HISTORIA MATHEMATICA 18 (1991), 393-402 ABSTRACTS Edited by DAVID E. ZITARELLI The purpose of this department is to give sufficient information about the subject matter of each publication to enable users to decide whether to read it. It is our intention to cover all books, articles, and other materials in the field. Books for abstracting and eventual review should be sent to this department. Materials should be sent to Prof. David E. Zitarelli, Department of Mathematics, Temple University, Philadelphia, PA 19122, U.S.A. Readers are invited to send reprints, autoabstracts, corrections, additions, and notices of publications that have been overlooked. Be sure to include complete bibliographic informa- tion, as well as transliteration and translation for non-European languages. We need volun- teers willing to cover one or more journals for this department. Readers interested in receiving a computer-readable version of the abstracts, beginning with # 11.3.1, are invited to write to the Abstracts Editor. In order to facilitate reference and indexing, entries are given abstract numbers which appear at the end following the symbol #. A triple numbering system is used: the first number indicates the volume, the second the issue number, and the third the sequential number within that issue. For example, the abstracts for Volume 17, Number 1, are numbered: 17.1.1, 17.1.2, 17.1.3, etc. For reviews and abstracts published in Volumes 1 through 13 there is an author index in Volume 13, Number 4, and a subject index in Volume 14, Number 1. The initials in parentheses at the end of an entry indicate the abstractor. In this issue there are abstracts by Irving Anellis (Ames, IA), Ivor Grattan-Guinness (Herts), Victor J. Katz (Washington), Joseph D. E. Konhauser (St. Paul, MN), Albert C. Lewis (Hamilton), Ivica Martinovid (Dubrovnik), Karen V. H. Parshall (Charlottesville), Lynn Arthur Steen (North- field, MN), and David E. Zitarelli. ABDULLA-ZADE, KH. F., AND ROZHANSKAYA, M. M. 1989. On the scientific heritage of the astrono- mer and mathematician of the tenth century KUSHJAR IBN LABBAN DZHILI. Istoriko-Astronomicheskie Zssledovaniya 21, 164-174. A report on the preparation by the authors of three treatises by Dzhili. One of their main achievements is the foundation of a sexagesimal system for both the integers and the fractions. See the review by H. Eelsalu in Zentralblatt 697(01002). (ACL) #l&4.1 ABELES, FRANCINE. 1991. Sixteenth annual meeting. Canadian Society for History and Philosophy of Mathematics. University of Victoria, B.C., 31 May-l June, 1990. Historia Mathematics 18(2), 178-179. A list of speakers with the titles of their papers in two sessions, one general and the other a special session on history and PEDAGOGY. (DEZ) #18.4.2 AKIRA, HIRAYAMA. 1987. On the paper of Prof. [In Japanese.] See Zentralblatt 6%(01021). (ACL) CHIN KANG SHEN. Stigakushi Kenkyn u&37-40. #18.4.3 AKIRA, HIRAYAMA. 1987. The method of the wooden box for measuring. Stigakushi Kenkyti 114, 41-45. [In Japanese.] See Zentralblatt 698(01011). (ACL) #18.4.4 393 03150860/91 $3.00 Copyright Q 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.
Transcript
HISTORIA MATHEMATICA 18 (1991), 393-402
ABSTRACTS
Edited by DAVID E. ZITARELLI
The purpose of this department is to give sufficient information about the subject matter of each publication to enable users to decide whether to read it. It is our intention to cover all books, articles, and other materials in the field.
Books for abstracting and eventual review should be sent to this department. Materials should be sent to Prof. David E. Zitarelli, Department of Mathematics, Temple University, Philadelphia, PA 19122, U.S.A.
Readers are invited to send reprints, autoabstracts, corrections, additions, and notices of publications that have been overlooked. Be sure to include complete bibliographic informa- tion, as well as transliteration and translation for non-European languages. We need volun- teers willing to cover one or more journals for this department.
Readers interested in receiving a computer-readable version of the abstracts, beginning with # 11.3.1, are invited to write to the Abstracts Editor.
In order to facilitate reference and indexing, entries are given abstract numbers which appear at the end following the symbol #. A triple numbering system is used: the first number indicates the volume, the second the issue number, and the third the sequential number within that issue. For example, the abstracts for Volume 17, Number 1, are numbered: 17.1.1, 17.1.2, 17.1.3, etc.
For reviews and abstracts published in Volumes 1 through 13 there is an author index in Volume 13, Number 4, and a subject index in Volume 14, Number 1.
The initials in parentheses at the end of an entry indicate the abstractor. In this issue there are abstracts by Irving Anellis (Ames, IA), Ivor Grattan-Guinness (Herts), Victor J. Katz (Washington), Joseph D. E. Konhauser (St. Paul, MN), Albert C. Lewis (Hamilton), Ivica Martinovid (Dubrovnik), Karen V. H. Parshall (Charlottesville), Lynn Arthur Steen (North- field, MN), and David E. Zitarelli.
