of Felix Klein's Erlanger Programm David E. Rowe ................................................... 448--454 D'Alembert and the Fourth Dimension Rosine G. Van Oss ............................................... 455--457 ESSAY REVIEW Emmy Noether, 1882--1935, by Auguste Dick, translated by H. I. Blocher Emmy Noether: A Tribute to Her Life and Work, edited by James W. Brewer and Martha K. Smith (David E. Rowe) ................................................. 462--466 BOOK REVIEWS Geometry in Ancient and Medieval India, by T. A. Sarasvati Amma (Michio Yano) ................................................... 467--470 The Medieval Latin Translation of the Data of Euclid, by Shuntaro Ito (Edith Dudley Sylla) ............................................ 471--475 Leonhardi Euleri commentationes mechanicae ad theoriam machinarum pertinentes volumen posterius, Series secunda, Opera mechanica et astronomica, Vol. 16 Leonhardi Euleri commentationes mechanicae et astronomicae ad scientiam navalem pertinentes volumen posterius, Series secunda, Opera mechanica et astronomica, Vol. 21 (Robin E. Rider) ................................................ 476--477 šber die Handschrift CLM 26639 der Bayerischen Staatsbibliothek Mnchen , by Wolfgang Kaunzner (S. A. Jayawardene) ............................................. 478--479 Problemgeschichte der Mathematik, I, by Herbert Meschkowski Problemgeschichte der Mathematik, II, by Herbert Meschkowski Problemgeschichte der Neueren Mathematik (1800--1950), by Herbert Meschkowski (Emmanuil Papamastorakis and Roland Stowasser) .................. 480--482 Felix Hausdorff: Ein Mathematiker seiner Zeit, by Herbert Mehrtens (A. F. Monna) ................................................... 483--484 ABSTRACTS...................................................... 485--490 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 10.......................................................... 495 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 10...................................... 496--499 VOLUME 11, PAGES 1--124, FEBRUARY 1984 Editorial Joseph W. Dauben ....................................................... 1 Richardson Extrapolation and Romberg Integration Jacques Dutka .......................................................... 3 Alexis Fontaine's Route to the Calculus of Several Variables John L. Greenberg ..................................................... 22 A Brief Chronological and Bibliographic Guide to the History of Chinese Mathematics Frank J. Swetz and Ang Tian Se ........................................ 39 A Chronology and Historical Analysis of the Mathematical Manuscripts of Gregorius a Sancto Vincentio (1584--1667) Herman Van Looy ....................................................... 57 NOTES Euclid, Relativity, and Sailing Wilfred Theisen ....................................................... 81 What Are Propositions 84 and 85 of Euclid's Data All About? Roger Herz-Fischler ................................................... 86 BOOK REVIEWS Elie Cartan-Albert Einstein. Letters on Absolute Parallelism 1929--1932. Original text, English translation by Jules Leroy and Jim Ritter, edited by Robert Debever (Dirk J. Struik) ...................................................... 94 Drer: Kunst and Geometrie, by Eberhard Schr”der (Warren Van Egmond) ................................................... 97 Mathematicians and Their Times: History of Mathematics and Mathematics of History by Laurence Chisholm Young (Philip C. Enros) ..................................................... 99 A Source Book of Medieval Science, edited by Edward Grant (Menso Folkerts) ..................................................... 100 Sophie Germain. An Essay in the History of the Theory of Elasticity: Studies in the History of Modern Science , by Louis L. Bucciarelli and Nancy Dworsky (Robrt Fox) .......................................................... 102 Wissenschaft und Bildung in der Mathematik des 19.~Jahrhunderts, by Hans Niels Jahnke (Linda Wessels) ...................................................... 104 History of Functional Analysis, by Jean Dieudonn‚ (Bernard Aupetit) .................................................... 106 The Prehistory of the Theory of Distributions: Studies in the History of Mathematics and Physical Sciences , by Jesper Ltzen (Jeremy Gray) ........................................................ 108 ABSTRACTS............................................................. 112 VOLUME 11, PAGES 125--252, MAY 1984 In Memorium: Abraham J. Sachs (1914--1983) John L. Berggren ..................................................... 125 In Memorium: Eric Gardner Turner (1911--1983) D. H. Fowler ......................................................... 126 Zum Beweis von C. F. Gauss fr die Irreduzibilit„t des $p$-ten Kreisteilungspolynoms ................................................ 131 A Note by Gauss Referring to Ideals? William C. Waterhouse ................................................ 142 The Arabic Textual Traditions of Euclid's Elements Gregg De Young ....................................................... 147 The Poincar‚-Volterra Theorem: A Significant Event in the History of the Theory of Analytic Functions Giorgio Israel and Laura Nurzia ...................................... 161 Applied Mathematics in the Tenth Century: Abu'l-Wafa Calculates the Distance Baghdad-Mecca E. S. Kennedy ........................................................ 193 Some Methodological Aspects of Getaldic's Mathematical Works Zarko Dadi'c ......................................................... 207 NOTE G”del's Contribution to the Justification of Leibniz' Notion of the Infinitesimals Curt C. Christian .................................................... 215 SOURCES H. Davenport Papers and Letters ...................................... 231 BOOK REVIEWS The Land of Stevin and Huygens: Studies in the History of Modern Science, Vol. 7 and Het Land van Stevin en Huygens: Sunschrift , Vol. 134, by Dirk J. Struik (Jan A. van Maanen) .................................................. 234 The Collected Letters of Colin Maclaurin, edited by Stella Mills (A. Rupert Hall) ..................................................... 237 Medieval Mensuration: Quadrans Vetus and Geometrie due sunt Partes Principales}, by Nan L. Hahn (Anthony Lo Bello) ................................................... 239 Geschichte der Geometrie, by Klaus Mainzer (Joan Livingston Richards) ........................................... 240 ABSTRACTS............................................................. 242 VOLUME 11, PAGES 253--358, AUGUST 1984 This issue of Historia Mathematica is dedicated to Helmuth Gericke in honor of his 75th birthday. Helmut Gericke: On the Occasion of His 75th Birthday Menso Folkerts ....................................................... 253 The Establishment of Functional Analysis Garrett Birkhoff and Erwin Kreyszig .................................. 258 BOOK REVIEWS Sisyadhivrddhida Tantra of Lalla with the Commentary of Mallikarjuna Suri Part 2, Translation and Mathematical Notes. Critical edition with introduction, English translation, notes, and indices, by Bina Chatterjee (G. J. Tee) .......................................................... 327 The Scottish Book: Mathematics from the Scottish Cafe, edited by R. Daniel Mauldin (M. S. Klamkin) ...................................................... 329 Geschichte des Mannigfaltigkeitsbegriffs von Riemann bis Poincar‚ , by Erhard Scholz (S. S. Chern) ........................................................ 330 The Mathematical Science of Christopher Wren, by J. A. Bennett (Ivor Bulmer-Thomas) ................................................. 330 Descartes on Polyhedra, by P. J. Federico (Marjorie L. Senechal) ............................................... 333 The Beginnings of Greek Mathematics, by Arp˜d Szabo (translated by A. M. Ungar from Anf„nge der Greichischen Mathematik) (Alan C. Bowen) ...................................................... 335 Nicolas Chuquet: La g‚om‚trie. Premiere g‚om‚trie alg‚braique en langue francaise (1484). Introduction, text, and notes by Herv‚ l'Huillier (Stillman Drake) ..................................................... 345 ABSTRACTS............................................................. 347 VOLUME 11, PAGES 359--490, NOVEMBER 1984 Kenneth O. May, 1915--1977. His Early Life to 1946 Charles V. Jones, Philip C. Enros, and Henry S. Tropp ................ 359 Kenneth O. May---Bibliography Philip Enros ......................................................... 380 History of Greek Mathematics: A Survey of Recent Research J. L. Berggren ....................................................... 394 Eratosthenes on the ``Measurement'' of the Earth Bernard R. Goldstein ................................................. 411 Changing Canons of Mathematical and Physical Intelligibility in the Later 17th Century Internalism, Externalism, and Beyond: 19th-Century British Algebra Helena M. Pycior ..................................................... 424 The Erlanger Programm of Felix Klein: Reflections on Its Place in the History of Mathematics Thomas Hawkins ....................................................... 442 Artificial Intelligence: Debates about Its Use and Abuse Judith V. Grabiner ................................................... 471 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 11 ......................................................... 487 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 11 .......................................... 488 VOLUME 12, PAGES 1--100, FEBRUARY 1985 Eloge. Jean Itard (1902-1979) M. Caveing, R. Rashed, and R. Taton .................................... 1 La tablette babylonienne AO 17264 du Mus‚e du Louvre et le probl‚me des six fr‚res Maurice Caveing ........................................................ 6 SrŒpati: An Eleventh-Century Indian Mathematician Kripa Nath Sinha ...................................................... 