PII: 0315-0860(76)90027-6 110 Abstracts HM3 ABSTRACTS The purpose of the abstracts is to give sufficient informa- tion about the subject matter of each publication to enable readers to decide whether to read it. No review or evaluation is intended. The indexing terms (in boldface capitals) refer only to aspects of the publication of interest to historians of mathematics, including some topics in general history of science and historiography, but not other topics unless there is a fair- ly close link with mathematics or its history. We hope to pub- lish cumulative subject indices. Readers are invited to send reprints, autoabstracts, correc- tions,additions,and notices of publications that have been overlooked. Be sure to include complete bibliographic informa- tion. We need volunteers willing to cover one or more journals for this department. NR 46 #3255 means that the item is numbered 3255 in volume 46 of Mathematical Reviews. RZ 1973 #3A14 means that the item is numbered 3Al4 in the third number of the 1973 volume of the Referativny Zhurnal. Z 50 4 means volume 50, page 4 of the Zentralblatt. The symbol * in the margin indicates a publication that deserves more discussion than it may ordinarily get in the Reviews Department (either because it is an article rather than a book or because it is such a large book that a single review cannot deal with it fully). Readers are invited to comment by letter for our Correspondence Department and by submitting manuscripts of reviews or articles. HUGHES, Rarnabas 1975 A course in history of mathematics for mathematics teachers HM 2, 333-335 HISTORY IN MATHEMATICS. EDUCATION. TEACHER EDUCATION. FLEGG, Graham 1975 History of mathematics course (AM289) at the Open University, Great Britain HM 2, 332-333 HISTORY IN MATHEMATICS EDUCATION. SCRIBA, Christoph J 1975 The place and function of a "historical introduction" in the curriculum for mathematics students HM 2, 327-331 HISTORY IN MATHEMATICS EDUCATION. WALLIS, Peter J 1975 The BOOK SUBSCRIPTION LISTS project -- its relevance for historians of mathematics HM 2, 321-325. HN 3 Abstracts 111 MAY, Kenneth 0 1975 Historiographic vices II. Priority chasing HM 2, 315-317 HISTORIOGRAPHY. Continued from HM 2, 185-187. PEDOE, Dan 1975 Ausz disem wirdt vi1 dings gemacht: a Diirer construction for TANGENT CIRCLES HM 2, 312-314 CONSTRUCTIONS. A DijRER. . . . . MUURSEPP, Peeter 1975 D'Alembert's letter to Euler of 3 March 1766 HM 2, 309-311 J le R d'ALEMBERT. L EULER. CORRESPONDENCE. MIKOLAS, M 1975 Some historical aspects of the development of mathematical ANALYSIS in HUNGARY HM 2, 304-408 L FEZER. M. RIESZ. A HAAR. HERMELINK, Heinrich 1975 The earliest reckoning books exist- ing in the Persian language HM 2, 299-303 Abi Ja 'far Muh. b. Ayyib TABARI. XI. PERSIAN ARITHMETIC. COXETER, H S M 1975 The space-time continuum HM 2, 289-298 A CAYLEY. NON-EUCLIDEAN GEOMETRY. L SCHLAFLI. MINKOWSKI WORLD. de SITTER WORLD. CLOCK PARADOX. H. MINKOWSKI. W de SITTER. DAUBEN, Joseph W 1975 The invariance of DIMENSION: Problems in the early development of SET THEORY and TOEOLOGY. HM 2, 273-288 G CANTOR. J LUROTH. J THOMAE. E JURGENS. E NETTO. CROWE, Donald W 1975 The geometry of African art II. A cata- log of Benin patterns HM 2, 253-271 AFRICA. ART. Continues an article on Bakuba patterns in the 1971 Journal of Geometry 1, 169-182. See also the erratum in HM 2, 617. Many illustrations. YATES, Samuel 1975 Prime divisors of repunits Journal of Recreational Mathematics 8, 33-37 PRIME NUMBERS. History, period lengths, and current table from n = 2 to 100 of prime DIVISORS of R, = (lon - 1)/g. (J. H. Bauznwell) SMITH, Cyril Stanley 1975 A seventeenth-century octonary arithmetic Isis 66, 390-394 NUMERATION. XVII. OCTONARY NUMERATION. Facsimile reproduction of two pages of notes in a contemporary volume. 112 Abstracts HM 3 BIRKHOFF, Garrett and Sue Ann GARWOOD, editors 1975 Proceedings of the American Academy Workshop on the Evolution of Modern Mathematics held at the American Academy in Boston, Massachusetts, August 7-9, 1974. HM 2, 425-615 MEETINGS. With a foreword by John VOSS, introductions to the Parts (A: Historiography; B: History of Foundations; C: Foundations; D: Algebra; E: Analysis) by Birkhoff, additional discussion questions by Garwood, and bibliographies by the editors. Discussion after most papers. GRABINER, J V 1975 The mathematician, the historian and the history of mathematics HM 2, 4X9-447 HISTORIOGRAPHY. MAY, Kenneth 0 1975 What is good history and who should do it? HM 2, 449-45s HISTORIOGRAPHY. KOPPELMAN, Elaine 1975 Progress in mathematics HM 2, 457-463 HISTORIOGRAPHY. HISTORICAL THEORY. TROPP, Henry 1975 The role of ORAL COMMUNICATION HM 2, 465- 468 HISTORIOGRAPHY. CROWE, Michael J 1975 Ten “laws” concerning conceptual change in mathematics HM 2, 469-470 HISTORICAL THEORY. HISTORIOGRAPHY. JONES, Phillip S 1975 A role for the history of mathematics HM 2, 471-472 HISTORY OF MATHEMATICS IN EDUCATION. MATHEMATICS POLICY. POPULARIZATION. GRATTAN-GUINNESS, Ivor 1975 Preliminary notes on the historical significance of QUANTIFICATION and of the AXIOMS OF CHOICE in the development of mathematical ANALYSIS HM 2 475-488 LIMITS. MULTIPLE LIMITS. ANALYSIS FOUNDATIONS. GRATTAN-GUINNESS, Tvor 1975 Russell’s logical progress: some new light from manuscript sources HM 2, 489-493 B RUSSELL. LOGIC. N WIENER. FREUDENTHAL, Hans 1975 The cradle of modern TOPOLOGY, accord- ing to Brouwer’s inedita HM 2, 495-502 L E J BROUWER. With FACSIMILE of a letter to D HILBERT. HM 3 Abstracts 113 BISHOP, Errett 1975 The crisis in contemporary mathematics HM 2, 507-517 FOUNDATIONS. CONSTRUCTIVISM. PHILOSOPHY OF MATHEMATICS. KOPELL, Nancy and Gabriel STOLZENBERG 1975 Commentary on Bishop's talk HM 2, 519-521 FOUNDATIONS. CONSTRUCTIVISM. PHILOSOPHY OF MATHEMATICS. SACKS, Gerald 1975 Remarks against foundational activity HM 2, 523-528 "I want to discourage people...from trying to build FOUNDATIONS for all of mathematics." PUTNAM, Hilary 1975 What is mathematical TRUTH? HM 2, 529-533 PHILOSOPHY OF MATHEMATICS. DIEUDONNE, Jean 1975 Introductory remarks on ALGEBRA, TOPOLOGY, and ANALYSIS. HM 2, 537-548 HISTORICAL THEORY. Stresses the concept of FUSION OF THEORIES, CENTERS OF ATTRACTION, and CENTERS OF RADIATION. BAKER, Alan 1975 Some historical remarks on NUMBER THEORY HM 2, 549-553 CATALAN CONJECTURE. MACKEY, Gecrge 1975 Some remarks on HARMONIC ANALYSIS HM 2, 555-562 HISTORICAL THEORY. GENERALIZATION. SPECIALIZATION. HAWKINS, Thomas 1975 Mathematical progress without fusion HM 2, 563-566 HISTORICAL THEORY. FUSION OF THEORIES. ABHYANKAR, Shreeram S 1975 High-school ALGEBRA in ALGEBRAIC GEOMETRY HM 2, 567-572. KLINE, Morris 1975 Opening remarks at session on ANALYSIS HM 2, 575. ZYGMUND, Antoni 1975 The role of FOURIER SERIES in the devel- opment of ANALYSIS HM 2, 591-594 114 Abstracts HM3 BROWDER, Felix E 1975 The relation of FUNCTIONAL ANALYSIS to CONCRETE ANALYSIS in XX century mathematics HM 2, 577-590 SOFT ANALYSIS. HARD ANALYSIS. DIFFERENTIAL EQUATIONS, KAHANE, J P 1975 A central object in mathematics, the BROWNIAN MOTION HM 2, 595-600. DIAZ, Joaquin B 1975 How mathematics progresses HM 2, 601-602 EDUCATION. DOCTORAL DEGREE. The importance of the doctoral “family” in which the supervisor is the “father” of the candidate. WILLIAMS, M R 1974 The Calculator's Quadrant Calgary, Alberta, Canada (Division of Computing Science, University of Calgary) 13 p (mimeographed) Description of a QUADRANT in the Physics Department of ST ANDREWS UNIVERSITY. ARCHIVES. STIPANIC, Ernest 1972 Renaissance polymath FEDERIC GRISOGONO and his views on mathematics (in Serbo-Croatian) Dijalektika 4, 115-138. BOGOLYUBOV, A N 1975 Narisi z istorii mekhaniki [Essays on the history of MECHANICS] Kiev (Naukova Dumka) 191 p A POPULAR1 ZATION without formulas. From ancient times to modern TECHNOLOGY. VERA, Francisco 1970 Cientfficos Griegos [Greek Scientists] Madrid (Agui lar) 2 volumes 2188 p PYTHAGORAS. ARISTOTLE. PLATO. EUCLID. ARISTARCHUS. DEMOCRITUS. EUDEMUS. ARCHIMEDES. APOLLONIUS. PAPPUS. PTOLEMY. PROCLUS. THEODOSIUS. HERON. NICHOMACHUS. DIOPHANTUS. ERATOSTHENES. HIPPARCHUS among others. This is a sourcebook, containing several complete translations (up to some obscure or uninteresting passages), with introductory notes, individual bibliographies and footnotes by the compiler. Some of the translations are very old, as the one of Dioscoride’s REP? ‘i?hn< ~CXTPIK~~L;, published by Andres Laguna in 1555 (Antwerp), and some of them appear for the first time in Spanish. (Victor S. Albis) SNEATH, Peter H A and Robert R SOKAL 1973 Numerical Taxonomy San Francisco (Freeman) 588 p No history but a 60 page (about 1500 items) BIBLIOGRAPHY. HM3 Abstracts 115 MICHAEL, Emily 1974 Peirce’s Early Study of the Logic of Relations, 1865-1867 Transactions of the Charles S. Peirce Society 10: 2 (1974) 63-75 G BOOLE. ALGEBRA OF CLASSES. A discussion of C S PEIRCE'S early writing on LOGIC showing how his interest in the logic of RELATIVES emerged from his consideration of dyadic relations. The traditional syllogism only deals with propositions ofconcurrence, but is unable to deal with propositions of opposition. Further, it must be supplemented with a new form of SYLLOGISM (what Peirce refers to as a “double subsumption of the case under the rule”) in order to handle the arguments used in mathematical demonstrations. It is also shown that it is very likely that Peirce developed his logic of relations entirely independently of A DE MORGAN'S seminal memoir on RELATIONS of 1859. (C. V. Jones) GOTLIEB, C C 6 A BORODIN 1973 Social Issues in Computing (Academic Press) 298 p MATHEMATICS POLICY. COMPUTERS. MATHEMATICS AND SOCIETY. Requires a technical knowledge of computer science. HOWSON, A G 1975 Addendum to ‘Euler and the Zeta Function’ Amer. Math. Monthly 82, 737 EDUCATION. Two examples of questions on INFINITE SERIES which appeared on the first LONDON UNIVERSITY Matriculation EXAMINATION in 1838. See Ayoub, R HM 2, 390. (H. S. Tropp) SCHAAF, William L 1975 Postal history of mathematics School Science and Mathematics 75, 217-228 POSTAGE STAMPS. Many black and white illustrations of stamps with some historical comments. (J. K. Bidwell) DRAKE, Stillman 1975 Impetus theory reappraised Journal of the History of Ideas 36:l (1975) 27-46 EUCLIQ'S ELEMENTS, DESCARTES, PIERRE GASSENDI, G B BALIANI, HONORE FABRI, G B BENEDETTI, TORRICELLI, ALBERT QF SAXONY, NICOLE ORESME, LEONARDO DA VINCI, PIERRE CAZRE, FRANCISCUS DE MARCHIA, JEAN BURIDAN, ARITHMETIZATION OF THE CONTINUUM, TARTAGLIA, JACQUES ALEXANDRE LE TENNEUR. By analyzing published material, notably that of BURIDAN and ALBERT OF SAXONY, it is shown that the Medievalist had a view of IMPETUS THEORY based on QUANTUM JUMPS of velocity. This introduced discontinuity into the acceleration in free fall and is the key to understanding MEDIEVAL impetus theory, and therefore cannot be the source from which Galileo derived his continuous theory of FREE FALL. (C. V. Jones) 116 Abstracts HM3 WILDER, Raymond L 1974 Evolution of Mathematical Concepts. An Elementary Study London (Transworld Student Library) 236 p (paperback) Reprinted from the first 1968 edition “in associa- tion with Richard Sadler Ltd” for the Open University in whose course it is a “set book.” A four page preface to this edition gives a “brief clarification” of some “misunderstandings which have arisen concerning this work.” ERNEST, John 1975 Mathematics and Sex (Mathematics Department, University of California at Santa Barbara) 29 p WOMEN IN MATHEMATICS, SOCIOLOGY OF MATHEMATICS, MATHEMATICS EDUCATION. Sex differences in education as the root cause of sex differences in mathematical employment and accomplishment. BIBLIOGRAPHY of 23 titles. BALINSKI, M