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242 Reviews HM3 Basic Philosophical Language Was, As Was That of His CORE Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector 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 philoso- phical 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 mathema- tical 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 ACADEMY OF SCIENCES OF TURIN for distin- guished 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, his- tory and present theory). Rostov (Rostov U P) 308 p CIRCLE SQUARING. ANGLE TRISECTION. DELIAN PROBLEM.
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