25 W. R. Hamilton's View of Algebra as the Science of Pure time and His Revision of This View Peter Ohrstom. ........................................................ 45 NOTES A Second-Order Interpolation Scheme Described in the Zij-i Ikani Javad Hamadani-Zadeh .................................................. 56 Unknown Manuscript Material of Christian Huygens Jan A. van Maanen ..................................................... 60 Completing the G”del-Zermelo Correspondence John W. Dawson, Jr. ................................................... 66 SOURCES La ``correspondance math‚matique'' de Camille Jordan dans les archives de l'Ecole Polytechnique Claudine Billoux ...................................................... 80 REVIEWS Books IV to VII of Diophantus' Arithmetica in the Arabic Translation Attributed to Qusta ibn Luqa, by J. Sesiano (Jan P. Hogendijk) .................................................... 82 The Origins of Cauchy's Rigorous Calculus, by Judith V. Grabiner (Jean Dhombres) ....................................................... 86 ABSTRACTS.............................................................. 91 VOLUME 12, PAGES 101--202, MAY 1985 Additive Progression in Prehistoric Mathematics: A Conjecture Karl M. Petruso ...................................................... 101 Mathematical Bases of Ancient Egyptian Architecture and Graphic Art Gay Robins and Charles C. D. Shute ................................... 107 Felix Klein's ``Erlanger Antrittsrede.'' A Transcription with English Translation and Commentary David E. Rowe ........................................................ 123 Aus den wissenschaftlichen Anf„ngen Hermann Minkowski Walter Strobl ........................................................ 142 ESSAY REVIEW Digging for Structure into the Elements. Euclid, Hilbert, and Mueller. Philosophy of Mathematics and Deductive Structure in Euclid's Elements, by Ian Mueller REVIEWS Albertus (Magnus)' Commentaar op Euclides' Elementen der Geometrie, by Paul M. J. E. Tummers (Anthony lo Bello) ................................................... 185 The Boole-De Morgan Correspondence: 1842--1864, by Gordon C. Smith (Calvin Jongsma) ..................................................... 186 ABSTRACTS............................................................. 191 VOLUME 12, PAGES 203--312, AUGUST 1985 Peirce e Dedekind: La Definizione di Insieme Finito Francesco Gana ....................................................... 203 The Chinese Concept of Cavalieri's Principle and Its Applications Lam Lay-Yong and Shen Kangsheng ...................................... 219 The So-called Fibonacci Numbers in Ancient and Medieval India Parmanand Singh ...................................................... 229 The Mathematical Miscellany (1836--1839) Edward R. Hogan ...................................................... 245 NOTES Wladyslaw Kretkowski and Hilbert's Third Problem Walerian Piotrowski .................................................. 258 Three Alternate Methods of Obtaining the Ancient Egyptian Formula for the Area of a Circle Paulus Gerdes ........................................................ 261 Thabit ibn Qurra and the Pair of Amicable Numbers 17296, 18416 Jan P. Hogendijk ..................................................... 269 ESSAY REVIEW Felix Klein, Biographien hervorragender Naturwissenschaftler, Techniker, und Mediziner, Band 50, by Renate Tobies with Fritz K”nig. Universit„t, Technische Hochschule und Industrie. Ein Beitrag zur Emanzipation der Technik im 19.~Jahrhundert unter besonderer Bercksichtigung der Bestrebungen Felix Kleins, by Karl-Heinz Manegold. And Neohumanism and the Persistence of Pure Mathematics in Wilhelmian Germany}, by Lewis Pyenson (David E. Rowe) ...................................................... 278 REVIEWS Number: Their History and Meaning, by Graham Flegg (Philip S. Jones) .................................................... 292 Introduzione all'aritmetica mercantile del Medioevo e del Rinascimento}, by Raffaella Franci and Laura Toti Rigatelli (Silvio A. Bedini) ................................................... 293 Geschichte der Zahlentheorie im Orient im Mittelalter und zu Beginn der Neuzeit under besonderer Bercksichtigung persischer Mathematiker , by Alireza Djafari Naini (Jan P. Hogendijk) ................................................... 295 La Raccolta Carlo Vigan•, by Pier Luigi Pizzamiglio (Judith R. Goodstein) ................................................ 296 ABSTRACTS........................................................ 300 VOLUME 12, PAGES 313--407, NOVEMBER 1985 Editorial Joseph W. Dauben ..................................................... 317 A Farewell from the Parting Chairman of the International Commission on the History of Mathematics Christoph J. Scriba .................................................. 321 A Study of Some Early Investigations into Exchangeability A. I. Dale ........................................................... 323 The Emergence of Some of the Nonlogical Paradoxes of the Theory of Sets, 1903--1908 Alejandro R. Garciadiego ............................................. 337 NOTES Thomas Simpson and the Arithmetic Mean Eddie Shoesmith ...................................................... 352 The Theorem on Planar Graphs John W. Kennedy, Louis V. Quintas, and Maciej M. Syslo ............... 356 REVIEWS Il Circolo Matematico di Palermo, by Aldo Brigaglia and Guido Masotto (Giorgio Israel) ..................................................... 383 Penser les math‚matiques. S‚minaire de philosophie et math‚matiques de L'Ecole Normale Sup‚rieure., edited by J. Dieudonn‚, M. Loi, and R. Thom (John L. Greenberg) .................................................. 388 100 Years of Mathematics. A Personal Viewpoint, by George Temple (David E. Rowe) ...................................................... 390 Great Moments in Mathematics (beore 1650), by Howard Eves. Great Moments in Mathematics (after 1650), by Howard Eves (Philip C. Enros) .................................................... 391 ABSTRACTS........................................................ 394 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 12.......................................................... 406 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 12........................................... 407 VOLUME 13, PAGES 1--98, FEBRUARY 1986 It is with great sadness that we announce the death of Professor Kurt Vogel, to whose memory this issue is dedicated. Professor Vogel was born on September 30, 1888, in Altdorf, and died on October 27, 1985, in Munich. A member of sevEloge by Menso Folkerts will appear in a later issue. A Message from the International Commission on the History of Mathematics Joseph W. Dauben ....................................................... 1 Editorial Eberhard H. Knobloch and Helena M. Pycior .............................. 3 Auszge aus einer unver”ffentlichten Korrespondenz von Emmy Noether und Hermann Weyl mit Heinrich Brandt Werner Jentsch . 5 Refugee Mathematicians: A German Crisis and a British Response, 1933--1936 NOTES Euler's Work on Number Theory: A Concordance for A. Weil's Number Theory J. J. Burckhardt ...................................................... 28 Chinese Mathematics: Some Bibliographic Comments A. P. Youschkevitch ................................................... 36 On Rewriting the History of the Foundations of Mathematics at the Turn of the Century Alejandro R. Garciadiego .............................................. 39 SOURCES Contemporary Scientific Archives Centre ............................... 42 Discovery of an 11th-Century Geometrical Compilation: The Isikmaal of Yusuf al-Mu'taman ibn Hud, King of Saragossa Jan P. Hogendijk ...................................................... 43 The Three Parts of the Dirichlet Nachlass Gert Schubring ........................................................ 52 REVIEWS Little Sparrow: A Portrait of Sophia Kovalevsky, by Don H. Kennedy (Roger Cooke) ......................................................... 74 Frege, Dedekind, and Peano on the Foundations of Arithmetic. Methodology and Science Foundation, by D. A. Gillies (Thomas Drucker) ...................................................... 77 Never at Rest. A Biography of Isaac Newton, by Richard S. Westfall (E. J. Aiton) ......................................................... 78 A Calculating People: The Spread of Numeracy in Early America, by Patricia Cline Cohen (Nathan J. Swetz) ..................................................... 86 Geometry and Algebra in Ancient Civilizations, by B. L. van der Waerden (Frank J. Swetz) ...................................................... 83 Number Theory: An Approach through History: Hammurapi to Legendre, by A. Weil (Jeremy Gray) ......................................................... 86 ABSTRACTS........................................................ 89 VOLUME 13, PAGES 99--214, MAY 1986 A Chinese Mathematical Classic of the Third Century: The Sea Island Mathematical Manual of Liu Hui Ang Tian Se and Frank J. Swetz ........................................ 99 Mathematics and German Politics: The National Socialist Experience Sanford L. Segal ..................................................... 118 On Spherical Trigonometry in the Medieval Near East and in Europe N. G. Hairetdinova ................................................... 136 A Neglected Note Showing Gauss at Work William C. Waterhouse ............................................... 147 NOTES Huygens' Solution to the Gambler's Ruin Problem Eddie Shoesmith ...................................................... 157 Remarks to the Third Entry in Gauss' Diary Karsten Johnsen ...................................................... 168 SOURCES Papers of C. A. Truesdell and R. L. Wilder ........................... 171 REVIEWS A Convergence of Lives---Sofia Kovalevskaia: Scientist, Writer, Revolutionary , by Ann Hibner Koblitz (G. J. Tee) .......................................................... 191 Classics of Mathematics, edited by Ronald Calinger (Nathaniel Grossman) ................................................. 