ABDULLA-ZADE, KH. F., AND ROZHANSKAYA, M. M. 1989. On the scientific heritage of the astrono- mer and mathematician of the tenth century KUSHJAR IBN LABBAN DZHILI. Istoriko-Astronomicheskie Zssledovaniya 21, 164-174. A report on the preparation by the authors of three treatises by Dzhili. One of their main achievements is the foundation of a sexagesimal system for both the integers and the fractions. See the review by H. Eelsalu in Zentralblatt 697(01002). (ACL) #l&4.1
ABELES, FRANCINE. 1991. Sixteenth annual meeting. Canadian Society for History and Philosophy of Mathematics. University of Victoria, B.C., 31 May-l June, 1990. Historia Mathematics 18(2), 178-179. A list of speakers with the titles of their papers in two sessions, one general and the other a special session on history and PEDAGOGY. (DEZ) #18.4.2
AKIRA, HIRAYAMA. 1987. On the paper of Prof. [In Japanese.] See Zentralblatt 6%(01021). (ACL)
CHIN KANG SHEN. Stigakushi Kenkyn u&37-40. #18.4.3
AKIRA, HIRAYAMA. 1987. The method of the wooden box for measuring. Stigakushi Kenkyti 114, 41-45. [In Japanese.] See Zentralblatt 698(01011). (ACL) #18.4.4
393
03150860/91 $3.00 Copyright Q 1991 by Academic Press, Inc.
All rights of reproduction in any form reserved.
394 ABSTRACTS HM 18
AKIRA, HIRAYAMA. 1987. Wasan in Kyusyu. Stigakushi Kenkyti ll.3, 57-61. [In Japanese.] See Zentrulblatt 69&(01007). (ACL) #18.4.5
ARTMANN, BENNO. 1991. A meeting on Greek mathematics. Mathematisches Forschungsinstitut Oberwolfach, August 19-25, 1990. Historiu Muthemuticu 18(2), 180. A list of speakers, with the titles of their papers, who contributed to a special issue of the journal Apeiron. (DEZ) #18.4.6
ARTMANN, BENNO. 1991. The cloisters of Hauterive. The Mathematical Zntelligencer w(2), 44-49. The role of GEOMETRY in GOTHIC ARCHITECTURE as exemplified by the tracery (German: MaBwerk; French: reseau) seen in the windows of the Cistercian monastery of Hauterive in Switzerland. (DEZ) #18.4.7
ASPRAY, WILLIAM. 1990. John Von Neumann and the origins of modern computing. Cambridge/ London: The MIT Press. xvii1 + 376 pp. $35. (History of Computing series.) JOHN VON NEUMANN. COMPUTERS. (ACL) #18.4.8
ATAGARRYEV, M. A. 1989. The outstanding middle-Asian scientist of the twelfth century ABD AL- DZHABBAR AL-KHARAKI. Zzvestiyu Akudemii Nuuk Turkemnskoi SSR. Seriyu Fiziko-Tekhnicheskikh., Khimicheskikh i Geologicheskikh Nuuk 5,101-107. [In Russian with English summary.] The author of two geocentric ASTRONOMY treatises. See Zentrulblutt @8(01013). (ACL) #18.4.9
BABBAGE, CHARLES. 1989. Science and reform: Selected works of Charles Bubbuge. Cambridge: Cambridge University Press. vii + 356 pp. $59.50. The topics were chosen by Anthony Hyman, who also wrote the introduction and added some discussion. Included are Babbage’s early mathematical work, the first difference engine, life assurance, reform of science, economic theory, the analytical engine, and lighthouse signalling. CHARLES BABBAGE. See the review by I. Grattan-Gu’nness in Zentrulblutt @8(01022). (ACL) #18.4.10
BAIMISHEVA, K. SH. 1982. The first geometric proof of the rule of the parallelogram of forces. Zstoriyu i Methodologiyu Estestvennykh Nuuk 29, 107-111. [In Russian with English summary.] D. BERNOULLI'S proof of the composition of forces. See Zentrulbfutt 699(01010). (ACL) #18.4.11
BARREAU, HERVB. See #18.4.30.
