242 Reviews HM3 Basic Philosophical Language Was, As Was That of His

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242 Reviews HM3

basic philosophical language was, as was that of his readers. This explains why he defines new terms such as the various measures of vis centripeta, but does not define other terms, such as actio, reactio, status, or mutatio, that were part of the common philosophical language of the time. (As for vis insita and vis impressa, terms that had a long history before Newton, the special senses he gives them cannot be fully understood without reference to their previously accepted meanings. (For example, in reading Definition 111 (Materiae vis insita est potentia resistendi...) one is re- minded of Goclenius’ article on “Vis” (in the general sense): Vis Insita est, vel Violentia. Insita, ut naturalis potestas.) Three short examples will illustrate the point. In Eli and ~~a Newton deleted the opening line of Lex III, Actioni contrariam semper & aequalem esse reactionem, leaving only the sentence Corporum duorum actiones in se mutuo semper esse aequales & in par- tes contrarias dirigi. Whatever the full interpretation of this deletion may be, it seems at least to imply that the term reactio (though not the idea) is not indispensable for a statement of the Law. Of course this is the case, since reactio means simply actio mutua, as the explanatory paragraph accompanying Lex III suggests, and as Micraelius [1653, Actio] explicitly states: Actio mutua est, qua agens repatitur propter contactum corporeum, & dicitur reactio .,. . Goclenius’ article on Reactio [Lexicon Philosophicurn 16131 makes the same point in a more developed way: Reactio est retributa seu reciprocata patientis actio quaedam, qua resistit agenti, (renititur adversus agens) & id commutat dum ab eo commutatur. Itaque & agens pati, & patiens agere modo aliquo dicitur. Et repassio est reciprocata passio. (See Gabbey [1971, 29-301 where the comparison drawn between the actio-reactio coupling in Newton and the actio-passio coupling in Descartes, though still I think basically correct, would have benefited from a detailed background analysis of the Peripatetic notions of actio, reactio, passio, and repassio.) It is texts of this sort (and I have not mentioned the more fundamental question of how to interpret actio in Newton's writings) that must be the starting point in any adequate under- standing of Lex III and the mechanical theorems that follow from it. Secondly, there is the case of Lex II, which had been misin- terpreted until the work of Ellis and Dijksterhuis some dozen years ago. The law reads: Mutationem motus proportionalem esse vi motrici impressae, & fieri secundum lineam rectam qua vis illa imprimitur (unchanged in all eight texts). Here the key word is mutatio, which connotes more than the drab English translation “change” suggests . To see what this is we may consult Goclenius, who writes [1613, Mutatio]: Mutatio est, cum quid incipit vel definit esse, vel habere se aliquo modo posterius, quo se non habuit prius. Mutari est rem aliter se habere quam ante, sive id fiat transeundo in instanti ab uno statu in alterum, sive successive. (Itaque Mutationes aut sunt momentaneae vel subitaneae, aut successivae.) HM 3 Abstracts 245

SCRIBA, CHRISTOPH J 1974 John Pell's English edition of J H Rahn's Teutsche Algebra, in Cohen, R S 6 eds, For Dirk Struik, 261-274 JOHN COLLINS. J H RAHN. J PELL. T BRANCKER (BRANKER). ALGEBRA.

ROSEN, EDWARD 1974 RHETICUS as editor of SACROBOSCO, in Cohen, R S & eds, For Dirk Struik, 245-248

NIKOLIC, MILENKO 1974 The relation between Eudoxus' theory of proportions and Dedekind's theory of cuts, in Cohen, R S E eds, For Dirk Struik, 225-243 DEDEKIND CUTS. PROPORTIONS. EUDOXUS. REAL NUMBERS.

FREUDENTHAL, HANS 1974 The impact of von Staudt's foundations of geometry, in Cohen, R S 6 eds, For Dirk Struik, 189-200 GEOMETRY FOUNDATIONS. PROJECTIVE GEOMETRY. C G C von STAUDT.

BUSARD, H L L 1974 The second part of chapter 5 of the De Arte Mensurandi by JOHANNES DE MURIS, in Cohen, R S & eds, For Dirk Struik, 147-167 MEDIEVAL MATHEMATICS. ARAB MATHEMATICS. GERARD OF CREMONA. ABU BEKR. Latin text with analysis and commentary of influences and sources.

YUSHKEVICH, A P 1974 La notion de fonction chez Condorcet (The FUNCTION concept with M J A N C CONDORCET), in Cohen R S & eds, For Dirk Struik, 131-139

COHEN, I B 1974 ISAAC NEWTON, the CALCULUS OF VARIATIONS, and the design of ships. An example of pure mathematics in Newton's PRINCIPIA, allegedly developed for the sake of practical APPLICATIONS, in Cohen, R S & eds, For Dirk Struik, 169-187 HISTORIOGRAPHY OF MATHEMATICS. SOCIOLOGY OF MATHEMATICS. HISTORICAL THEORY. A critique of assertions of R K Merton and others on the alleged practical motivation of Newton's mathematics.