194 ABSTRACTS............................................................. 196 VOLUME 13, PAGES 215--324, AUGUST 1986 This issue of Historia Mathematica is dedicated to Adolph Pavlovich Yushkevich, on the occasion of his eightieth birthday. Adolph Pavlovich Yushkevich: On the Occasion of His Eightieth Birthday I. G. Bashmakova, S. S. Demidov, A. T. Grigorian, A. N. Kolmogorov, Yu. V. Prokhorov, and B. A. Rosenfeld .................... 215 Adolph Pavlovich Yushkevich: Selected Publications (1976--1986) Sergei Demidov ....................................................... 221 Eloge. Kurt Vogel (1888--1985) Menso Folkerts ....................................................... 224 Mesures invariantes---De Lebesgue … nos jours Jean-Paul Pier ....................................................... 229 The Rise of Cayley's Invariant Theory (1841--1862) Tony Crilly .......................................................... 241 Dio e l'uomo nella matematica di Kronecker Francesco Gana ....................................................... 255 SOURCES The Papers of Kurt G”del John W. Dawson, Jr. .................................................. 277 REVIEWS Carl Friedrich Gauss: A Bibliography. Compiled by Uta. C. Merzbach (Erwin Neuenschwander) ............................................... 297 Sur les fondements de l'analyse … la fin du XVIII d'apr‚s le trait‚ de Lacrois, by Pierre Dugac (Ren‚ Taton) ......................................................... 299 Writings of Charles S. Peirce: A Chronological Edition, Volume 2, 1867--1871}, Editor in Chief: Edward C. Moore (I. Grattan-Guinness) ................................................ 301 Studies in the Exact Sciences in Medieval Islam, by Ali A. Al-Daffa and John S. Stroyls (David A. King) ...................................................... 303 Matematiki i Astronomi Musulmanskogo Srednevekovya i Ihk Trudy (VIII-XIVV vv.) [Mathematicians and Astronomers of the Islamic Middle Ages (VII--XVII Centuries) and Their Works], by G. P. Matvievskaya and B. A. Rosenfeld (David A. King) ...................................................... 306 Nicolaus Cusanus und die Entstehung der exakten Wissenschaften, by Fritz Nagel (Helmut Gr”ssing) .................................................... 308 ABSTRACTS............................................................. 311 VOLUME 13, PAGES 325--423, NOVEMBER 1986 Circle Measurements in Ancient China Lam Lay-Yong and Ang Tian-Se ......................................... 325 Notes on the Correspondence between Luigi Cremona and Max Noether Marta Menghini ....................................................... 341 Leibniz et le probl‚me des partis. Quelques papiers in‚dits Maria Sol de Mora-Charles ............................................ 352 Le rapport di isou ( Euclide V, d‚finition 17):D‚finition, utilisation, transmission Germaine Aujac ....................................................... 370 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 13.......................................................... 390 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUMES 1--13....................................... 391 VOLUME 14, PAGES 1--118, FEBRUARY 1987 Two Leibnizian Manuscripts of 1690 Concerning Differential Equations Emily Grosholz ......................................................... 1 Joseph Louis Lagrange's Algebraic Vision of the Calculus Craig G. Fraser ....................................................... 38 SOURCES Mathesis: Revista de Divulgacion e Infromacion en la Historia y Filosofia de las Mathem˜ticas Alejandro R. Garciadiego .............................................. 54 The Nachlass of Wilhelm Lorey Gert Schubring ........................................................ 55 Resources in the History of Mathematics at the University of Alabama Joe Albree ............................................................ 57 REVIEWS Ibn al-Haytham's Completion of the Conics by Jan Pieter Hogendijk (Adel Anbouba) ........................................................ 65 Coloured Quadrangles, a Guide to the Tenth Book of Euclid's Elements by C. M. Taisbak (Sabetai Unguru) ...................................................... 67 Recherches sur l'oeuvre math‚matique de Mei Wending (1633--1721) by Jean-Claude Martzloff (J. Hoe) .............................................................. 70 SUBJECT INDEX OF PUBLICATIONS ABSTRACTED IN VOLUMES 1--13 ......................................................... 79 VOLUME 14, PAGES 119--234, MAY 1987 William Wallace and the Introduction of Continental Calculus to Britain: A Letter to George Peacock M. Panteki ........................................................... 119 The Continental Controversy over Arbuthnot's Argument for Divine Providence Eddie Shoesmith ...................................................... 133 D‚couverte d'un ‚crit math‚matique d'al-Hassa (XIIe s.): Le livre I du Kamil M. Aballagh and A. Djebbar ........................................... 147 Varahamihira's Pandiagonal Magic Square of the Order Four Takao Hayashi ........................................................ 159 An Early 15th-Century Algebra Codex: A Description Barnabas Hughes ...................................................... 167 NOTES Wie ist wohl Demokrit zum Rauminhalt der Pyramide gekommen? Joseph Ehrenfried Hofmann ............................................ 173 Observations on the Icosahedron in Euclid's Elements Jan P. Hogendijk ..................................................... 175 SOURCES A Note on the Koenigsberger-Zeuner Repertorium Nathan Houser ........................................................ 178 REVIEWS Sim‚on-Denis Poisson et la science de son temps, edited by Michel M‚tivier, Pierre Costabel, and Pierre Dugac (Lorraine Daston) .................................................... 198 I Want to Be a Mathematician: An Automathography, by Paul R. Halmos (Melvin Henriksen) ................................................... 200 The Nature of Mathematical Knowledge, by Philip S. Kitcher (Michael J. Crowe) ................................................... 204 The History of Combinatorial Group Theory: A Case Study in the History of Ideas}, by Bruce Chandler and Wilhelm Magnus (Olaf Neumann) ....................................................... 209 George Boole: His Life and Work, by Desmond MacHale (Theodore Hailperin) ................................................. 211 ABSTRACTS............................................................. 220 VOLUME 14, PAGES 235--310, AUGUST 1987 Algebraic Curves in Japan during the Edo Period Hidetosi Fukagawa .................................................... 235 Chuprov on Finite Exchangeability, Expectation of Ratios, and Measures of Association Infinitely Small Quantities in Cauchy's Textbooks Detlef Laugwitz ...................................................... 258 NOTE Thomas Jefferson and Douwes' Method for Determining Latitude James J. Tattersall .................................................. 275 SOURCES Le premier manuscrit de Condorcet sur le calcul des probabilit‚s (1772) Pierre Crepel ........................................................ 282 Correspondence of Carleman Gert Almkvist ........................................................ 284 ABSTRACTS............................................................. 298 VOLUME 14, PAGES 311--404, NOVEMBER 1987 The Calculus of the Trigonometric Functions Victor J. Katz ....................................................... 311 Was Bayes a Bayesian? Donald A. Gillies .................................................... 325 M‚chanique et th‚orie des surfaces: les travaux de Sophie Germain Amy Dahan-Dalm‚dico ............................................. 347 SOURCES Archives of American Mathematics Frederic F. Burchsted ................................................ 366 REVIEWS Humanistische Naturwissenschaft, Zur Geschichte der Wiener mathematischen Schulen des 15. und 16.~Jahrhunderts , by Helmuth Gr”ssing (Menso Folkerts) ..................................................... 381 Diophante: Les arithm‚tiques, Volumes III and IV, edited by Roshki Rashed (George Saliba) ...................................................... 383 Diophante: Les arithm‚tiques, Volumes III and IV, edited by Roshki Rashed (J. L. Berggren) ..................................................... 386 ABSTRACTS............................................................. 390 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 14.......................................................... 400 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 14........................................... 401 VOLUME 15, PAGES 1--100, FEBRUARY 1988 Boris A. Rozenfeld: On the 70th Anniversary of His Birth A. D. Aleksandrov, S. S. Demidov, A. T. Grigoryan, G. P. Matvievskaya, S. S. Sirazhdinov, and A. P. Yushikevich ................. 1 Esprit de rigueur et pr‚sentation math‚matique au XVIII-‚me si‚cle: le cas d'une d‚monstration d'Aepinus ................. 9 Prosthaphaeresis Revisited Victor E. Thoren ...................................................... 32 Die Entdeckung der Sylow-S„tze Winfried Scharlau ..................................................... 40 Un ``Probabilista Neoclassico'': Francesco Paolo Cantelli Margherita Benzi ...................................................... 53 Who is it? Christoph J. Scriba ................................................... 73 REVIEWS The History of Mathematics from Antiquity to the Present: A Selective Bibliography , edited by Joseph W. Dauben (Robin E. Rider) ...................................................... 87 En lisant le m‚moire de Seidel de 1847. Par Pierre Dugac (Eberhard Knobloch) ................................................... 88 ABSTRACTS ............................................................. 90 VOLUME 15, PAGES 101--200, MAY 1988 A Brief Report on a Number of Recently Discovered Sets of Notes on Riemann's Lectures and on the Transmission of the Riemann Nachlass Erwin Neuenschwander ................................................. 