BASHMAKOVA, I. G., AND MAISTROV, L. E. 1982. On the first course in the history of mathematics held at Moscow UNIVERSITY. Zstoriyu i Methodologiyu Estestvennykh Nuuk 29, 9-30. [In Russian.] Lectures by V. V. BOBYNIN. See Zentrulbfutt 699(01001). (ACL) #18.4.12
BEAULIEU, LILIANE. 1989. Bourbuki. Une histoire du groupe de muthemuticiens fruncais et de ses travuux (2934-1944). These de doctorat, Universitt de Montreal. A history and a description of the work of BOURBAKI from 1934 until 1944. An analysis of several aspects of the founding of the group based on published and unpublished material. A description of the initial goals of the members, their vision of the vast project titled Efements de muthtmutique, the principles that guided their choice of material and its applications, and the contributions of certain members. (DEZ) #18.4.13
BEAULIEU, LILIANE. 1990. Proofs in expository writing-Some examples from Bourbaki’s early drafts. Interchange 21(2), 35-45. An account of the collective activities of BOURBAKI before the publication of Elt?ments de muthtmatique. The PROOF of Stokes’ theorem is cited as an example of the secondary role played by proofs in Bourbaki’s discussions. The example of filters in topology illustrates Bourbaki’s concern with conceptual settings, showing that definitions play as important a role as proofs. The author concludes that “the motivation for new concepts did not arise exclusively from a dissatisfaction with proofs that were deemed not rigorous enough.” (DEZ) #18.4.14
BENVENUTO, EDOARDO. 1991. An introduction to the history ofstructural mechanics. Part I: Statics and resistance of solids, xxi + 306 pp. Part ZZ: Vaulted structures and elastic systems, xxi + 245 pp. $49 each. Berlin/Heidelberg/New York: Springer-Verlag. An outgrowth of the author’s La Scienzu delle Costruzioni e il suo Sviluppo Storico (1981). Clifford Truesdell, in the Foreword, calls the
HM 18 ABSTRACTS 395
book the “first to show how statics, strength of materials, and elasticity grew alongside existing ARCHITECTURE with its millenial traditions. [Adapted with permission from The American Mathemati- cal Monthly !M(5) (Ml), 462-463.1 (JDEK) #18.4.15
BEREZKINA, EH. I. 1982. On the mathematical methods of the ancients, Isroriya i Methodologiya Estestuennykh Nauk 29,31-40. [In Russian with English summary.] Ancient history of NOTATIONS for NUMERALS. See Zentrulblutt 699(01002). (ACL) #18.4.16
BESPAMYATNYKH, N. D. 1989. Stepan Aleksandrovich Bogomolov. 1877-1965. Leningrad: Nauka. 118 pp. R 0.25 [In Russian.] (Nauchno-Biograficheskaya Literatura.) Edited by E. P. Ozhigova. Life of STEPAN ALEKSANDROVICH BOGOMOLOV and his work in GEOMETRY and mathematical CRYSTALLOG- RAPHY. See Zentralblatt @X3(01017). (ACL) #18.4.17
BIERMANN, KWRT-R. See #18.4.40.
BIRYUKOVA, L. G. 1982. “Die Griissenlehre” by ROBERT GRASSMANN and the constructive trend in mathematics. Istoriya i Methodologiya Estestvennykh Nauk 29, 41-50. [In Russian with English summary.] Grassmann’s work anticipated aspects of the recent intuitionistic and constructive mathe- matics. See Zentralblutt 699(01011). (ACL) #18.4.18
BLASS, PIOTR. 1989. The influence of Oscar Zariski on modem ALGEBRAIC GEOMETRY. Australian Mathematical Society Gazette 16(6), 157-168. The personality and the work of OSCAR ZARISKI. See Zentralblatt 697(01007). (ACL) #18.4.19
BOROWCZYK, JACQUES. 1991. Sur la vie et l’oeuvre de Francois Budan (1761-1840). Historiu Muthe- matica 18(2), 129-157. The life and work of FRANCOIS BUDAN (1761-1840). Included are a notice on his mathematical works and a resume of his results, both from 1829. (DEZ) #18.4.20
BOTTAZZINI, UMBERTO. 1990. IlJZauto di Hilbert: Storia della matematica moderna e contempora- nea. Turin: UTET Libreria. 455 pp. Paperback; L 65.000. DAVID HILBERT and the history of modem mathematics. (ACL) #18.4.21
BRONSHTEHN, V. A. 1988. Claudius Ptolemy. Second Century A. D. Leningrad: Nauka. 241 pp. R 0.85. [In Russian.] (Nauchno-Biograficheskaya Literatura.) Edited with a preface and an afterword by A. A. Gurshtein. An overview for a general audience which, besides the contributions of CLAUDIUS PTOLEMY to astronomy, includes discussions of his work in optics, music, geography, and astrology. See the review by J. S. Joel in Zentralblatt 698(01019). (ACL) #18.4.22
BRU, BERNARD, AND DUGAC, PIERRE (Eds.) 1991. Lettres d’Henri Lebesgue a Emile Borel. Cuhiers du Se’minaire d’Histoire des Mathe’matiques 32, l-51 1. The correspondence from HENRI LEBESGUE to EMILE BOREL. The letters, covering the period Ml-1918 and discovered only in 1988 by Jean Lefebvre, are essential for understanding the genesis of Lebesgue’s theory. They attest to the influence Of RENfi BAIRE, suggest that Lebesgue possessed a geometric intuition of his integral, and describe the friction between his generation and those who worked in classical ANALYSIS in the late 19th century. The letters provide a glimpse into Lebesgue’s personality and provide details about his relationship with Bore& especially regarding their involvement in World War I. The editors have supplied volumi- nous notes (pp. 343-474), a bibliography, and a “Postface.” (DEZ) #18.4.23
CAVEING, MAURICE. See #18.4.34.