L & H P YOUNG 1975 The quota method of apportion- ment Amer. Math. Monthly 82, 701-730 APPORTIONMENT. A detailed history of the constitutional and mathematical problems of determining the allocation to each state in the U.S. HOUSE OF REPRESENTATIVES. Covers the periods 1792-1901 and 1910-1973 and discusses methods used and recommended, including HAMILTON METHOD (=VINT~N METHOD), JEFFERSON METHOD (=METHOD OF GREATEST DIVISORS =METHOD 0~ D'HONDT), WEBSTER METHOD (=METH~D 0~ MAJOR FRACTIONS), MODIFIED VINTON METHOD, and the HUNTINGTON METHOD. The authors discuss the problem of meeting constitution requirements, fair- ness and the avoidance of the ALABAMA PARADOX for each of the above and propose the QUOTA METHOD as a unique method best satisfying the essential requirements. TABLES. BIBLIOGRAPHY. (H.S. Tropp) GELLERT, W et al. 1975 Mathematics at a Glance. “A Compend- ium with 950 figures, over 700 multi-coloured, and 56 plates.” Leipzig (VEB Bibliographisches Institut) 760 p A REFERENCE WORK covering “elementary mathematics”, “steps toward higher mathematics” (from set theory to mathematical optimization through topics in undergraduate mathematics), and “brief reports on selected topics” (e.g. number theory, measure theory, found- ations). Plates are largely historical (PORTRAITS, INSTRUMENTS FACSIMILES, etc.), and there are occasional historical comments. DUGAC, Pierre 1973 Documents pour une &ude sur RICHARD DEDEKIND Paris (University of Paris VI) 175 p (Mimeographed) 57 documents, mostly CORRESPONDENCE to and from Dedekind and between other contemporary mathematicians, but a few MANUSCRIPTS. IM 3 Abstracts 117 KING, David A 1974 An ANALOG COMPUTER for solving problems of SPHERICAL ASTRONOMY: the Shakkaziya QUADRANT of Jamal al-din al-MARIDINI drch. ant. d'~ist. Sci. 24(95), 219-242. MEDIEVAL MATHEMATICS. SPHERICAL TRIGONOMETRY. XIV-XV. LENZEN, Victor F 1974 Peirce, Russell and Achilles ~rans- actions of the Charles S. Peirce Society 10:2 (1974) 3-7. ZEN0 OF ELEA, PARADOXES, ACHILLES AND THE TORTOISE, BERTRAND RUSSELL, C D BROAD, CONTINUUM. A discussion of C S PEIRCE’S physical solution to Zeno’s Paradox, which Peirce justifies by also analyzing the paradox using a geometric progression. (C. V. Jones) DRAKE, Stillman and James MacLachlan 1975 Galileo’s discovery of the parabolic trajectory Scientific American 232(3) (March), 102-110. GALILEO. CAVALIERI. PARABOLIC TRAJECTORY. LAW OF FREE FALL. Analysis of unpublished manuscripts and replication of experiments therein described show that Galileo discovered the parabolic trajectory while conducting experiments to establish a law of inertia. (C. V. Jones) INSTITUTE OF HISTORY, AC. SCI. UKRANIAN SSR 1975 Istoriya matematicheskogo obrazovaniya v SSSR. [History of the MATHEMATICAL EDUCATION in the USSR] Kiev (Naukova Dumka) 383 p This book is published by the section of the history of natural sciences and technics of the Institute of History. It contains an introduction “General problems of the mathematical education in the USSR” written by A N KOLMOGOROV, and two parts: (1)“Development of mathematical teaching in the general h-igh school”, and (1I)“Development of mathematical education in the higher school” (higher school = university level). The book contains PORTRAITS of activists in mathematical EDUCATION in the USSR. (B. M. Schein) . STIYANIC, Ernest 1973 The problem of parallels in the work of FEDERICGRISOGONO (In Serbo-Croatian) Matematizki vesnik 10(25), 369-376. An invalid XVI century effort to prove the existence of two non-equidistant lines that do not meet. ROZENFELD, B A 1975 Astonomicheskii trud al-Biruni “Kniga vrazumleniya nachatkam nauki zvezd” (The astronomical work of AL-BIRUNI “The book of instruction in the elements of the art of the stars.” Ist-ast issl 12, 205-226. 118 Abstracts HM 3 STIPANIC, Ernest 1974 The mathematical reviews of FEDERIC GRISOGONO (In Serbo-Croatian) in Actes du Symposium consacr6 2 la vie et 2 l'oeuvre du F&d&ic Grisogono, 2 l'occasion du 500isme anniversaire de sa naissance, Zadar, 60-85. CONNELLY, Ralph D and Brenda SMITH 1975 Measurement: a look at history and the metric system School Science and Mathematics 75, 485-491 Brief discussion of equivalents. METROLOGY. Development of TEMPERATURE SCALES of D G FAHRENHEIT and ANDERS CELSIUS. Brief history of METRIC SYSTEM and its units. (J. K. Bidwell) BRADLEY, A Day 1975 Alligation-relic and recreation School Science and Mathematics 75, 550-554. USA. Discusses ALLIGATION medial and alligation alternate problems as they appear in early American ARITHMETIC TEXTS, including modern algebraic solutions. (J. K. Bidwell) SEMENETS, H 1 1974 Rannii period istoriyi obhruntuvannya heometriyi [The early period in the history of foundations of geometry] Narysy z istoriui pryrodoznavstva i tekhniky Kyyiv [Kiev] (Naukova Dumka) 19, 7-15. A survey of papers on the FOUNDATIONS OF GEOMETRY in ANCIENT GREECE and MEDIEVAL ORIENT. (B. M. Schein) PYASKOVSKII, B V 1973 Rol materialistichnikh traditsii u rozvitkovi vitchisnyanoi matematiki [The role of the material- ist tradition in the development of the Russian and Ukrainian mathematics] Kiev (Kiev University) 183 p PHILOSOPHY OF MATHEMATICS. XVII. XVIII. XIX. XX. L P MAGNITSKII. M V LOMONOSOV. L EULER. RUSSIA. UKRAINE. T F OSIPOVSKII. M V OSTROGRADSKII. P L CHEBISHEV. USSR. ROSS, Richard P 1975 ORONCE FINE’S De sinibus libri II: the first printed trigonometric treatise of the French RENAISSANCE. Isis 66, 379-386. TRIGONOMETRY. VERNET, Juan 1974 Mathematics, astronomy, optics, in The Legacy of Islam (Oxford University Press) 461-489. ARAB MATHEMATICS. ASTRONOMY. OPTICS. HM 3 Abstracts 119 BAKER, Keith Michael 1975 Condorcet. From Natural Philosophy to Social Mathematics Chicago (University of Chicago Press) 552 p CONDORCET. PROBABILITY. Focus on the development of his conception of the SOCIAL