101 Zahl als Zeichen---Zur ``Technisierung'' der Arithmetik im Mittelalter Hans Georg Knapp ..................................................... 114 Mutual-Subtraction Algorithm and its Application in Ancient China Shen Kangsheng ....................................................... 135 SOURCES Neugebauer Microform Index of the Exact Sciences ..................... 148 REVIEWS Ptolemy's Almagest. Translated and annotated by G. T. Toomer (Y. Tzvi Langermann) ................................................. 174 Alfred North Whitehead: The Man and His Work. Volume 1: 1861--1910 , by Victor Lowe (Albert C. Lewis) .................................................... 176 Science and Technology in Medieval India---A Bibliography of Source Materials in Sanskrit, Arabic and Persian , by A. Rahman (Michio Yano) ........................................................ 179 šber die Entstehung von David Hilberts ``Grundlagen der Geometrie'' , by M.-M. Toepell (Jeremy Gray) ........................................................ 181 The Sulbasutras of Baudhayana,Apastamba, Katayana and Manava with Text, English Translation and Commentary}, by S. N. Sen and A. K. Bag (David Pingree) ...................................................... 183 Statistics in Britain, 1865--1930: The Social Construction of Scientific Knowledge , by Donald A. MacKenzie (Ivo Schneider) ...................................................... 185 ABSTRACTS ............................................................ 188 VOLUME 15, PAGES 201--298, AUGUST 1988 Graphs in Cultures: A Study in Ethnomathematics Marcia Ascher ........................................................ 201 Breaking a ``Vicious Circle'': Unscrambling A.-C. Clairaut's Iterative Method of 1743 John L. Greenberg ................................................... 228 Antonio de' Mazzinghi: An Algebraist of the 14th Century Raffaella Franci ..................................................... 240 Das Kontinuit„tsprogramm zwischen Cantor und der Nonstandard-Analysis Bernd J. Arnold ...................................................... 250 NOTE Dante-Kommentare und die Vorgeschichte der Stochastik Robert Ineichen ...................................................... 264 SOURCES Some Unpublished Papers of Jean van Heijenoort Irving H. Anellis .................................................... 270 Biography of John von Neumann Nicholas A. Vonneuman ................................................ 274 REVIEWS Leonard Euler 1707--1783: Beitr„ge zu Leben und Werk (Jean Dhombres) ...................................................... 287 Life and Works of Giuseppe Peano, edited by Hubert Kennedy (Ignacio Angelelli) .................................................. 289 ABSTRACTS............................................................. 291 VOLUME 15, PAGES 299--409, NOVEMBER 1988 Der Beweis des Weierstrasschen Approximationssatzes 1885 vor dem Hintergrund der Entwicklung der Fourieranalysis Reinhard Siegmund-Schultze ........................................... 299 Western Influence and Chinese Tradition in an Eighteenth Century Chinese Mathematical Work Catherine Jami ....................................................... 311 The Decline of Cayley's Invariant Theory (1863--1895) Tony Crilly .......................................................... 332 On Bayes' Theorem and the Inverse Bernoulli Theorem A. I. Dale ........................................................... 348 NOTE Who Put the ``C'' in A.-T. Vandermonde? James J. Tattersall .................................................. 361 SOURCES Resources in the History of Mathematics at the United States Military Academy David C. Arney ....................................................... 368 REVIEWS Native American Mathematics, edited by Michael P. Closs (Frank J. Swetz) ..................................................... 384 Mathematical Perspectives: Essays on Mathematics and Its Historical Development , edited by Joseph W. Dauben (Joan L. Richards) ................................................... 386 Intellectual Master of Nature: Theoretical Physics from Ohm to Einstein. Vol. 1, The Torch of Mathematics 1800--1870 Vol. 2, The Now Mighty Theoretical Physics 1870--1925, by Christa Jungnickel and Russell McCormmach (L. Pearce Williams) ................................................. 389 Philosophie als Analysis: Studien zur Entwicklung philosophischer Analysiskonzeptionen unter den Einfluss mathematischer Methoden- Modelle im 17.~und Frhen 18.~Jahrhundert, by Hans-Jrgen Engfer (Ronald Calinger) .................................................... 392 ABSTRACTS............................................................. 397 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 15.......................................................... 406 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 15........................................... 407 VOLUME 16, PAGES 1--106, FEBRUARY 1989 The Ideas of Hermann Grassmann in the Context of the Mathematical and Philosophical Tradition Since Leibniz Michael Otte ........................................................... 1 Newton's Mature Dynamics and the Principia: A Simplified Solution to the Kepler Problem J. Bruce Brackenridge ................................................. 36 P. L. Chebyshev (1821--1894) and His Contacts with Western European Scientists Paul L. Butzer and Fran‡ois Jongmans ................................. 46 Sharaf al-Din al-Tusi on the Number of Positive Roots of Cubic Equations Jan P. Hogendijk ...................................................... 69 SOURCES Edmund Landau Memorabilia Heinrich Wefelscheid .................................................. 86 REVIEWS Ada: A Life and a Legacy, by Dorothy Stein (Karen Hunger Parshall) ............................................... 94 Leonhard Euler, Opera Omnia, edited by Pierre Costabel, Eduard Winter, Asot T. Grigorijan, and Adolph P. Juskevic (Mary Terrall) ........................................................ 96 ABSTRACTS.............................................................. 98 VOLUME 16, PAGES 107--206, MAY 1989 Methods of Solving Linear Equations in Traditional China Lam Lay-Yong and Shen Kangshen ....................................... 107 Pour l'histoire des sept premiers nombres parfais Ettore Picutti ....................................................... 123 The 1740 Resolution of the Fermat-Descartes Controversy Luigi Indorato and Pietro Natasi ..................................... 137 NOTES Fermat's Theorem Colin R. Fletcher .................................................... 149 An Extremal Problem in Harriot's Mathematics P. C. Fenton ......................................................... 154 REVIEWS Gauss, Eine biographische Studie, by Walter Kaufmann-Bhler (Karen Reich) ........................................................ 178 Napoleon und die Naturwissenschaften, by Joachim Fischer (Christoph J. Scriba) ................................................ 180 Teubner-Archiv zur Mathematik, Teubner Verlagsgesellschaft, Leipsig , Vols. 1--6, by C. F. Gauss, et al. (Karen Reich) ........................................................ 180 La R‚publique avait besoin de savants, by Janis Langins, and Histoire de l'Ecole Polytechnique, by Ambroise Fourcy (W. A. Smeaton) ...................................................... 184 Episodes in the Mathematics of Medieval Islam, by J. L. Berggren (George Saliba) ...................................................... 188 Chinese Mathematics: A Concise History, by Li Yan and Du Shiran (Frank Swetz) ........................................................ 191 ABSTRACTS ............................................................ 194 VOLUME 16, PAGES 207--308, AUGUST 1989 This issue is dedicate to Professor Christoph J. Scriba on the occasion of his 60th Birthday. Christoph J. Scriba---60 Jahre Menso Folkerts and Eberhard Knobloch ................................. 207 The Arithmetical Triangle of Jordanus de Nemore Barnabas Hughes ...................................................... 213 The Metaphysics of the Calculus: A Foundational Debate in the Paris Academy of Sciences, 1700--1706 Paolo Mancosu ........................................................ 224 Pythagoras as a Mathematician Leonid Zhmud ......................................................... 249 REVIEWS Women of Mathematics: A Bibliographic Sourcebook, edited by Louise S. Grinstein and Paul J. Campbell (Joella G. Yoder) .................................................... 289 Cantorian Set Theory and Limitation of Size, by Michael Hallett (Gabrielle Lolli) .................................................... 291 Islamic Mathematical Astronomy, by D. A. King (Sonja Brentjes) ..................................................... 295 ABSTRACTS............................................................. 296 VOLUME 16, PAGES 309--413, NOVEMBER 1989 Kurt-Reinhard Biermann zum 70.~Geburtstag Reinhard Siegmund-Schultze ........................................... 309 Salomon Bochner as Historian of Mathematics and Science Charles C. Gillispie ................................................. 316 Durand's Rules for Approximate Integration Walter W. Piegorsch .................................................. 324 The Unpublished Papers of Joseph Liouville in Bordeaux Erwin Neuenschwander ................................................. 334 Ibn al-Haytham et les nombres parfaits Roshdi Rashed ........................................................ 343 A Simple, Accurate, Geometrical Approximation to the Keplerian Motion Y. Maeyama ........................................................... 353 Das Schriftenverzeichnis von Ewald Fettweis (1881--1967) samt einer Wrdigung von Olindo Falsirol Karin Reich, Menso Folkerts, and Christoph J. Scriba ................. 360 NOTE Notes on Thabit ibn Qurra and His Rule for Amicable Numbers Sonja Brentjes and Jan P. Hogendijk .................................. 373 SOURCES Manuscript Volumes and Lecture Notes of Salvatore Pincherle Umberto Bottazzini and Stefano Francesconi ........................... 