STRUIK, RUTH REBEKKA 1974 Some remarks on the concept of LIMIT, in Cohen, R S & eds, For Dirk Struik, 121-129 INFINITESIMALS. CALCULUS FOUNDATIONS. 246 Abstracts HM3

HOFMANN, J E 1974 iber ein Beispiel zur unbestimmten Analytik und seine allgemeine Bedeutung (On an example of &determinate analysis and its general meaning), in Cohen, R S 8 eds, For Dirk Struik, 75-89 SUMS OF SQUARES. DIOPHANTINE SYSTEMS. J OZANAM. L EULER.

DAVIS, CHANDLER 1974 Materialist mathematics, in Cohen, R S & eds, For Dirk Struik, 37-66 PHILOSOPHY OF MATHEMATICS. EXISTENCE. TRUTH. An original point of view based on careful analysis of previous work.

COXETER, H S M 1974 POLYHEDRAL NUMBERS, in Cohen, R S 6 eds, For Dirk Struik, 25-35 CLOSE PACKING OF SPHERES. R BUCKMINSTER FULLER.

BOS, H J M 1974 The LEMNISCATE of Bernoulli, in Cohen, R S & eds, For Dirk Struik, 3-14 ISOCHRONES. JACOB BERNOULLI. JOHANN BERNOULLI. CONSTRUCTIONS. HISTORIOGRAPHY OF MATHEMATICS. G HUYGENS. CATERNARY. G LEIBNIZ. TRACTRIX.

STRUIK, DIRK J 1974 A letter from Dirk Struik, in Cohen, R S & eds, For Dirk Struik, xiii-xvii Brief AUTOBIOGRAPHY.

ACKERMAN, MICHAEL 6 HERMANN, ROBERT 1975 Sophus Lie's 1880 Transformation Group Paper (Lie Groups: History, Frontiers and Applications Volume 1). Brookline, Mass (Math Sci Press) 587 p This first volume in a project that Hermann has "thought about for twenty years, theadaptation in moderntermsof some of the major works of 19th century differential geometry and Lie group theory", contains "background that I believe...is useful for the reader" (114 p), the translation by Ackerman with comments by Hermann (pp 115-374), and finally Hermann's "own version of the material, its ramifications, extensions, and applications." (pp 375-560) Short BIBLIOGRAPHY. No index. LIE THEORY. LIE GROUPS. DIFFERENTIAL GEOMETRY. TRANSFORMATION GROUPS. GALOIS THEORY OF DIFFERENTIAL EQUATIONS. CONTACT TRANSFORMATIONS. LIE ALGEBRAS.

LIE, SOPHUS 1975 Theory of Transformation Groups (Translation by Michael Ackerman of 1880 Theorie der Transformationsgruppen Math Ann 16, 441-528) in ACKERMAN, MICHAEL f, HERMANN, ROBERT 1975, pp 115-374 HM3 Abstracts 247

AKHUNDOV, M D 1974 0 matematicheskom atomizme Demo- krita [On the mathematical ATOMISM of DEMOCRITUS] Proc XIII ant con Hist sci 1971 Sect III, 28-30 INFINITES- IMALS. INDIVISIBLES.

ALEKSANDROV, P S et al 1972 Aleksandr Gennadievich Kurosh. Russ Math -Surveys 27(l), 176-193 OBITUARY. BIBLIOGRAPHY. PORTRAIT. ALGEBRA. GROUP THEORY. MATHEMATICS EDUCATION. MOS- COW MATHEMATICAL SOCIETY. Describes accomplishments in mathematical research, teaching and professional service. (D E Kullman)

ALEKSANDROV, P S et al 1972 Dmitrii Evgenevich Menskov (on his eightieth birthday). Russ Math Surveys 27(2), 161-171 FUNCTIONAL ANALYSIS. BIOGRAPHY. BIBLIOGRAPHY. TRIGONOMETRIC SERIES. (D E Kullman)

ANON 1975 The history of mathematics in Romania. NOESIS 3, 347-362 Part 2 (1934-1949) of a BIBLIOGRAPHY of work on the history of mathematics published by Romanians.