SCIENCES. BIBLIOGRAPHY (39 pages). SACCOMAN, John Joseph 1974 A study of the HAHN-BANACH THEOREM and its ramifications 170 p Doctoral Thesis at New York Univ- ersity supervised by Professor William Zlot. Contains a history of the theorem. (Dissertation Abstracts 35, 941-B. Order No. 74-17, 155.) (S. M. Eisenberg) STOLZE, Charles Henry 1974 A developmental study of the integral theorems of Gauss and Stokes 149 p Doctoral Thesis at New York University supervised by Professor William Zlot. STOKES THEOREM. GREEN THEOREM. DIVERGENCE THEOREMS. (Dissertation Abstracts 35, 942-B. Order No. 74-17, 161.) (S. M. Eisenberg) RESTIVO, Sal P f, Christopher K VANDERPOOL eds. 1974 Comparative Studies in Science and Society Columbus, Ohio (Charles E. Merrill 480 p An ANTHOLOGY of articles (almost all reprints) on SOCIOLOGY OF SCIENCE, including the 1960 paper by ALEXANDER VUCINICH on the background in RUSSIA for the mathematical tradition in the SOVIET UNION (J. Hist. Ideas 21, 161-179) and that by JOSEPH NEEDHAM on science and society in the East and West (Goldsmith, Maurice and A. Mackay, eds. 1964 Society and Science, 127-149). No index; one would have been useful. RASHED, Roshdi editor 1974 Condorcet: Mathgmatique et soci&t& [CONDORCET: MATHEMATICS AND SOCIETY] Choix de textes et commentaire par Roshdi Rashed Paris (Hermann) 218 p MATHEMATICAL SOCIOLOGY. SOCIAL SCIENCES. Commentary (pp. 9-87), biographical chronology (pp. 88-91)) and chosen excerpts mostly identified only by location in the 12 volume Oeuvres. CROSSLEY, J N 1975 Algebra and Logic. Papers from the 1974 Summer Research Institute of the Australian Mathematica.i Society, Monash University, Australia Springer (Berlin) 307 p This collection of research papers begins with 62 pages of joint reminiscence on MATHEMATICAL LOGIC by C-C CHANG, J CROSSLEY, J KEISLER, S KLEENE, M MORLEY, V MORLEY, A MOSTOWSKI, A NERODE, and G SACKS. Their discussion centers on the development of RECURSIVE FUNCTION 1HEORY from 1930, and paricularly by S C KLEENE and A TURNING. (G. H. Moore) 120 Abstracts HM 3 INDIAN JOURNAL OF HISTORY OF SCIENCE 1974 Proceedings of the Symposium on COPERNICUS and ASTRONOMY held in New Delhi on 19-20 February 1973 I.J.H.S. 9(l), i-iii, l-142 Articles of particular mathematical interest are abstracted below. GUPTA, R C 1974 Solution of the astronomical triangle as found in the Tantra-Samgraha (A.D. 1500) I.J.H.S. 9, 86-99 SPHERICAL TRIGONOMETRY. NILAKANTHA SOMAYAJI. INDIAN ASTRONOMY. XV-XVI. SEN, S N 1974 Epicyclic-eccentric PLANETARY THEORIES in ancient and medieval INDIAN ASTRONOMY I.J.H.S. 9, 107-121 BARONE, Jack 1974 An historical analysis of the development of PROBABILITY FOUNDATIONS 530 p Doctoral Thesis at New York University. BOREL. XX. STEINHAUS. A N KOLMOGOROV. A study of the period 1909-1933. (Dissertation Abstracts 35, 2299-B. Order No. 74-24, 980.) (S. M. Eisenberg) GARDNER, W Davis 1975 Core memory patents challenged by NCR Datamation 21(g), 108 COMPUTER HISTORY. CORE MEMORY. MIT. IBM. RCA. NCR. LITIGATION. JAY W FORRESTER. Includes portrait of Forrester. (H. S. Tropp) COOK, Nathan H 1975 Computer-managed parts manufacture Scientific American 232~2 (February 1975), 23-29 A brief historical survey of the use of COMPUTERS IN MANUFACTURING. (C. V. Jones) WEIL, Andre 1974 Two lectures on NUMBER THEORY, past and present L'Enseignement Math. 20, 87-110 In the 1972 RITT LECTURE SERIES, the author attempted to demonstrate the continuity of the devel- opment of number theory during the past three hundred years. The main threads of development examined are the ZETA FUNCTION and DIOPHANTINE EQUATIONS. Mathematical progress is seen in the works of FERMAT, EULER, LAGRANGE, GOLDBACH, GAUSS, RIEMANN and DEDEKIND, as well as several twentieth-century number theorists. (D. E. Kullman) KAVETT, Hyman & Phyllis F KAVETT 1975 The eye of Horus is upon YOU The Mathematics Teacher 68, 390-394 EGYPTIAN NUMERATION. Hieroglyphic and hieratics scripts, FRACTIONS and other special- ized numerals. (J. K. Bidwell) HM3 Abstracts 121 SHUBNIKOV, A V 6 KOPTSIK, V A 1974 Symmetry in Science and Art (Plenum Press) 445 p Translation of 1972 Simmetriya v nauke i iskusstve Moscow (Nauka). SYMMETRY. WEILING, Franz 1975 J.G. Mendel sowie die von M. Pettenkofer angeregten Untersuchungen des Zusammenhanges von Cholera-und- Typhus-Massenerkrankungen mit dem Grundwasserstand [The research by J G MENOEL on the CORRELATION of cholera and typhus mortality with the level of underground water suggested by M PETTENKOFER. Sudhoffs Archiv. 59(l), l-19 STATISTICS. Also the work of LUDWIG BUHL and L SEIDEL. GARDNER, Martin 1975 Mathematical games: the curious magic of anamorphic ART Scientific American 232: 1 (January 1975)) 110- 116. ANAMORPHIC ART is art produced by PERSPECTIVE distortions that are co-ordinate transformation; e.g., by reflecting the image through a cylindrical mirror. (C. v. Jones) VARCROUX, Andre G 1975 Microcomputers Scientific American 232:5 (May 1975)) 32-40 COMPUTERS. A description and history of MICROCOMPUTERS and their applications. (C. v. Jones) BERMAN, Gerald 1975 Forward Citations in GRAPH THEORY Waterloo, Ontario (Department of Combinatorics and Optimization, University of Waterloo) 246 p A BIBLIOGRAPHY by author (no indication of the period covered or sources) with a topical INDEX (no indica- tion of the indexing method, though it appears to be free index- ing without much vocabulary control), and a CITATION INDEX (for each paper are indicated later papers that cite it.) FEDERICO, P J 1975 The number of polyhedra Philips Res Repts 30, 220*-231* A survey work on the POLYHEDRONS ENUMERATION beginning with L EULER. BIBLIOGRAPHY of 25 references. NAIMAN, Arnold Ross 1974 The role of QUATERNIONS in the history of mathematics 186 p Doctoral Thesis at New York University under Dr. William Zlot. W R HAMILTON. A CAYLEY. (Dissertations Abstracts 35, 2315-B. Order No. 74-25, 010). (S. M. Eisenberg) JAMES, R D 1975 The age of Gage Canadian Mathematical Congress Notes 8(2), 6-7 A note on the career of WALTER GAGE at the UNIVERSITY OF BRITISH COLUMBIA. 