379 REVIEWS Rudolf Lipschitz: Briefwechsel mit Cantor, Dedekind, Helmholtz, Kronecker, Weierstrass und Anderen , bearbeitet von Winfried Scharlau (Reinhard Siegmund-Schultz) .......................................... 387 Studies in the History of Mathematics, edited by Esther R. Phillips (Erhard Scholz) ...................................................... 390 ABSTRACTS............................................................. 393 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 16.......................................................... 409 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 16........................................... 410 VOLUME 17, PAGES 1--98, FEBRUARY 1990 Editorial: New Year's Greetings from the ICHM Joseph W. Dauben ....................................................... 1 The Fading Amateur: William Lenhart and 19th-Century American Mathematics Edward R. Hogan ........................................................ 6 E. W. von Tschirnhaus: His Role in Early Calculus and His Work and Impact on Algebra Manfred Kracht and Erwin Kreyszig ..................................... 16 Redfield's Proofs on MacMahon's Conjecture E. Keith Lloyd ........................................................ 36 SOURCES On Correspondence between B. Boncompagni and A. Genocchi Giorgio Israel ........................................................ 48 REVIEWS Die Geschichte der Geometrischen Mechanik im 19.~Jahrhundert, by Renatus Ziegler (Jeremy Gray) ......................................................... 76 Cultura, Scienze e Tecniche nella Venezia del Cinquecento. Atti del Convegno Internazionale di Studio: Giovan Battista Benedetti e il suo Tempo, edited by Antonio Manno (Michael Segre) ....................................................... 78 ABSTRACTS.............................................................. 81 VOLUME 17, PAGES 99--200, MAY 1990 Lubos Novy: Sexagenarian Jaroslav Folta ........................................................ 99 Thus Spake al-Khwarizimi: A Translation of the Text of Cambridge University Library Ms. li.vi.5 John N. Crossley and Alan S. Henry ................................... 103 Einstein and the Quintic Equation S. J. Patterson ...................................................... 132 African Slave and Calculating Prodigy: Bicentenary of the Death of Thomas Fuller John Fauvel and Paulus Gerdes ........................................ 141 SOURCES The British Association Mathematical Tables Committee Maurice V. Wilkes .................................................... 152 REVIEWS La th‚orie des parall‚les en pays d'Islam. Contribution a la pr‚histoire des g‚om‚tries non-euclidiennes, by Khalil Jaouiche (B. A. Rozenfeld) ......................................................... 170 Was ist ein Tonsystem? Eine historisch-systematische Theorie der abendl„ndischen Tonsysteme, gegrndet auf die antiken Theoretiker Aristoxenos, Eukleides und Ptolemaios, dargestellt mit Mitteln der modernen Algebra , by Wilfried Neumaier (Jens Hoyrup) ........................................................ 172 A Mathematical History of Division in Extreme and Mean Ratio, by Roger Herz-Fischler (Jens Hoyrup) ........................................................ 175 Die Krise der Anschauung, by Kurt Th. Volkert (Gert Schubring) ..................................................... 178 The History of Mathematics in Finland 1828--1918, by Gustav Elfving (Clas-Olof Selenius) ................................................. 180 Die Entstehung des Mathematiklehrerberufs im 19.~Jahrhundert: Studien und Materialien zum Prozess der Professionalisierung in Preuss en (1810--1870) , by Gert Schubring (Renate Tobies) ...................................................... 182 ABSTRACTS............................................................. 187 VOLUME 17, PAGES 201--312, AUGUST 1990 Dynamis, the Babylonians, and Theaetetus 147c7--148d7 Jens Horup ........................................................... 201 The Missing Link: Riemann's ``Commentatio,'' Differential Geometry and Tensor Analysis Ruth Farwell ......................................................... 222 NOTE Noch einmal zu den Ausnahmeregen der Gauss'schen Osterformel Werner Bergmann ...................................................... 255 ESSAY REVIEWS Mathematical Visions: The Pursuit of Geometry in Victorian England , by Joan L. Richards (Albert C. Lewis) .................................................... 272 Die gesammelten Werke der Mathematiker und Physiker der Familie Bernoulli. Daniel Bernoulli: Die Werke. Band 3: Mechanik. Hrsg. von D. Speiser, A. de Baenst-Vandenbroucke, J. L. Pietenpol, und R. Radelet-de Grave. Mit Beitr„gen von H. Straub. Johann (1) Bernoulli: Der Briefwechsel. Band 2: Der Briefwechsel mit Pierre Varignon. Ester Teil: 1692--1702}. Hrsg. von P. Costabel und J. Peiffer under Benutzung von Vorarbeiten von J. O. Fleckenstein (Heinz-Jrgen Hess) .................................................. 279 REVIEWS Il Circolo matematico di Palermo, by Aldo Brigaglia and Guido Masotto (Adolf P. Yushkevich) ................................................ 287 Die Mathematik und ihre Dozenten an der Berliner Universit„t, 1810--1933 , by Kurt Biermann (S. L. Segal) ........................................................ 287 Mathematics: People, Problems, Results, edited by Douglas M. Campbell and John C. Higgins (Richard M. Davitt) .................................................. 289 The Examiner, James Booth and the Origins of Common Examinations, by Frank Foden (I. Grattan-Guinness) ................................................ 291 ABSTRACTS............................................................. 295 VOLUME 17, PAGES 313--423, NOVEMBER 1990 The Varieties of Mechanics by 1800 Ivor Grattan-Guinness ................................................ 313 Un demi-siecle de fractales: 1870--1920 Jean-Luc Chabert ..................................................... 339 NOTE A Survey of Japanese Publications on the History of Japanese Traditional Mathematics (Wasan) from the Last 30 Years Jean-Claude Martzloff ................................................ 366 REVIEWS Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century , by I. M. Yaglom (David E. Rowe) ...................................................... 385 Riemann, Topology, and Physics, by Michael Monastyrsky (John McCleary) ...................................................... 389 A List of Certain Letters Inserted in Books from the Library of August de Morgan (1806--1871) , by Maxine Merrington (I. Grattan-Guinness) ................................................ 391 Kurt G”del. Collected Works. Volume II. Publications 1938--1974, edited by Solomon Feferman (I. Grattan-Guinness) ................................................ 392 ABSTRACTS............................................................. 394 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 17.......................................................... 418 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 17........................................... 419 VOLUME 18, PAGES 1--106, FEBRUARY 1991 Garcia de Galdeano's Works on Algebra Mariano Hormigon ....................................................... 1 Intensional vs Extensional Probabilities from Their Origins to Laplace U. Garibaldi and M. A. Penco .......................................... 16 SOURCE A Catalog of the Works of Jacob Hermann (1678--1733) Fritz Nagel ........................................................... 36 ESSAY REVIEWS Classical Probability in the Enlightenment, by Lorraine Daston. The Rise of Statistical Thinking 1820--1900, by Theodore M. Porter. The History of Statistics---The Measurement of Uncertainty before 1900}, by Stephen M. Stigler (Ivo Schneider) ....................................................... 67 REVIEWS A History of Probability and Statistics and Their Applications before 1750 , by Anders Hald (Eugene Senata) ....................................................... 75 Boole: L'oiseau de nuit en plein jour, by Souleymane Bachir Diagne (Joan L. Richards) .................................................... 79 Mathematics and Its History, by John Stillwell (Paul R. Wolfson) ..................................................... 80 A Century of Mathematics in America, edited by Peter A. Duren (George B. Seligman) .................................................. 82 The Development of Newtonian Calculus in Britain, 1700--1800, by Niccol• Guicciardini (Erik Sageng) ......................................................... 85 ABSTRACTS.............................................................. 90 VOLUME 18, PAGES 107--208, MAY 1991 On a Medieval Circle Quadrature: De circulo quadrando Wilbur R. Knorr ...................................................... 107 Sur la vie et l¢e uvre de Fran‡ois Budan (1761--1840) Jacques Borowcyzk .................................................... 129 ``A Proper Spirit is Abroad'': Peirce, Sylvester, Ward, and American Mathematics, 1829--1843 Edward Hogan ......................................................... 158 NOTES An Elementary Interpretation of Entry 12 in Gauss's Tagebuch William C. Waterhouse ................................................ 173 A Note on Waring's Rule A. W. F. Edwards ..................................................... 177 REVIEWS Kepler's Geometrical Cosmology, by J. V. Field. Kepler's Physical Astronomy, by Bruce Stephenson (Sheila J. Rabin) .. 188 Das Prinzip der kleinsten Wirkung und die Kraftkonzeptionen der rationalen Mechanik: Eine Untersuchung zur Grundlegungs- problematik bei Leonard Euler, Pierre Louis Moreau de Maupertuis, und Joseph Louis Lagrange , by Helmut Pulte (Craig G. Fraser) .................................................... 191 ABSTRACTS............................................................. 195 VOLUME 18, PAGES 209--310, AUGUST 1991 Isabella Grigoryevna Bashmakova on the 70th Anniversary of Her Birth S. S. Demidov, S. S. Petrova, and A. P. Yushkevich ................... 