ANON 1975 Officers and lecturers of the society. Bull Amer Math Sot 81, 1150-1151 A biennial listing of officers, GIBBS LECTURERS, and COLLOQUIUM LECTURERS of the AMERICAN MATHEMATICAL SOCIETY since 1888. (D E Kullman)

ANON 1975 Endowment fund. Bull Amer Math Sot 81, 1144- 1148 A biennial report, listing mathematical PRIZES awarded by the AMERICAN MATHEMATICAL SOCIETY since 1923 along with prize- winning works of the recipients. (D E Kullman)

ANON 1975 Announcement of the 1975 PREMIO MODESTO PANETTI AWARD to DONALD RIVLIN of Lehigh University. SIAM News 8(S), 7 Inter- national AWARD by the ACADEMYOF SCIENCES OF TURIN for distinguished work in MECHANICS. Previous awards to G I TAYLOR (1958), .J A BURGERS (1960), W PRAGER (1963), J LIGHTHILL (1965), C TRUESDELL (1967), N I MUSKHELISHVILI (1969), and W I KOITER (1971). W s Tropp)

ANON 1975 Announcement of the 1974 ALSTON S HOUSEHOLDERAWARD to 0 H HALD of NYU at GATLINBURG VI. SIGNUM Newsletter 10,(2-3), 5, 11-12. W s Tropp) 248 Abstracts HM3

BABAEV, V G 1975 Vosniknovenie i razvitie osnovnykh ponyatii matematicheskogo analyza--beskonechno malay, predel (Origin and growth of the fundamental concepts of analysis--INFINITESMALS, and LIMITS). Autoabstract of thesis for the degree of candidate supervised by A P Yushkevich. Moscow (Inst for the Hist of Sci and Tech) 25 p ANALYSIS FOUNDATIONS. Three chapters cover resp. GREEK; XVI, XVII, XVIII; and XIX and XX.

BANSANESCU, STEFAN 1975 Les academies de Bucarest et de Jassy et les dgveloppement de la science. NOESIS 3, 229-236 BUCHAREST. JASSY. UNIVERSITIES. ACADEMIES.

BATCHELOR, G K 1975 An unfinished dialogue with G.I.Taylor Journal of Fluid Mechanics 70, 625-638 GEOFFREY INGRAM TAYLOR. FLUID MECHANICS. TURBULENCE. An interesting discussion between Batchelor and Taylor, originally produced in 1971. Taylor's sources of inspiration and underlying personal philosophy. The influence of his grandfather, GEORGE BOOLE. W S Tropp)

BELOZEROV, S E 1975 Pyat znamenitykh zadach drevnosti, istoriya i sovremennaya teoriya (Five famous problems of antiquity, history and present theory). Rostov (Rostov U P) 308 p CIRCLE SQUARING. ANGLE TRISECTION. DELIAN PROBLEM. LUNE QUADRATURE. CYCLOTOMY. From Hippocrates through the impossibility proofs to recent work by Soviet mathematicians. 149-item BIBLIOGRAPHY.

BELYAEV, Yu K et al 1972 BORIS VLADIMIROVICH GNEDENKO (on his sixtieth birthday). Russ Math Surveys 27(2), 173-179 BIBLIOGRAPHICAL NOTE. BIBLIOGRAPHY. HISTORIANS OF MATHEMATICS. PROBABILITY. STATISTICS. (D E Kullman)

BEMER, R W 1971 A view of the history of COBOL. Honeywell Computer Journal S(3), 130-135 Reprinted from: Berk, M., n.d., "The Programmer's COBOL," Inter-ACT/McGraw-Hill. COMPUTERS. PROGRAMMINGLANGUAGES. COBOL. G HOPPER. C PHILLIPS. CODASYL. SOFTWARE. A personal recollection of the development of the COBOL programming language, complementing the formal histories cited. (H S Tropp)

BOCHNER, SOLOMON 1974 Mathematical Reflections. American Mathematical Monthly 81, 827-852 U.S.A. PRIME DECOMPOSITION. ALGEBRAS. COMPLEX ANALYSIS. CALCULUS OF VARIATIONS. RIEMANN- ROCH THEOREM. STATISTICS. CONTINUITY. C S PEIRCE. L DICKSON. HM3 Abstracts 249

B PEIRCE. M MORSE. J ALEXANDER. H WEYL. E RITTER. R,ADRIAN. J L COOLIDGE. G LEIBNIZ. J W GIBBS. Presented at the Confer- ence On American Mathematics at Texas Tech University (May 1973.) World impact of late XIX and early XX century U.S.A. mathematics. Attacks the myth of American impotence prior to the 1930's. (H S Tropp)

BOGOLYUBOV, N N et al 1972 IOSIF BENEDIKTOVICH POGREBYSSKII. Russ Math Surveys 27(l), 195-206 OBITUARY. BIBLIOGRAPHY. HIS- TORIANS OF MATHEMATICS. He was both mathematician and historian. (D E Kullman)

BOLGARSKII, B V 1974 Ocherki po istorii matematiki (Sketches on the history of mathematics). Edited by V D Chistyakov Minsk (Vysheishaya Shkola) 287 p 70 copecks A GENERAL HISTORY OF MATHEMATICS up to a brief sketch of the XIX century, following the periodization given by A N Kolmogorov in his famous article on mathematics in the Great Soviet Encyclopedia -- prehistoric and early period (26 p); theory of elementary mathematics or the constant quantities from -VI to XVII (99 p); the mathematics of variable quantities from XVII to XIX (65 p); and contemporary mathematics (not treated in general). In addition, chapters on the development of mathematics in RUSSIA from ancient times and in the SOVIET UNION (a brief sketch describing the work of A N KRYLOV, I M VINOGRADOV, N G CHEBOTAREV) with a list of winners of Soviet PRIZES FOR MATHEMATICIANS and numerous sketched POR- TRAITS. The price of 70 copecks and the original edition of 20,000 are consistent with the stated purpose of POPULARIZATION.