122 Abstracts HM3 DRAKE, Stillman 1975 The role of music in Galileo's experiments Scientific American 232(6) (June 1975) 98-104 TIME. GALILEO. RATIO. MEASUREMENT. ERROR. Deciphering of unpublished manuscript shows Galileo's technique of measuring small intervals of time and how it was used in deriving the correct law of FREE FALL. (C. V. Jones) CORR, Charles A 1975 Christian Wolff and Leibniz Journal of the History of Ideas 36:2 (1975) 241-262 G W LEIBNIZ, CHRISTIAN WOLFF, OTTO MENCKE, ACTA ERUDITORIUM, ALGEBRA, MATHEMATICAL METHOD, SYLLOGISM, R DESCARTES, E W TSCHIRNHAUS, LOGIC. (C. V. Jones) MOORE, Charles W 6 ?Jicholas PYLE Editors 1974 The Yale Mathe- maticsBui1dingCompetition. Architecture for a Time of Question- ing New Haven and London (Yale University Press) 117 p SOCIOLOGY OF MATHEMATICS. MATHEMATICAL FACILITIES. YALE UNIVERSITY. ARCHITECTURE. An illustrated chronicle of the competition. ERSHOV, Andrei P 1975 A history of computing in the U.S.S.R. Datamation 21 (9) 80-81 COMPUTER HISTORY. USSR. Collection of fragmentary information on hardware, software, operating systems, research and training from 1951 to the present. Discusses the effect of isolation, the social system and geography on the development of the data processing industry in Russia. (H. S. Tropp) ROSS, Bertram 1974 The development, theory, and applications of the GAMMA FUNCTION and a profile of fractional calculus 412 p Doctoral Thesis at New York University supervised by Prof. William Zlot. Presents a historical survey and a chronological BIBLIOGRAPHY of the FRACTIONAL CALCULUS. (Disser- tationAbstracts 35, 941-B. Order No. 74-17, 154.) (S. M. Eisenberg) KAHN, Henry Frank 1974 A study of the manner in which selected topics in ELEMENTARY ALGEBRA were presented to students in America between 1900 and 1970 as revealed in selected commercially published TEXTBOOKS. 317 p Doctoral thesis at Temple University. A study of the pressures of social and historical events on the CURRICULUM. (Dissertation Abstracts 35, 1320-B. Order No. 74-19, 756.) (5'. M. Eisenberg) HM 3 Abstracts 123 CANGUILHEM, Georges editor 1972 ~a mathgmatisation des doctrines informes [The MATHEMATISATION of mathematically unstructured theories] Report of a colloquium held at the Institute of the History of Science at the University of Paris, 24-26 June 1970 under the direction of the editor. Paris (Hermann -- Actualit& scientifiques et industrielles 1346) 237 p MATHEMATICAL MODELLING. AXIOMATIZATION. ROLE OF MATHEMATICS. Includes papers on GALILEO and MECHANICS (J.R. Ravetz), MEDICINE (J. Guillerme), SOCIAL SCIENCES (R. Rashed), PSYCHOLOGY (F. Bresson), ECONOMICS (F. Perroux), and the general question (M.-A. Tonnelat, J. Piquemal) -- in which it becomes clear that the meaning of “informes” is unclear. * BROUWER, L E J 1975 Collected Works. Volume 1: Philosophy and Foundations of Mathematics Edited by A. Heyting Amsterdam (North-Holland) and New York (American Elsevier) 643 p This volume reprints his papers on PHILOSOPHY OF MATHEMATICS, FOUNDATIONS, and INTUITIONIST MATHEMATICS. Papers (including his thesis) that originally appeared in Dutch are here translated into English. BIBLIOGRAPHIES of his papers in these fields and of related papers by others, editor’s introduction and notes (51 pages), and indexes in German and English. Brouwer ‘s other mathematical work (mainly on topology) and a complete publication list will be included in the other of the two volumes. WEISSENBORN, Hermann 1972 Die Principien der haheren Analysis in ihrer Entwickelung von Leibniz bis auf Lagrange als ein historisch-kritischer Beitrag zur Geschichte der Mathematik [The principles of higher ANALYSIS in its development from Leibniz to Lagrange as a historical-critical study of the history of mathematics) Leipzig (Zentralantiquariat der Deutschen Demokratischen Republik) 166 p Facsimile REPRINT of the original edition of 1856. CALCULUS FOUNDATIONS. The author divides the CALCULUS into three approaches: FLUXIONS (G P ROBERVAL, I BARROW, I NEWTON, C MACLAURIN), DIFFERENTIAL CALCULUS (GREGORY ST. VINCENT, I BARROW, G LEIBNIZ, BERNOULLIS, BERNHARD NIEUWENTIJT, BROOK TAYLOR, L EULER), and the calculus of derivatives of L LAGRANGE. No commentary. POLYA, George 1974 Collected Papers. volume II: Location of Zeros Edited by R P BOAS Cambridge, Mass. (M. I.T. Press) 454 p SELECTED WORKS. The chronological bibliography of 244 of his publications permits reader to repair the fragmentation induced by chopping up a person’s work according to conventional class- ifications. Youthful PORTRAIT. Volume I contains papers on singularities of analytic functions, and other volumes are promised. 124 Abstracts HM 3 FROLOV, B A 1974 Chisla v grafike paleolita [Numbers in paleo- lithic graphic art] Novosibirsk (Nauka) 238 p PREHISTORIC MATHEMATICS. ARCHEOLOGY OF MATHEMATICS. ART. Survey and analysis of STONE AGE artifacts found on the territory of the USSR and elsewhere, illustrating primitive concepts of ARITH- METIC and ASTRONOMY. Some discussion of findings of ANTHRO- POLOGY and PSYCHOLOGY. 61 plates displaying photographs and drawings of hundreds of artifacts. Independently comes to conclusions similar to those of A MARSHAK. Postscript by I3 M KEDROV and A P AKLADNIKOV. BIBLIOGRAPHY. HODEL, R E 1974 Some results in metrization theory, 1950-1972 Topology Conference Springer-Verlag Lecture Notes in Mathematics, vol. 375, pp. 120-136 BIBLIOGRAPHY. GENERAL METRIZATION PROBLEM. DEVELOPABLE SPACES. POINT-SET TOPOLOGY. 