209 Why Did Liu Hui Fail to Derive the Volume of a Sphere? Daiwie Fu ............................................................ 212 Aritmetike Stoigeiosis: Un trait‚ perdu de Diophante d'Alexandrie? Jean Christianidis ................................................... 239 NOTES Einige Anmerkungen zu Sophus Lies Krankheit Bernd Fritzsche ...................................................... 247 Der schlecte Wrfel---Ein selten behandeltes Problem in der Geschichte der Stochastik Robert Ineichen ...................................................... 253 REVIEWS Popularizing Mathematical Methods in the People's Republic of China: Some Personal Experiences , by Hua Loo-Keng and Wang Yuan (Daiwie Fu) .......................................................... 284 History and Philosophy of Modern Mathematics, edited by William Aspray and Philip Kitcher (Reuben Hersh) ....................................................... 288 IN MEMORIAM Pierre Costabel (1912--1989) Ren‚ Taton ........................................................... 292 ABSTRACTS ............................................................ 296 VOLUME 18, PAGES 311--410, NOVEMBER 1991 A. P. Yushkevich Celebrates 85th Birthday .................................. 311 Thomas Bayes's Work on Infinite Series A. I. Dale ........................................................... 312 The Life and Mathematics of George Campbell, F.R.S. Dennis Weeks ......................................................... 328 A Reconstruction of the Frenicle-Fermat Correspondnece of 1640 Colin R. Fletcher .................................................... 344 ESSAY REVIEW Zermelo's Axiom of Choice: Its Origins, Development and Influence, by Gregory H. Moore (Thomas Drucker) ......................................................364 REVIEWS Nathan Jacobson: Collected Mathematical Papers, by Nathan Jacobson (Brian J. Parshall) .................................................. 370 A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space , by B. A. Rosenfeld (Jeremy Gray) ........................................................ 373 A History of Algebraic and Differential Topology, 1900--1960, by Jean Dieudonn‚ (Jeremy Gray) ........................................................ 374 Symmetrie-Gruppe-Dualit„t, by Erhard Scholz (Branko Grnbaum and Marjorie Senechal) .............................. 377 IN MEMORIAM Evert Marie Bruins (1909--1990) Eberhard Knobloch .................................................... 381 Eric John Aiton (1920--1991) Curtis Wilson ........................................................ 390 ABSTRACTS ............................................................ 393 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 18.......................................................... 406 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 18........................................... 407 VOLUME 19, PAGES 1--124, FEBRUARY 1992 Editorial: A Message to Readers of Historia Mathematica Joseph W. Dauben ....................................................... 1 Isoperimetric Problems in the Variational Calculus of Euler and Lagrange Craig G. Fraser ........................................................ 4 On the History of the Strong Law of Large Numbers and Boole's Inequality E. Seneta ............................................................. 24 Zur Geschichte des Halbgruppenbegriffs Karl H. Hofmann ....................................................... 40 Newton's Principia and Inverse-Square Orbits: The Flaw Reexamined Robert Weinstock ...................................................... 60 NOTE W. H. Young at Aberystwyth M. R. Chowdhury ....................................................... 71 SOURCES A Note on The Educational Times and Mathematical Questions I. Grattan-Guinness ................................................... 76 ESSAY REVIEW The History of Modern Mathematics, edited by David E. Rowe and John McCleary (John Ewing) .......................................................... 93 IN MEMORIAM Evangelos S. Stamatis (1989--1990) Jean P. Christianidis and Nikos Kastanis .............................. 99 Hans Freudenthal (1905--1990) Henk J. M. Bos ....................................................... 106 ABSTRACTS............................................................. 109 VOLUME 19, PAGES 125--232, MAY 1992 Quelques jeux de hazard selon Leibniz (Manuscrits in‚dits) S. de Mora-Charles ................................................... 125 Irrational Numbers in English Language Textbooks, 1890--1915: Constructions and Postulates for the Completeness of the Real Numbers R. P. Burn ........................................................... 158 On a Seventeenth Century Version of the ``Fundamental Theorem of Arithmetic'' Catherine Goldstein .................................................. 177 Ishaq ibn Hunayn, Hunayn ibn Ishaq, and the Third Arabic Translation of Euclid's Elements Gregg de Young ....................................................... 188 SOURCES Guo Schuchun's Edition of the Jiu Zhang Suan Shu. (Nine Chapters on the Mathematical Art) Guo Schuchun ......................................................... 200 REVIEWS Introduction to Analysis of the Infinite, Book I, by Leonhard Euler (Ronald Calinger) .................................................... 213 Hermann Weyl 1885--1985, edited by K. Chandrasekharan (Gnther Frei) ....................................................... 214 ABSTRACTS ............................................................ 217 VOLUME 19, PAGES 233--340, AUGUST 1992 An Invitation to Read Book X of Euclid's Elements D. H. Fowler ......................................................... 233 Nicholaus de Haybech and His Table for Finding True Syzygy Jos‚ Chab˜s and Bernard R. Goldstein ................................. 265 ESSAY REVIEWS Convolutions in French Mathematics, 1800--1840, by Ivor Grattan-Guinness (Thomas Archibald) ................................................... 303 Ethnomathematics: A Multicultural View of Mathematical Ideas, by Marcia Ascher. The Crest of the Peacock: Non-European Roots of Mathematics , by George Gheverghese Joseph (Victor J. Katz) ..................................................... 310 REVIEWS Norbert Wiener: 1894--1964, by P. R. Masani (Albert C. Lewis) .................................................... 316 La France math‚matique. La Soci‚t‚ Math‚matique de France (1870--1914) , by H. Gispert, with essays by R. Bkouche, C. Gilain, C. Houzel, J.-P. Kahane, and M. Zerner (Ivor Grattan-Guinness) .............................................. 319 The Invisible Hand: Economic Equilibrium in the History of Science , by Bruna Ingrao and Giorgio Israel (Margaret Schabas) ................................................... 322 Die Streitschriften von Jacob und Johann Bernoulli, Variations- rechnung , bearbeitet und kommentiert von Herman H. Goldstine, mit historischen Anmerikungen von Patricia Radelet-de Grave (Eberhard Knobloch) .................................................. 323 IN MEMORIAM Clas-Olof Selenius (1922--1991) Christoph J. Scriba .................................................. 325 ABSTRACTS............................................................. 328 VOLUME 19, PAGES 341--464, NOVEMBER 1992 ``Das letzte Ziel ist immer die Darstellung einer Funktion'': Grundlagen der Analysis bei Weierstrass \ 1886, historische Wurzeln und Parallelen Detlef Laugwitz ...................................................... 341 Nicholas Saunderson: The Blind Lucasian Professor J. J. Tattersall ..................................................... 356 Mathematical Foundations of a Cultural Project or Ramchandra's Treatise ``Through the Unsentimentalised Light of Mathematics'' Dhruv Raina .......................................................... 371 Eighty Years of Sommerfeld's Radiation Condition Steven H. Schot ...................................................... 385 Newton's Solution to the Equiangular Spiral Problem and a New Solution Using Only the Equiangular Property Herman Erlichson ..................................................... 402 NOTES On the Authorship of ``A Calculation of the Credibility of Human Testimony'' A. I. Dale ........................................................... 414 Dynamis, mithartum, and square David H. Fowler ...................................................... 418 REVIEWS The Taming of Chance, by Ian Hacking (Gerardo G. Tango) ................................................... 431 Mathematische Schriften, by G. W. Leibniz (Genevi‚ve Boulet) ................................................... 435 IN MEMORIAM Ahmad Salim Saidan (1914--1991) Boris A. Rosenfeld ................................................... 438 Bibliography of Publications of Ahmad Salim Saidan (1914--1991) on the History of Mathematics and Astronomy in Islamic Civilization, and List of Medieval Arabic Texts Published by Him Jan P. Hogendijk ..................................................... 439 ABSTRACTS............................................................. 444 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 19.......................................................... 460 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 19........................................... 461 VOLUME 20, PAGES 1--120, FEBRUARY 1993 EDITORIAL A 20th Anniversary Message from the International Commission on the History of Mathematics Joseph W. Dauben ....................................................... 1 DEDICATION Bartel Leendert van der Waerden Gnther Frei ........................................................... 5 On Euler's Contributions to the Four-Squares Theorem Herbert Pieper ......................................................... 12 The Early History of the Moment Problem Tinne Hoff Kjeldsen .................................................... 19 Bernard Bolzano---Not as Unknown to His Contemporaries as Is Commonly Believed? Gert Schubring ........................................................ 45 Euler's Troublesome Series: An Early Example of the Use of Trigonometric Series Louise Ahrndt Golland and Ronald William Golland ...................... 