BOLODOMONOV,N V 1974 Kalendar: proshloe, nastoyashchee, budushchee (The calendar: past, present, future). Moscow (Nauka) 63 p Popular description of various CALENDARS, their faults, and a proposed world calendar.

BOREL, EMILE 1972 Oeuvres. 4 Volumes. Paris (Centre National de la Recherche Scientifique) 2489 p COMPLETE WORKS. Contains all 261 of Borel's scientific publications, excluding 51 books and monographs. Vol 1: 90-p biography by Maurice Frechet. Com- plete list of publications plus short commentaries on Borel's work on MONOGENIC NON-ANALYTIC FUNCTIONS; SUMMABILITY METHODS; MEASURE THEORY; and ARITHMETIC ANALYSIS all by Amand Denjoy; EN- TIRE AND MEROMORPHIC FUNCTIONS by Georges Valiron; INTERPOLATION FORMULAE by Maurice Frechet; DENUMERABLEPROBABILITIES by Paul L&y. Papers are classified under the following subject headings (within which they appear chronologically). FUNCTION THEORY; 250 Abstracts HM3

POLYNOMIALS and RATIONAL FUNCTIONS; DIVERGENT SERIES; ENTIRE FUNCTIONS. Vol 2: ANALYTIC CONTINUATION; INTEGRATION; DIFFER- ENTIAL EQUATIONS; various ANALYSIS; PROBABILITY and STATISTICS. Vol 3: SET THEORY; NUMBER THEORY; MECHANICS; MATHEMATICAL PHYSICS and RELATIVITY. Vol 4: GEOMETRY; ALGEBRA and LINEAR ALGEBRA; ECONOMICS; PHILOSOPHY; EDUCATION; speeches and polemics (including SCIENCE POLICY). PORTRAI,T. Biographies (J TANNERY, G HUMBERT, H POINCARE, P PAINLEVE, G DARBOUX, R DESCARTES, P VALERY). (J Gray)

BRECHT, BERTOLT 1974 Leben des Galilei (Life of Galileo). Leipzig (Philipp Reclam) 157 p With forewords to the first (1938/39) and later editions and other comments by the play- wright and a postscript by Wilfried Adling. Reprint of this famous antifascist play which utilized the GALILEO theme without historical inhibitions.

BRETT, WILLIAM F f, FELDMAN, EMILE B & SENTLOWITZ, MICHAEL 1974 An Introduction to the History of Mathematics, Number Theory and Operations Research. New York (MSS Information Corporation) 165 p POPULARIZATIONS. TEXTBOOKS USING HISTORY. The first section of 64 pages is a GENERAL HISTORY of mathematics intended to show the beginning student that mathematics is a human creation. The expositions of number theory and operations research are not historical.

BROOK, RICHARD J 1973 Berkeley's Philosophy of Science. The Hague (Martinus Nijhoff) 210 p GEORGEBERKELEY. Chapters are on his SEMANTICS, theory of vision, philosophy of physics, and PHILOSOPHY OF MATHEMATICS and Berkeley and I NEWTON. BIB- LIOGRAPHY.

* BRUSH, STEPHEN G 1975 Publications in the history of physics during 1973. American Journal of Physics 43(10), 850-860 This TOUR DE FORCE discusses "as many as possible" of the "substan- tial contributions" in a selected list of 64 books and journals (over 150 individual titles). Would someone like to follow this excellent example for the history of mathematics or some part of it?

BRUTER, C P 1973 Sur la nature des mathematiques (On the nature of mathematics). Paris (Gauthier-Villars) 132 p The first half is an exposition of a personal objective-realist-construc- tivist-Listoricist PHILOSOPHY OF MATHEMATICS, the second a HM 3 Abstracts 251 popular introduction to the concepts of matroid (dating from the work of Van der Waerden, Hassler Whitney and S MacLane in the 1930's) as an example of a mathematical structure of very broad applicability.

BULATOV, M S 1974 Arkhitekturnaya nauka vostoka--nauka mate- maticheskaya (The science of ARCHITECTURE in the East--a mathematical science). Proc XIII Int Con Hist Sci 1971 Sectz, 130- 133 MIDDLE EAST. MEDIEVAL MATHEMATICS.

BULGAKOV, P G 1972 Zhizni i trudy Beruni (Life and works of Biruni). Tashkent ("Fan") 425 p A full-scale biographical and scientific study of AL-BIRUNI. BIBLIOGRAPHIES of Arabic and western-language sources, name index, list of his publications.