'The history of METRIZ- ATION from 1923 (theorem of Alexandroff and Urysohn) through 1972, with emphasis on more recent results. Most depend on some generalization of the notion of COUNTABLE (LOCAL) BASE. (D. E. Kullman) JAHODA, Cerhard 1971 Identische Strukturen Pythagoreischer Zahlenschemata [Identical structures of Pythagorean number schemata] Vienna (Verlag Elisabeth Lafite) 104 p MYSTICISM. PYTHAGOREANISM. Numbers and geometric forms, FIGURATE NUMBERS, and MUSIC. TURNER, G L'E 1975 Descriptive Catalogue of van Marum's ScientificInstrumentsin Teyler's Museum Part 11 (pages 129-401) of Turner 1973 van Marum's Scientific Instruments...(abstracted in HM 1, 501) here reprinted in paper cover. ARIOTTI, Piero E 1975 BONAVENTURY CAVALIERI, MARIN MERSENNE, and the REFLECTING TELESCOPE Isis 66, 303-321 Shows that Cavalieri, Mersenne, and others considered and attempted to construct reflecting TELESCOPES well before the work of I NEWTON, traditionally giving him priority. The realtion of the work to BURNING MIRRORS and the use of CONIC SECTIONS are described. MUMFORD, David 1975 Curves and their Jacobians Ann Arbor (University of Michigan Press) 106 p No history but a ten- page annotated BIBLIOGRAPHY. HM 3 Abstracts 125 BELL, John et al editors 1973 The Proceedings of the Bertrand Russell Memorial Loqic Conference, Uldum, Denmark 1971 Leeds (Bertrand Russell Memorial Logic Conference, Leeds University) 404 p (Out of print) PHILOSOPHY OF MATHEMATICS Includes the history of this "counter-conference" (to a NATO-sponsored logic conference) and papers abstracted below. BELL, John 1973 Some remarks on current mathematical practice in Proc. B. Russell Mem. Logic Conf. 54-57 SOCIOLOGY OF MATHE- MATICS. MATHEMATICS POLICY. EDUCATION. CLARK, Peter 1973 Note on the PHILOSOPHY OF MATHEMATICS in Proc. B. Russell Mem. Logic Conf. 112-114. PRIEST, Graham 1973 A bedside reader's guide to the convention- alist PHILOSOPHY OF MATHEMATICS in Proc. B. Russell Mem. Logic Conf. 115-132 CONVENTIONALISM. PEPPINGHAUS, Benedikt 1973 Some aspects of Wittgenstein's PHILOSOPHY OF MATHEMATICS in Proc. B. Russell Mem. Logic Conf. 133-140 L WITTGENSTEIN. KENNEDY, H C 1975 Nine letters from GIUSEPPE PEANO to BERTRAND RUSSELL Journal of the History of Philosophy 13(2), 205-220. The originals from the Russell ARCHIVES at McMASTER UNIVERSITY. English translation, and commentary. JACOBSON, Nathan 1974 ABRAHAM ADRIAN ALBERT, 1905-1972 ~~11. Amer. Math. Sot. 80, 1075-1100 BIOGRAPHY. BIBLIOGRAPHY. ASSO- CIATIVE ALGEBRAS. NONASSOCIATIVE ALGEBRAS. LIE GROUPS. RIEMANN MATRICES. (D. E. Kullman) BULLETIN AMER. MATH. SOC., 1975 General Index, Volumes 71-80, 1965-1974. Bull. Amer. Math. Sot. 81(3), Part 2, 51 p AMERICAN MATHEMATICAL SOCIETY. JOURNAL INDEXES. Categories indexed are: research announcements; research problems; invited addresses; book reviews; meetings; errata, corrigenda and addenda; and miscellaneous. Within each category (except meetings), entries are alphabetized by authors' last names. (D. E. Kullman) 126 Abstracts HM3 STEEN, Lynn A 1975 Foundations of mathematics: unsolvable problems Science 189 (18 July) 209-210 UNDECIDABILITY. IMPOS- SIBILITY. CONTINUUM HYPOTHESIS. MODELS. SOUSLIN. CONJECTURE. HILBERT TENTH PROBLEM. A popular account of recent history. DZHALALOVA, z G 1975 Uchenie al-Biruni o dvizhenii solntsa [The teaching of AL-BIRUNI on the motion of the SUN] Istoriko-astron- omicheskie issledovaniya 12, 227-236. STARTSEV, P A 1975 0 kitaiskom kalendare [On the CHINESE CALEN- DAR] Ist.-ast. issl. 12, 253-334. KDZHANCHIKOV, V I 1975 Printsipy postroeniya i deistviya kalendarya maiya [Principles of construction and operation of the MAYAN CALENDAR] Ist.-ast. issl. 12, 335-356. MCLAUGHLIN, Richard A 1!)75 The IBM 704: 36-bit floating point money-maker Datamation 21(8), 45-50 COMPUTER HISTORY. IBM 704. SHARE. A description of the primary innovations in the 704, and its impact on the evolution of the commercial computer industry. (H. S. Tropp) GUPTA, R C 1975 Circumference of the Jambudvipa in JAINA COSMOGRAPHY. Indian Journal of History of Science 10(l), 38-46 JAINA MATHEMATICS. PI. MEDIEVAL MATHEMATICS. ROBINSON, G de B 1975 HANS A HEILBRONN Canadian Mathematical Congress Notes 8(l), 15 An OBITUARY. APOKIN, 1 A and L E MAISTROV 1974 Razvitie vychislitelnykh mashin [The development of CALCULATING MACHINES] Moscow (Nauka) 399 p The ABACUS, CALCULATING INSTRUMENTS, MECHANICAL CALCULATORS ELECTRICAL CALCULATING MACHINES, and (226 p) electronic digital COMPUTERS. Chronology and bibliographic note. ANON., 1975 Award of the 1975 CHAUVENET PRIZE to Professors MARTIN D DAVIS and REUBEN HIRSCH Amer. Math. Mon. 82, 108-109 AWARDS. For their paper on HILBERT'S TENTH PROBLEM (Scientific American 229, 84-91) (H. S. Tropp) HM3 Abstracts 127 BUSARD, H L L 1974 Ein mittelalterlicher Euklid-Kommentar, der Roger Bacon zugeschrieben werden kann (A MEDIEVAL EUCLID commentary that may be due to ROGER BACON) Arch. Int. c2'Hist. Sci. 24(95), 199-218 In question is the MS Florence, Bib]. Naz. Conv. Soppr. J. IX, 26, XV-XVI 46'-5Sr formerly attributed to ADELARD OF BATH. The text is in an appendix. NEEDHAM, Joseph 1974 La tradition scientifique chinoise Paris (Hermann) 306 p REPRINTS. SELECTED WORKS. Eleven articles (without clear indication of sources or whether reprinted or translated) from 1954 to 1962, of which one compares CHINESE MATHEMATICS with the western. SZUPROWICZ, Bohdan 0 1975 China's computer industry Datamation 21(6), 83-88 COMPUTER HISTORY. CHINA. Brief chronology of the development of computers in China, beginning with manufacture of copies of Soviet machines in 1958 to the current production of third generation computers. (H. S. Tropp) KUNITZSCH, Paul 1974 Der Almagest. Die Syntaxis Mathematics des Claudius Ptolemxus in arabisch-lateinischer cberlieferung [The ALMAGEST. The Syntaxis Mathematics of CLAUDIUS PTOLEMY in Arabic-Latin transmission] Wiesbaden (Otto Harrassowitz) 410 p DM 160 ARAB MATHEMATICS. MEDIEVAL MATHEMATICS. ABU MASAR. ABUL WAFA. AL-BIRUNI. GERHARD