54 The Development and Understanding of the Concept of Quotient Group Julia Nicholson ....................................................... 68 NOTE Harmonic Means and Diophantus 1.39 William C. Waterhouse ................................................. 89 SOURCE New Archives of American Mathematics Collections Frederic F. Burchsted ................................................. 92 REVIEW Indo-European Numerals, edited by Jadranka Gvozdanovic (Jens Hoyrup) ......................................................... 99 ABSTRACTS.............................................................. 104 VOLUME 20, PAGES 121--238, MAY 1993 DEDICATION For Matthias Schramm on His Sixty-Fifth Birthday Eberhard Knobloch .................................................... 121 Zum ersten Mal: Blick in einen Brief Kowalewskajas an Weierstrass Reinhard B”lling ..................................................... 126 Charles L. Dodgson's Geometric Approach to Arctangent Relations for Pi Francine F. Abeles ................................................... 151 El‚ments de r‚flexion sur les r‚actions chinoises … la g‚om‚trie euclidienne … la fin du XVIIe si‚cle--Le Jihe lunyue {a} de Du Zhigeng {b} vu principalement … partir de la pr‚face de l'auteur et deux notices bibliographiques r‚dig‚es par des lettr‚s illustres Jean-Claude Martzloff ................................................ 160 Arithmˆetikˆ stoichei…sis :On Diophantus and Hero of Alexandria Wilbur R. Knorr ...................................................... 180 NOTE On an Alleged Error in Archimedes' Conoids, Prop. 1 Wilbur R. Knorr ...................................................... 193 ESSAY REVIEWS Joseph Liouville 1809--1882. Master of Pure and Applied Mathematics , by Jesper Ltzen (David E. Zitarelli) ................................................. 205 The Space of Mathematics, Philosophical, Epistemological, and Historical Explorations , edited by Javier Echeverria, Andoni Ibarra, and Thomas Mormann (Moritz Epple) ....................................................... 210 REVIEWS The Mathematical Philosophy of Bertrand Russell: Origins and Development , by Francisco Rodriguez-Consuegra (Nicholas Griffin) ................................................... 216 Before Writing. Vol. I. From Counting to Cuneiform, by Denise Schmandt-Besserat (Frank J. Swetz) ..................................................... 220 ABSTRACTS ............................................................ 223 VOLUME 20, PAGES 239--342, AUGUST 1993 History of Medieval Islamic Mathematics: Research in Uzbekistan G. P. Matvievskaya ................................................... 239 Chuprov, Slutsky, and Chetverikov: Some Comments Oscar B. Sheynin ..................................................... 247 On Plato's ``Fairest Triangles'' (Timaeus 54a) Benno Artmann and Lothar Sch„fer ..................................... 255 Algebraic Analysis in Germany, 1780--1840: Some Mathematical and Philosophical Issues Hans Niels Jahnke .................................................... 265 Mario Pieri and His Contributions to Geometry and Foundations of Mathematics Elena Anne Marchisotto ............................................... 285 NOTES A Note on the Cattle Problem of Archimedes Peter Schreiber ...................................................... 304 On Helmholtz' Paper ``šber die thats„chlichen Grundlagen der Geometrie'' Klaus Volkert ........................................................ 307 SOURCE Indian Doctoral Theses in the Field of History of Mathematics R. C. Gupta .......................................................... 310 REVIEW Revolutions in Matheamtics, edited by Donald Gillies (David E. Rowe) ...................................................... 320 ABSTRACTS ............................................................ 324 VOLUME 20, PAGES 343--471, NOVEMBER 1993 On the Relation between Georg Cantor and Richard Dedekind Jos‚ Ferreiros ....................................................... 343 Hilda Geiringer-von Mises, Charlier Series, Ideology, and the Human Side of the Emancipation of Applied Mathematics at the University of Berlin during the 1920s Reinhard Siegmund-Schultze ........................................... 364 Der Nachlass von Erich Bessel-Hagen im Archiv der Universit„t Bonn Erwin Neuenschwander ................................................. 382 On the First History of Portuguese Mathematics Luis Manuel Ribeiro Saraiva .......................................... 415 NOTE Oresme's Proof of the Density of Rotations of a Circle through an Irrational Angle Jan von Plato ........................................................ 428 ESSAY REVIEW Histoire des math‚matiques chinoises, by Jean-Claude Martzloff (Joseph W. Dauben) ................................................... 437 ABSTRACTS............................................................. 447 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 20.......................................................... 466 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 20........................................... 467 VOLUME 21, PAGES 1--120, FEBRUARY 1994 EDITORIALS A Message to Readers of Historia Mathematica from the Past Chairman of the International Commission on History of Mathematics Joseph W. Dauben ....................................................... 1 A Message from the International Commission on the History of Mathematics Eberhard H. Knobloch ................................................... 3 David E. Rowe and Karen Hunger Parshall ...................................... 5 Pietro Mengoli and the Six-Square Problem P. Natasi and A. Scimone .............................................. 10 Der ``Vierfeldertest'' von Carl Liebermeister (Bemerkungen zur Entwicklung der medizinischen Statistik im 19.~Jahrhundert) Robert Ineichen ....................................................... 28 Dirichlet's Contributions to Mathematical Probability Theory Hans Fischer .......................................................... 39 NOTE Riemann and the Cauchy-Hadamard Formula for the Convergence of Power Series Detlef Laugwitz and Erwin Neuenschwander .............................. 64 SOURCES Bibliography of Publications by B. L. van der Waerden since 1983 on Ancient and Medieval Science ......................................... 71 REVIEWS Math‚matisations. Augustin-Louis Cauchy et l'‚cole francaise, by Amy Dahan Dalmedico (I. Grattan-Guinness) ................................................. 88 Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory, Probability Theory, edited by A. N. Kolmogorov and A. P. Yushkevich (Jeremy Gray) ......................................................... 93 Operations Analysis in the U.S. Army Eighth Air Force in World War II, by Charles W. McArthur (Robin E. Rider) ...................................................... 95 ABSTRACTS ................................................................... 97 VOLUME 21, PAGES 121--244, MAY 1994 Wine Gauging in Late 16th- and Early 17th-Century Antwerp Ad Meskens ........................................................... 121 The Visualization of Quadratures in the Mystery of Corollary 3 to Proposition 41 of Newton's Principia Herman Erlichson ..................................................... 148 al-Farisi and the Fundamental Theorem of Arithmetic Ahmet G. Agn and Colin R. Fletcher .................................. 162 Ivory's Treatment of Pendulum Observations Oscar Sheynin ........................................................ 174 Die Anf„nge von Gottlob Freges wissenschaftlicher Laufbahn Karl-Heinz Schlote and Uwe Dathe ..................................... 185 NOTE Newton on the Equiangular Spiral: An Addendum to Erlichson's Account Curtis Wilson ........................................................ 196 SOURCE Contributing to The Educational Times: Letters to W. J. C. Miller I. Grattan-Guinness .................................................. 204 ESSAY REVIEW Perspectives on the History of Mathematical Logic, edited by Thomas Drucker (Michael Scanlan) .................................................... 209 REVIEWS Augustin-Louis Cauchy: A Biography, by Bruno Belhoste (Judith V. Grabiner) ................................................. 215 Les M‚thodes rapides pour la trigonom‚trie et le rapport pr‚cis du cercle (1774). Tradition chinoise et apport occidental en math‚matiques, by Catherine Jami (Karine Chemla) ...................................................... 220 ABSTRACTS............................................................. 225 VOLUME 21, PAGES 245--400, AUGUST 1994 DEDICATION Dirk Jan Struik and His Contributions to the History of Mathematics David E. Rowe ........................................................ 245 Reminiscences of a Former M.I.T. Student Helen May Walther .................................................... 274 On My Trip to Europe, August 1--9, 1989 Dirk J. Struik ....................................................... 276 On Connecting Socialism and Mathematics Dirk Struik, Jan Burgers, and Jan Tinbergen Gerard Alberts ....................................................... 280 "Scientific Control" in Mathematical Reviewing and German-U.S.-American Relations between the Two World Wars Reinhard Siegmund-Schuktze ........................................... 306 How Probabilities Came to Be Objective and Subjective Lorraine Daston ...................................................... 330 On Mathematics in the History of Sub-Saharan Africa Paulus Gerdes ........................................................ 345 On Jacobi's Remarkable Curve Theorem John McCleary ........................................................ 377 ABSTRACTS .................................................................. 386 VOLUME 21, PAGES 401--491, NOVEMBER 1994 Origins of the Analysis of the Euclidean Algorithm Jeffrey Shallit ...................................................... 401 Considerazioni di Giovanni Rizzetti sul calcolo delle probabilit… e sul teorema di Jakob Bernoulli A. Belcastro, G. Fenaroli, and A. C. Garibaldi ....................... 