BURGESS, C E 1975 Embeddings of surfaces in Euclidean three- space. Bull Amer Math Sot 81, 795-818 TOPOLOGICAL MANIFOLDS. TAME SPHERES. WILD SPHERES. CRUMPLED CUBES. BIBLIOGRAPHY. Progress since 1908 toward the solution of EMBEDDING PROBLEMS. (D E Kullman)

CAMPAN, FLORIAN 1975 Le role de Universites de Jassy dans l'gvolution de I'activitG mathematique sur le territorie de la Romanie. NOESIS 3, 255-257 JASSY. ROMANIA.

CARNAP, RUDOLF 1974 An Introduction to the Philosophy of Sci- ence. Edited by Martin Gardner New York (Basic Books) (Also paperback by Harper Torchbooks) 312 p PHILOSOPHY OF SCIENCE. PROBABILITY. MEASUREMENT. TIME. NON-EUCLIDEAN GEOMETRIES. SPACE. RELATIVITY. Reprint of the original 1966 edition with a foreword by the editor and some minor changes.

CARTAN, ELIE 1974 Notice sur les travaux scientifiques, suivi de Le parallelisme absolut et la thgorie unitaire du champ. Paris (Gauthier-Villars) (Distributed also by Bordas - Dunod Montreal) 128 p A CHRONOLOGYof ELIE CARTAN- (1869-1951), list of his works, REPRINTS of the Notice (prepared in 1931 in con- nection with his candidacy for the Academy), and of the paper that first appeared in Rev MBtaph Morale (1931) and as Actualitgs scient et ind no 44 (1932). (J Grabiner) 252 Abstracts HM 3

COSTABEL, PIERRE 1975 Florimond de Beaune: Doctrine de l'angle solide. Inventaire de sa bibliothgque. Paris (Lib Philosophique J Vrin) 157 p A critical edition of this manuscript of FLORIMOND de BEAUNE (sometimes erroneously written DEBEAUNE) on SOLID ANG- LES, unpublished and lost until the editor's rediscovery, here printed with facsimile diagrams and minimal changes, preceded by a biography of this little-known contemporary (1601-1652) and correspondent of R DESCARTES and M MERSENNE, and followed by a transcription into modern terminology and symbolism, letters of nobility (in facsimile), genealogy, inventory of his library (of interest as a BIBLIOGRAPHY), inventory of his instruments, remarks and statistical summary, and name index. (J Grabiner)

CROSLAND, MAURICE editor 1976 The Emergence of Science in Western Europe. New York (Science History Publications) 201 p The first paper is "Mathematicians, mechanics and experimental MACHINES in Northern ITALY in the sixteenth century" by KELLER, A G. Other papers touch on various topics from the RENAISSANCE to the middle of the nineteenth century.

DAIGNEAULT, AUBERT editor 1974 Studies in Algebraic Logic. (Mathematical Association of America) 207 p Very brief historical remarks on ALGEBRAIC LOGIC in the introduction to this ninth volume in the distinguished series of expositions Studies In Mathematics.

DANCY, R M 1975 Sense and Contradiction: A Study in ARISTOTLE. Dordrecht and Boston (Reidel) 196 p A clarification of the arguments in the Metaphysics dealing with the NONCONTRADICTION LAW.

DANIELS, NORMAN 1972 THOMAS REID'S discovery of a NON-EUCLIDEAN GEOMETRY. Philosophy of Science 39, 219-234 A plane "geometry of visibles" modelled on the surface of a sphere in 1764.

DANIELS, NORMAN 1974 Thomas Reid's Inquiry, The Geometry of Visibles and the Case for Realism. With a foreword by Hilary Putnam New York (Burt Franklin 6 Co) 165 p Based on his 1970 Harvard Ph.D. dissertation titled Thomas Reid's Discovery of a Non-Euclidean Geometry. Describes and philosophically analyses the construction of a NON-EUCLIDEAN GEOMETRY "of visibles" (with a spherical surface as model) by THOMAS REID in his The Inquiry into the Human Mind (1764) and its relation to his campaign for realism against the idealism. G BERKELEY and D HUME. HM3 Abstracts 253

DEE, JOHN 1975 The Mathematical1 Praeface to the Elements of Geometrie of Euclid of Megara (1570) with an Introductionby ALLEN B DEBUS. New York (Science History Publications) 90 p NATURE OF MATHEMATICS. RENAISSANCE MATHEMATICS. A facsimile REPRINT of the preface by JOHN DEE (1527-1608) to the first English translation of Euclid by HENRY BILLINGSLEY. The 30-page introduction sketches Dee's life and the scientific context summarizes the work, and is followed by a 3-page bibliographic note. The main content of Dee's preface is the descriptive classification of the "Sciences and Artes Mathematicall", summarized in a foldout "Groundplat".