OF CREMONA. IBN AL-QIFTI. IBN AS-SALAH. NASIR AL-DIN. THABIT IBN QURRA. A detailed analysis of texts, documents, and terminology with 10 facsimile photo- graphs, word concordances, and star catalogues. PERRY, Z Gustav0 1973 Apuntes para la historia de las ciencias basicas en Colombia [History of the basic sciences in Colombia] Rev. Acad. Colombiana Ci. Ex. Fis. Nat. 14, 5-32 A short but well-documented account of the development of SCIENCES (including mathematics) in Colombia from the beginning of the COLONIAL PERIOD to the present day. The influence of certain political, social and economic aspects on this development is stressed. (V. S. Albis Gonzdlez) JONES, Burton W 1975 An Introduction to Modern Algebra New York (MacMillan Pub. Co.) 366 p ABSTRACT ALGEBRA. ALGEBRA. A very well-written TEXTBOOK WITH HISTORICAL MATERIAL (biographical notes at the end of each chapter). (V. S. Albis Gonz6lez) 128 Abstracts HM 3 WALDSCHMIDT, Michel 1974 Initiation aux nombres transcendants [Introduction to TRANSCENDENTAL NUMBERS] L'Enseiqnement Math. 20, 53-85 Emphasis is on the theorem of A 0 GELFOND and T SCHNEIDER concerning the transcendence of ab and the theorem of A BAKER on the linear independence of logarithms of algebraic numbers. A brief historical survey of results from the time of Liouville is included. (0. E. Kullman) MARDEN, Morris 1975 Joseph L. Walsh in memoriam Bull. Amer. Math. Sot. 81, 45-65 J L WALSH (OBITUARY, PORTRAIT, BIBLIOG- RAPHY, LIST OF PH.D STUDENTS). COMPLEX ANALYSIS. (D. E. Kullman) GLUCK, Herman 1975 MANIFOLDS with preassigned CURVATURE -- a survey Bull. Amer. Math. Sot. 81. 313-329 RIEMANNIAN GEOMETRY. BIBLIOGRAPHY. Discusses the MINKOWSKI PROBLEM and its generalization, as well as the converse to the GAUSS- BONNET THEOREM. (D. E. Kullman) FISHER, R A 1971-1975 Collected Papers Edited by J.H. Bennett Adelaide (Department of Genetics, University of Adelaide, South Australia 5001) Five volumes 2972 p US $115 COLLECTED WORKS. Nearly 300 papers, including joint articles and selected letters, reviews, etc. Reprinted with some corrections and comments by Fisher. Complete BIBLIOGRAPHY, subject, author, and self- citation INDEXES. PORTRAITS. SHAMSI, F A 1973 Towards a Definitive Solution of Zeno's Paradoxes with foreword by Hakim M. Said Karachi (Hamdard Academy) 84 p The author accepts the ZEN0 PARADOXES and rejects actual INFINITY. BIBLIOGRAPHY. GRATTAN-GUINNESS, I 1974 Achilles is still running Transactions of the Charles S. Peirce Society lo:1 (1974) 5-16 C S PEIRCE, ACHILLES AND THE TORTOISE, LEWIS CARROLL, PARADOX, CONTRADICTION, TIME, KARL POPPER, INFINITESIMALS, LIMITS, LIMIT-AVOIDANCE, ZEN0 OF ELEA. The Achilles-Tortoise argument is, in fact, a contra- diction as stated by Zeno. It is only by adding extra premises that Zeno's formulation becomes a paradox. The typical extra premise added is that of the orthodox theory of time. The same analysis is applied to Carroll's "What the Tortoise Said to Achilles" article in Mind (n.s.) 4 (1895), 278-280. (C. V. Jones) HM3 Abstracts 129 LINNIK, V P 1975 Trudy Keplera v oblasti optiki [The work of KEPLER in OPTICS] Istoriko-astronomicheskie issledovaniya 12, 89-100. TAGI-ZADE, A K and S A VAKHABOV 1975 Astrolyabii srednevekovogo Vostoka [ASTROLABES of the MEDIEVAL MIDDLE EAST] Ist-ast issl 12, 169-204 AL-BIRUNI. AL-ZARKALI. WILLERDING, Margaret F 1975 The Pythagorean legacy Schoo.1 Science and Mathematics 75, 145-154 PYTHAGOREAN MATHEMATICS. A summary of the life of PYTHAGORAS and the contributions of the Pythagorean Brotherhood. (J. K. Bidwell) ROGERS, L F 1975 Finding out in the History of Mathematics (Private preprint available from the author at Digby Stuart College, Roehampton, London S.W. 15. England. Price: 35 pence) 33 pages with supplement May 1975 on non-book materials, 10 pages. "A resourcefile of bibliographic, audio-visual and other materials for students and teachers." AUDIO-VISUAL MEDIA. BIOGRAPHY. EDUCATION. FILMS. SLIDES. WALL-CHARTS. A BIBLIOGRAPHY of English language source material. Contains mainly secondary and some primary sources available through English library or source material loan systems. Further collections on Geometry, Algebra, Calculus, Calculating Devices, and a Time-Chart are in preparation. The author welcomes any comments from users on accuracy of entries and classification of sections. (L. F. R.) SCHLISSEL, Arthur 1974 The development of ASYMPTOTIC SOLUTIONS of LINEAR ORDINARY DIFFERENTIAL EQUATIONS, 1819-1930 210 p Doctoral Thesis at New York University supervised by Professor Morris Kline (Dissertation Abstracts 35, 941-B. Order No. 74-18, 196.) (S. M. Eisenberg) KODAIRA, Kunihiko 1975 Collected Works (Iwanami Shoten and Princeton University Press) 1634 p PORTRAIT, 9 page biographical preface, and reprints of 70 articles 1937-1971 by the author (who was 60 years old in March 1975) on TOPOLOGY, HILBERT SPACES, HARMONIC INTEGRALS, ALMOST PERIODIC FUNCTIONS, SHEAVES, ALGEBRAIC GEOMETRY, COMPLEX MANIFOLDS, DEFORMATION THEORY. SCHMIDT, Olaf 1975 A system of Axioms for the Archimedean theory of equilibrium and centre of gravity Centaurus 19, l-35 ARCHIMEDES. STATICS IN ANTIQUITY. An axiomatic exposition following the Archimedean line which corrects the formal and mathematical defects of Archimedes' "On the equilibrium of planes or the centre of gravity of planes." (K. M. Pedersen) 130 Abstracts HM 3 BROWN, David K 1975 Letter to the American Scientist 63(3) (Flay-June), 261 Precursors of the development by RICHARD V SOUTHWELL of RELATION METHODS, reported by G Birkhoff in Amer. Scientist 63(l), 83-91 BIRKHOFF, Garrett 1975 Reply to the letter by D K Brown American Scientist 63(3) (May-June), 261-262 He did not claim a first for RICHARD V SOUTHWELL but merely BIERMANN, K-R 1975 Mit dem Wissen kommt das Denken, und mit dem Denken der Ernst und die Kraft in die Menge. A.v. Humboldts