420 NOTE Carl Liebermeister's Hypergeometric Tails E. Seneta ............................................................ 453 REVIEWS L'Oeuvre de Torricelli: Science galil‚enne et nouvelle g‚ometrie , edited by Fran‡ois De Gandt (James Evans) ........................................................ 463 Euclides Reformatus: La teoria delle proporzioni nella scuola galileiana , by Enrico Giusti (Ken Saito) .......................................................... 465 ABSTRACTS............................................................. 469 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 21 ......................................................... 486 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 21 .......................................... 487 VOLUME 22, PAGES 1--112, FEBRUARY 1995 Al-Mu'taman ibn Hud, 11th Century King of Saragossa and Brilliant Mathematician Jan P. Hogendijk ....................................................... 1 Halley, Cotes, and the Nautical Meridian Ronald Gowing ......................................................... 19 ``What Fermented in Me for Years'': Cantor's Discovery of Transfinite Numbers Jos‚ Ferreiros ........................................................ 33 Dubbiezze e controversie: Il dibattito su logica e probabilit… in Italia nei prima anni del Novecento Margherita Benzi ...................................................... 43 NOTE Zwei mittelalterlich arabische Ausgaben der ``Sphaerica'' des Menelaos von Alexandria Gulnava Yussupova ..................................................... 64 REVIEWS Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China , by Lam Lay Yong and Ang Tian Se (Jean-Claude Martzloff) ............................................... 67 Briefwechsel zwischen Karl Weierstass und Sofia Kowalewskaja, edited by Rienhard B”lling (Roger Cooke) ......................................................... 73 The Search for E. T. Bell, Also Known as John Taine, by Constance Reid (Albert C. Lewis) ..................................................... 78 Math‚matiques Egyptiennes. Recherches sur les connaissances math‚matiques de l'Egypte pharaonique, by Sylvia Couchoud (Maurice Caveing) ..................................................... 80 Peri Ton Mathematon (Apeiron, Vol. XXIX, No. 4)}, edited by Ian Mueller (Jens Hoyrup) ......................................................... 84 IN MEMORIAM Fedor Andreevich Medvedev (1923--1993) Evgeny A. Zaitsev ..................................................... 88 ABSTRACTS ............................................................. 93 VOLUME 22, PAGES 113--224, MAY 1995 IN MEMORIAM Adolph Andrei Pavlovich Yushkevich (1906--1993) Isabella Bashmakova, A. N. Bogolyubov, S. S. Demidov, B. V. Gnedenko, E. Knobloch, Galina Matvievskaya, D. E. Rowe, B. A. Rozenfeld, O. B. Sheynin, and V. M. Tikhomirov ....................... 113 Doubling the Cube: A New Interpretation of Its Significance for Early Greek Geometry Ken Saito ............................................................ 119 Euclidean Geometry in the Mathematical Tradition of Islamic India Gregg De Young ....................................................... 138 Outline of a Scientific Biography of Ernst Meissel (1826--1895) Jaak Peetre .......................................................... 154 Gaston Darboux and the History of Complex Dynamics Daniel S. Alexander .................................................. 179 NOTES On the Cattle Problem of Archimedes William C. Waterhouse ................................................ 186 On Euler's Partition of Forms into Genera A. A. Antropov ....................................................... 188 ESSAY REVIEW La Sph‚re, instrument au service de la d‚couverte du monde: D'Autolycos de Pitane … Jean de Sacrobosco , by Germaine Aujac (Bernard Vitrac) ..................................................... 196 REVIEWS Lakatos' Philosophy of Mathematics: A Historical Approach, by Teun Koetsier (John Shosky) ........................................................ 203 Berkeley's Philosophy of Mathematics, by Douglas M. Jesseph (Marina Frasca-Spada) ................................................ 206 Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education , edited by Sal Restivo, Jean Paul Van Bendegem, and Roland Fischer (Joan L. Richards) ................................................... 208 ABSTRACTS............................................................. 210 VOLUME 22, PAGES 225--344, AUGUST 1995 EDITORIAL Note from the Managing Editor Karen V. H. Parshall ................................................. 225 A General Outline of the Genesis of Vector Space Theory Jean-Luc Dorier ...................................................... 227 The Axiomatization of Linear Algebra: 1875--1940 Gregory H. Moore ..................................................... 262 L. E. J. Brouwer: Toward Intuitionistic Logic Miriam Franchella .................................................... 304 REVIEWS Die Entwicklung des Tensorkalkls. Vom absoluten Differentialkalkt zur Relativit„tstheorie , by Karin Reich (Dirk J. Struik) ..................................................... 323 La Mesure de l'‚tat, By Eric Brian (Peirre Cr‚pel) ...................................................... 327 ABSTRACTS............................................................. 331 VOLUME 22, PAGES 345--480, NOVEMBER 1995 IN MEMORIAM In Memoriam: Guy Hirsch (1915--1993) Karen V. H. Parshall ................................................. 345 Models and Maps from the Marshall Islands: A Case in Ethnomathematics Marcia Ascher ........................................................ 347 Branch Points of Algebraic Functions and the Beginnings of Modern Knot Theory Moritz Epple ......................................................... 371 >From Student Club to National Society: The Founding of the London Mathematical Society in 1865 Adrian C. Rice, Robin J. Wilson, and J. Helen Gardner ............... 402 NOTE A Supplement to J. Shallit's Paper ``Origins of the Analysis of the Euclidean Algorithm'' Peter Schreiber ...................................................... 422 ESSAY REVIEW Amphora, Festschrift fr Hans Wussing zu seinem 65.~Geburtstag/ Festschrift for Hans Wussing on the Occasion of His 65th Birthday , edited by S. S. Demidov, M. Folkerts, D. E. Rowe, and C. J. Scriba (Jeremy Gray) ........................................................ 425 REVIEWS Sofia Kowalewskaja. Ein Leben fr Mathematik und Emanzipation, by Wilderich Tuschmann and Peter Hawig (Reinhard B”lling) ................................................... 442 On the Shoulders of Merchants: Exchange and the Mathematical Conception of Nature in Early Modern Europe , by Richard W. Hadden (Frank Swetz) ........................................................ 446 ABSTRACTS............................................................. 449 INDEX OF AUTHORS OF ARTICLES AND REVIEWS IN VOLUME 22.......................................................... 474 INDEX OF AUTHORS OF PUBLICATIONS REVIEWED AND ABSTRACTED IN VOLUME 22........................................... 475 VOLUME 23, PAGES 1--116, FEBRUARY 1996 EDITORIAL The History of Mathematics, the History of Science, Mathematics, and Historia Mathematica Karen Hunger Parshall and Jan P. Hogendijk ........................... 1 Drawing the Boundaries: Mathematical Statistics in 20th-Century America Patti W. Hunter ........................................................ 7 Medieval Hebrew Texts on the Quadrature of the Lune Y. Tzvi Langermann .................................................... 31 Mendeleev and the Mathematical Treatment of Observations in Natural Science oscar Sheynin ................................................. 54 Stanislaw Piatkiewicz and the Beginnings of Mathematical Logic in Poland Tadeusz Bat'og and Roman Murawski ..................................... 68 ESSAY REVIEW Euclide d'Alexandrie, Les Elements . Traduction et commentaires par Bernard Vitrac (Ian Mueller) ......................................................... 85 Leonardo Pisani Liber abbaci oder Lesevergngen eines Mathematikers ,by Heinz Lneburg (Peter Schreiber) ..................................................... 88 A History of Mathematics: An Introduction, by Victor J. Katz (Tom Archibald) ....................................................... 89 lie Cartan (1869--1951)}, by M. A. Akivis and B. A. Rosenfeld (Thomas Hawkins) ...................................................... 92 ABSTRACTS ................................................................... 96 VOLUME 23, PAGES 117--238, MAY 1996 A Birthday Tribute to R. C. Gupta Christoph J. Scriba ................................................. 117 Leonhard Euler: The First St. Petersburg Years (1727--1741) Ronald Calinger ..................................................... 121 An Episode in the History of Dynamics: Jakob Hermann's Proof (1716--1717) of Proposition 1, Book 1, of Newton's ,Principia Niccolo Guicciardini ................................................ 167 Ludvig Sylow's Lectures on Algebraic Equations and Substitutions, Christiania (Oslo), 1862: An Introduction and a Summary Bent Birkeland ...................................................... 182 REVIEWS The Golden Years of Moscow Mathematics, edited by Smilka Zdravkovska and Peter Duren (Roger Cooke) ....................................................... 200 Creating Modern Probability: Its Mathematics, Physics and Philosophy in Historical Perspective, by Jan von Plato (Thomas Hochkirchen) ................................................ 203 La reforme de la dynamique, De corporum concursu (1678) et autres textes inedits, by G. W. Leibniz (Christiane Vilain) ................................................. 207 Geometrie et dioptrique au X-e siecle: Ibn Sahl,al-Quhi et Ibn al-Haytham, by Roshdi Rashed (Gerard Simon) ...................................................... 210 ABSTRACTS ................................................................. 217