DIEUDONNg, J A 1975 The Weil conjectures. The Mathematical Intelligencer 10, 7-21 WEIL CONJECTURES. GAUSS SUMS. RIEMANN ZETA FUNCTION. ALGEBRAIC GEOMETRY. ALGEBRAIC TOPOLOGY. COHO- MOLOGY. DESLIGNE THEOREFl.

DOBROVOLSKII. V A 1973 JOSIP PLEMELJ (on the centenary of his birth). Russ Math Surveys 28(6), 97-106 BIOGRAPHY. ANALYTIC FUNCTIONS. DIFFERENTIAL EQUATIONS. (D E Kullman)

DOBROVOLSKII, V A 1973 Iz istorii problem Rimana (On the history of the Riemann differential equations problem). Mathematics Balkanica 3(15), 88-97 HILBERT PROBLEM 21. B RIEMANN. The author describes the problem as central in analysis during the last century.

DOHSE, FRITZ-EGBERT 1975 G Waldo Dunnington. Gauss-Gesellschaft Mitteilungen 12, 3 OBITUARY. PORTRAIT. G W DUNNINGTON (1906- 1974)

DONALDSON, JAMES A 1975 HOWARDUNIVERSITY news release. Can Math Cong Notes 8(4), 12-13 Reports presentation to LEE LORCH of a plaque honoring him for his contributions to human rights, mathematical research, and education, especially of BLACK MATHE- MATICIANS.

DOU, ALBERT0 1972 De la verdad a la validez en geometria (1733-1871) (From truth to validity in geometry (1733-1871) Pensamiento 28, 413-429 NON-EUCLIDEAN GEOMETRY. G SACCHERI. J H LAMBERT. F A TAURINUS. C F GAUSS. 254 Abstracts HM3

DUMITRIU, A 1971 Histoire de la logique (History of LOGIC). Scientia 106, 565-600, 863-914 (including Engish trans.) A quasi-bibliographical survey, from various ancients to some living ancients. (I Grattan-Guinness)

DUPAC, V 1975 Jaroslav Hgjek. 1926-1974. Annals of Statistics 3, 1031-1037 OBITUARY. BIBLIOGRAPHY. PORTRAIT. (J W Drane)

DUSSINE, R 1971 Evolution of ROM in computers. Honeywell Computer Journal 5(2), 79-87 COMPUTERS. M WILKES. READ ONLY MEMORY. MICROPROGRAMMING. Historical background and principles of Read Only Memories, followed by a brief survey of semi-conductor ROM's.

DZHANYBEKOV, E 1974 Muzykalnaya akustika u al-Farabi (Musical ACOUSTICS in AL-FARABI). Proc XIII Int Con Hist Sci 1971 Sect Iv, 177-180 MUSIC. MUSICAL SCALES.

EDGERTON, SAMUEL Y Jr 1975 The Renaissance Rediscovery of Linear Perspective. New York (Basic Books) 223 p L B ALBERTI. ALHAZEN. ROGER BACON. F BRUNELLESCHI. CARTOGRAPHY. DONATELLO. EUCLID. PERSPECTIVE. PTOLEMY. OPTICS. P da1 P TOSCANELLI. PROJECTIVE GEOMETRY. CHRONOLOGYof LINEAR PERSPECTIVE -300 to 1436. The year 1425 is given as the date of rediscovery by Brunelleschi. GLOSSARY.

EDWARDS, H M 1974 Riemann's Zeta Function. (Academic Press) 326 p Historical background, discussion, and translation (in an appendix) of B RIEMANN's famous 1859 paper "On the number of primes less than a given magnitude", and the subsequent history reaching to recent times of questions relating to the PRIME NUMBER THEOREM, the RIEMANN HYPOTHESIS, the RIEMANN ZETA FUNCTION, including the work of P L CHEBYSHEV, J HADAMARD, G H HARDY, H C F MANGOLDT, T J STIELTJES, J E LITTLEWOOD, and others. Selected BIBLIOGRAPHY (101 titles).

EISENHART, CHURCHILL 1975 Samuel S. Wilks and the Army Experi- ment Desien Conference Series. Proceedines of the Twentieth Conferenc: on Design of Experiments in Army Research, Develop- ment and Testing, held at Ford Belvoir, Virginia, 23-25 October 1974 (AR0 Rep-art 75-2) Research Triangle Park, North Carolina (U.S. .Army Research Office) 47 p (in typescript reprint). Biography (35 p) of WILKS, S S and list of 19 CONFERENCESwith names and topics of speakers. HM3 Abstracts 255

ESENOV, SH E & A KHASYMZHANOV 1974 Problema klassifikatsii nauk u AL-FARABI (The problem of CLASSIFICATION of the sciences in al-Farabi). Proc XIII Int Con Hist Sci 1971 Sect IV, 180-182 IX. x. NATURE OF MATHEMATICS.

FARARO, THOMAS J 1973 Mathematical Sociology. An Introduction to Fundamentals. (John Wiley) 828 p A pre-calculus level textbook on MATHEMATICAL SOCIOLOGY of interest because of a brief guide to the literature and a BIBLIOGRAPHY of about 250 items.