Einflussnahme auf Reformen der Berliner Akademie der Wissenschafter ("With knowledge comes thought and with thought earnestness and strength in abundance." The influence of A.v. Humboldt on the reform of the BERLIN ACADEMY OF SCIENCE). Wissenschaft u. Fortschritt 25(4), 162-168 DRAKE, Stillman 1975 FREE FALL from ALBERT OF SAXONY to HONORE FABRI Stud. Hist. Phil. Sci. S(4), 347-366 LEONARDO DA VINCI. GALILEO. PROPORTION. EISELE, Carolyn 1975 Salomon Bochner on Charles S. Peirce-I Amer. Math. Monthly 82, 477-478 Brief criticism of S. BOCHNER'S analysis of C.S. PEIRCE'S philosophy and mathematical competence in "Mathematical Reflections" (Amer. Math. Monthly 81, 427-478) which ignored unpublished Peirce manuscripts. (H. S. Tropp) FISCH, Max H 1975 Salomon Bochner on Charles S. Peirce-II Amer. Math. Monthly 82, 478-481 C. S. PEIRCE. PHILOSOPHY. LOGIC. CONTINUITY. Brief critique of some strengths and weak- nesses in S. BOCHNER'S "Mathematical Reflections" (Amer. Math. Monthly 81, 427-488). (H. S. Tropp) GAUSS, C F 1975 Carl Friedrich Gauss - Friedrich Wilhelm Bessel Briefwechsel (The C. F. GAUSS-F. W. BESSEL CORRESPONDENCE) Carl Friedrich Werke Erganzungsreihe, Band I Hildesheim (George Olms) 623 p. Facsimile REPRINT of the original edition of 1880, Leipzig somewhat reduced in size. An essential source for both Gauss and Bessel. Letters run from 1804 to 1844. HACKING, Ian 1975 The Emergence of Probability. A Philosophi- cal Study of Early Ideas about Probability, Induction and HM3 Abstracts 131 Statistical Inference. Cambridge University Press and Macmillan in Canada. 212 p. $17.95. A historical-philosophical study of the beginnings of mathematical theory of PROBABILITY and STATISTICS in the XVII century. BIBLIOGRAPHY (16 p.) of primary and second- ary sources attempts complete coverage of 1654-1700. HILTON, Peter 1975 The new emphasis on applied mathematics Newsletter of the Conference Board of the Math. Sciences lo(Z), 17-19. CURRENT HISTORY. A thoughtful critique of the PURE AND APPLIED MATHEMATICS chimera. HINES, Peter 1975 Surprises, Problems and Paradoxes Games and Puzzles no. SS(February), 7-13. Describes some well-known para- doxes that have baffled mankind through the ages, together with others that are little-known and few of recent origin. PARADOXES, LOGIC. HOUGHTON, Bernard 1975 Scientific Periodicals, Their Historical Development, Characteristics and Control. Hamden, Connecticut (Linnet Books). 135 p. $10. SERIALS. BIBLIOGRAPHY. Very little on mathematics. ISTORIYA NAUKI I NAUKOVEDENIE 1975 (History of science, and science of science). Tenth Baltic Conference on the History of Science. Abstracts of Papers. Riga (Zinatne). 211 p. Sponsored by the Academy of Science of the Latvian SSR and the Society of the History and Philosophy of Science and Technology of the USSR, held in Riga and Elgava, concentrating on the BALTIC COUNTRIES. Abstracts of 90 papers by 96 authors including P. V. Miliirsepp on G. W. LEIBNIZ, A. P. Yushkevich on mathematics in the PETERSBURG ACADEMY in XVIII, N. 1. Nevskaya and E. P. Ozhigova on the FUSS family, P. Vitkevichyus on mathematical sciences in LITHUANIA in the early XIX, Yu. M. Gaiduk, and I. A. Naumov on M. V. OSTROGRADSKII, Ya. P. Stradyn and A. P. Erglis on 0. YU. SHMIDT, D. Ya. Zilmanovich on E. I. BINEMAN and his work in MECHANICS and AERONAUTICS, 1. A. tieninya on mathematics in the Petrov Academy at ELGAVA (METAVA). "Naukovedenie"has no exact translation, but as used here it covers "general questions on the development of science" including SOCIOLOGY OF SCIENCE, SCIENCE POLICY, HISTORICAL THEORY, GEOGRAPHY OF SCIENCE, and SCIENCE OF SCIENCE. MAUCHLY, John W. 1975 Retrospective: Mauchly on the trials of building ENIAC Spectrum 12 (April), 70-76. COMPUTER HISTORY. 132 Abstracts HM 3 ENIAC. J.P. ECKERT. M. MAUCHLY. H. GOLDSTINE. A. BURKS. Personal account of evolution, design, and construction of ENIAC. (H. S. Tropp) LAM, T. Y. and M. K. SIU 1975 K. and Kl - An Introduction to Algebraic K-Theory Amer. Math. Monthly 82, 329-364. ALGEBRAIC K-THEORY. Survey plus a brief historical note citing some ger- minal work of GROTHENDIECK, H. BASS, M. ATIYAH, F. HIRZEBRUCH, and J. MILNOR. Bibliography. (H. S. Tropp) KOLATA, Gina Bari 1975 Foundations of Mathematics: Ties to Infinite Games Science 188, 923-924. FOUNDATIONS. GAME THEORY. THEORY OF SETS. AXIOM OF DETERMINANCY. Brief discussion of the role of game theory in the study of mathematical foundations, beginning with D. GALE and F. M. STEWART'S work on infinite games (1953) and concluding with work of D. A. MARTIN (1975) on the determinancy of BOREL SETS. (H. S. Tropp) PRICE, Derek de Solla 1975 Science Since Babylon. Enlarged Edition. New Haven & London (Yale University Press). 231 p. $15 ($3.45 paper) SCIENCE OF SCIENCE. SOCIOLOGY OF SCIENCE. HISTORICAL THEORY. GROWTH. QUANTITATIVE HISTORY. A reprint of the original of 1961 plus an additional preface, postscripts to three of six chapters, three new chapters (AUTOMATA, CLOCKS, REGULAR POLYGONS, GEOMETRIC MYSTICISM, PHILOSOPHY OF TECHNOLOGY), minor changes, and a smaller index. STEEN, Lynn A 1975 Public understanding of the mathematical sciences Newsletter of the Conference Board of the Math. Sciences 10(2), 21-23 COMMUNICATION. POPULARIZATION. INFORMATION RE- TRIEVAL. MATHEMATICS POLICY. CURRENT HISTORY. SMITH, F G and others 1975 Three hundred years of Greenwich Nature 255(5510) (19 June), 581-606 Seven articles on the history of ASTRONOMY and GREENWICH OBSERVATORY. REGHINI BONELLI, M L 6 William R SHEA, editors 1975 Reason, Experiment, and Mysticism in the Scientific Revolution New York (Science History Publications) 320 p. An ANTHOLOGY including Stillman Drake on GALILEO and FREE FALL, Pierre Costabel on mathematics and Galileo's inclined plane experiment, and Reng Taton on the mathematical revolution of the XVII century.