FISHER, JOHN, Editor 1973 The Magic of Lewis Carroll. New York (Simon and Schuster) 288 p A collection of MATHEMATICAL RECRE- ATIONS from LEWIS CARROLL, with an introductory essay arguing for the important role played in his development by an interest in MAGIC.

FOLKERTS, MENSO 1974 Die Kenntnis der negativen Zahlen in Westeuropa bis zum 16. Jahrhundert (Knowledge of NEGATIVE NUMBERS in Western Europe to the XVI century). Proc XIII Int Con Hist Sci 1971 Sect IV, 86-94 MEDIEVAL MATHEMATICS.

FOLKERTS, MENSO 1974 18. Mathematikgreschischtliches Kolloquium in Oberwolfach. Praxis der Math 16, 129-132 Brief account of the 18th MEETING at OBERWOLFACHwith abstracts of 28 papers.

FOLKERTS, MENSO 1974 Problemgeschichte der Mathematik. Tagung im mathematischen Forschungsinstitut Oberwolfach 23 x - 28 x 1972. Arch Int d'Hist des Sci 24(94), 151-156 Brief account of the 17th MEETING at OBERWOLFACHwith list of participants with abstracts of 20 papers.

FOLKERTS, MENSO 1974 Regiomontans Euklidhandschriften (MANU- SCRIPTS of EUCLID owned by REGIOMONTANUS). Sudhoffs Archiv 58(2), 149-164 Discusses the one extant manuscript of four he owned, and includes the text of eight of his annotations.

FOLKERTS, MENSO 1973 Joseph Eherenfried HOFMANN. Sudhoffs Archiv 57(3), 227-230 Brief biography and PORTRAIT.

FORBES, ERIC G 1974 TOBIAS MAYER's debt to LEONHARD EULER. Proc XIII Int Con Hist Sci 1971 Sect VI, 295-299. 256 Abstracts HM3

FORBES, ERIC G 1975 Die Entwicklung der Navigationswissenschaft im 18. Jahrhundert (The development of NAVIGATION in the XVIII century). Rete Z(4), 307-321 LONGITUDE DETERMINATION. .JOHN HADLEY. TOBIAS MAYER. NEVIL MASKELYNE. JOHN HARRISON. CHRO- NOMETRY. NAVIGATION INSTRUMENTS. English summary.

FORMIGARI, LIA 1973 Linguistic theories in British seventeenth- century philosophy. Dictionary of the History of Ideas 3, 73-76 LINGUISTICS. XVII.

FRAJESE, A 1972 Da Eudosso a Euclide (From Eudoxus to Euclid). Scientia 107, 563-574 (including English trans.) EUDOXUS's de- fination of PROPORTIONS as treated by EUCLID. (I Grattan-Guinness)

FRANK, R G 1973 Science, medicine and the universities of early modern England: Background and sources. Hist Sci 11, 194-216, 239-269 UNIVERSITIES. SCIENCE EDUCATION. SOURCES. MEDICINE. (M E Baron)

FRANKOWSKA-TERLECKA,MALGORZATA 1974 Some considerations on the role of the mediaeval postulates to base scientific cognition on mathematics. Proc XIII Int Con Hist Sci 1971 Sect IV, 72-77 AXIOMATICS. MEDIEVAL MATHEMATICS. FOUNDATIONS OF MATHEMATICS. SCIENTIFIC METHOD. PHILOSOPHY OF MATHEMATICS. ROLE OF MATHE- MATICS.

FREGE, GOTTLOB 1971 On the Foundations of Geometry and Formal Theories of Arithmetic. Translated with an introduction by Eike-Henner W. Kluge. (Yale University Press) 163 p GOTTLOB FREGE. FORMAL SYSTEMS. FORMALISM. DAVID HILBERT. A KORSELT. HEINRICH LIEBMANN. J THOMAE. This is a collection of trans- lations of Frege's more important work on the notion of a purely formal theory and on independence proofs for axiomatic systems. Correspondence between Frege, Heinrich Liebmann, and David Hilbert, an article on the foundations of geometry by A Korselt, and an exchange of papers between Frege and J. Thomae. There is a two- page introduction and a detailed index. This is an important addition to our sourcebooks in the history of logic and foundations

FRIBUS, E A 1972 X Kniga "Nachal" Evklida v "Arifmetike v Tselom" M. Shtifelya (The 10th Book of Euclid's Elements in M. Stifel's Arithmetica Integra) Moskov Oblast Bed. Inst. UEen-Zap. 311(g), 171-183 M. STIFEL. EUCLID'S ELEMENTS. The author HM3 Abstracts 257 presents Stifel's exposition of the 10th book of Euclid's Elements. Stifel considered IRRATIONAL NUMBERS to arise non-geometrically, solely from the EXTRACTION OF ROOTS. (H L Skala)

FROLfK, ZDENEK ij FRANTISEK ZfTEK 1975 The seventieth anniversary of Professor JOSEF NOVAK Czechoslovak Mathematical Journal ZS(lOO), 330-335 TOPOLOGY. PROBABILITY. PORTRAIT. An update of an account written ten years ago of the recent activities of J. Novak, including an appendix to his BIBLIOGRAPHY. (David E Zitarelli)

FUCHS, WERNER 1975 Von Gauss bis Hilbert Gauss-Gesellschaft Mitteilungen 12, 4-20 C F GAUSS. REAL NUMBERS. COMPLEX NUMBERS. GAUSS INTEGERS. NUMBER FIELDS.

FUKAGAWA, HIDETOSHI 1974 % I'\ && 1: 3 1 1 7 (MGKO KITAGAWA) Sugakushi Kenkyu (J Hist Math Japan)(61), 14-27 Life and works (especially a book on ARITHMETIC and INDETERMINATE EQUATIONS) by this WASAN scholar (1763-1833). (Katsuhiko Yoshida)

FULKERSON, D R, editor 1975 Studies in Graph Theory Parts I and -II (Vols. 11 and 12 of MAA Studies in Mathematics) (Mathematical Association of America) 432 p Useful comments and BIBLIOGRAPHY for CURRENT HISTORY of GRAPH THEORY

FULLER, A T, editor 1975 Stability of Motion London (Taylor and Francis); New York (Halsted) 236 p STABILITY THEORY. REPRINTS of the classic 1877 Stability of a given state of motion by E J ROTH, 3 other papers by him (1874, 1875, 1905), one by W K CLIFFORD, and one by C STURM, preceded by the editor's historical introduction on these men and their associates, followed by a reprint of the 1911 paper on Sturm by M BOCHER

FURLEY, DAVID 1973 Rationality among the Greeks and Romans Dictionary of the History of Ideas 4, 46-51 GREEK MATHEMATICS. ROMAN MATHEMATICS. LOGIC. PROOF.

GAIDUK, YU M 1974 Do istoriyi teoriyi maizhe periodychnykh funktsii (On the history of the theory of ALMOST PERIODIC FUNCTIONS) Narysy z ist pryrod i tek 18, 35-42 Influence of P BOL on the BOHR THEORY and the BOHR-ESCLANGONTHEORY. Influence of J HADAMARD and N N BOGOLYUBOV. (B M Schein) 258 Abstracts HM3

GARDNER, MARTIN 1975 Mathematical Carnival. New York (Alfred A Knopf) 274 p $8.95 ALEPH-NULL. CARD SHUFFLES. 'PASCAL'S TRIANGLE. SPROUTS. TESSERACT. Seventh RECREATIONS book from the author's column in Scientific American 1965 to 1968 with addenda and chapter bibliographies. (J H Baumwell)

GARDNER, W DAVID 1976 Microprocessors are old stuff to him Datamation 22(l), 103-104, 106 COMPUTERS. Evolution of the MICROPROCESSOR, beginning in 1969, by VICTOR POOR and HARRY PYLE for Datapoint's 2200 business processor. CH S Tropp)

GHEORGIEV, GHEORGI & ILIE POPA 1973 Edna Bulgarska aritmetika ot minaliya vek (A 19th-century Bulgarian arithmetic textbook). Bulgarian Academy of Sciences Physico-Mathematical Journal 16(49)(4), 291-294 XIX. ARITHMETIC. TEXTBOOKS. BULGARIA.

GILLINGS, R J 1975 What is the relation between EMLR and the RMP recta? Arch Hist Exact Sciences 14(3), 159-167 RHIND PAPYRUS. EGYPTIAN MATHEMATICS.

GILLMOR, C STEWART 1971 Coulomb and the Evolution of Physics and Engineering in Eighteenth-Century France. Princeton, N.J. (Princeton Univ. Press) 328 p $15 XVIII-XIX. FRANCE. C A COULOMB worked in PHYSICS and ENGINEERING, but there are references to mathematics recoverable from the index.

GNEDENKO, B v 1974 Vplyv P. L. Chebyshova na rozvytok teoriyi yimovirnostei (Influence of P L CHEBYSHEV on the development of PROBABILITY THEORY). Narysy z istoriyi pryrodoznavstva i tekhniky Kiev (Naukova Dumka), Issue 18, 13-23 His teaching activity, four papers on the probability, and their influence. (B M Schein)

GNEDENKO, B V 1973 Matematika i sovremennoe estestvoznanie (Mathematics and contemporary science), in Sintez sovremennogo nauchnogo znaniya (The synthesis of contemporary scientific knowledge). Moscow (Nauka) 143-158 PHILOSOPHY OF MATHEMATICS. MATHEMATICAL RESEARCHMETHODS. HEURISTJC. PURE AND APPLIED MATHEMATICS. HISTORICAL THEORY.