CHANDRASEKHAR, S. 1991. Selected papers, S. Chandrasekhar, Volume 6: The mathematical the- ory of black holes and of colliding plane waves. Chicago: Univ of Chicago Press. xix + 739 pp. Hardbound; $79.95. Paperbound; $35. Papers taken from the years 1975-1985 when Chandrasekhar returned to the theory of black holes, which he pioneered 40 years earlier. Includes a personal retrospective on this phase of his career written by his colleague BASILIS XANTHOP~ULOS. ASTRONOMY. PHYSICS. [Adapted with permission from The American Mathematical Monthly W(6) (1991), 583.1 (LAS) #18.4.24
3% ABSTRACTS HM 18
CHUI, CHARLES K. (Ed.) 1991. Approximation theory undfunctionalunalysis. San Diego: Academic Press, x + 247 pp. Hardbound; $49.95. A compilation of 11 papers on APPROXIMATION THEORY and FUNCTIONAL ANALYSIS to honor GEORGE G. LORENTZ on his 80th birthday. Includes a brief autobiography, a list of publications, and a list of doctoral students. [Adapted with permission from The American Mathematical Monthly 98(5) (1991), 462-463.1 (JDEK) #18.4.25
CRUMP, THOMAS. 1990. The anthropology of numbers. Cambridge/New York/Melbourne: Cam- bridge University Press. 197 pp. $49.50. (Cambridge Studies in Social Anthropology, No. 70.) ANTHRO- POLOGY. (ACL) #18.4.26
D’AMBROSIO, UBIRATAN. 1990. Etnomutemtiticu: Arte ou te’cnicu de explicur e conhecer. S&o Paulo: Editora Utica S. A. 88 pp. Paperback. An examination of the field of ETHNOMATHEMATICS, presenting the symbiotic relation between mathematics and various cultural contexts in their historical settings. There is a critical vocabulary list and an annotated bibliography. (DEZ) #18.4.27
DA SILVA, CL&IS PEREIRA. 1991. A. Comte: Suas influencias sobre la matematica Brasileira. [A. Comte: His influence on Brazilian mathematics.] Parana, Brazil: Departamento de Matematica, Universidade Federal do Parana. 11 pp. A study of the influence of the positivist ideology of A. COMTE (1798-1857) on Brazilian mathematics, emphasizing why BRAZIL from 1850 to 1920 was not an integral part of the main lines of 19th-century scientific developments. The focus is on ALENCAR SILVA and his role in mathematics EDUCATION in Brazil. (DEZ) #18.4.28
DELEDALLE, GERARD. 1990. Charles S. Peirce: An intellectual biography. Amsterdam/Philadel- phia: John Benjamins Publishing Co. xxxii + 91 pp. $3 1. Translated and introduced by Susan Petrilli. CHARLES S. PEIRCE. (ACL) #18.4.29
DHOMBRES, J. G., AND PIER, J.-P. (Eds.) 1987. La Philosophie des sciences de Henri Poincurb. Collogue des 22 et 23 Mui 1986. Centre Universituire de Luxembourg. SociM Fruncuise d’Histoire des Sciences et des Techniques. Cuhiers d’Histoire et de Philosophie des Sciences, Nouvelle Se’rie 23. Paris: Belin. 130 pp. FF 60.00. This colloquium on HENRI POINCARF. includes H. Barreau on Poincare’s philosophy of time and space, J. Dieudonne on Poincare’s conception of mathematical objects, G. Heinzmann on Poincare’s reaction to Cantor’s set theory and the axiom of choice, P. Kerzberg on truth and convention, A. I. Miller on the relation of geometry to the theories of electricity and relativity for Poincare, R. Thorn on why Poincare was too much of a mathematician to be ranked as a philosopher, and E. Zahar on paradoxes in Poincare’s philosophy. See the review by J. J. Burckhardt in Zentrulblutt 698(01016). (ACL) #18.4.30
DIEUDONN~, JEAN. See #18.4.30.
DOROFEEVA, A. V. 1982. The CALCULUS OF VARIATIONS in the last third of the 19th century. Istoriyu i Methodologiyu Estestvennykh Nuuk 29,64-74. [In Russian with English summary.] WEIER- STRASS was the first to give a strict proof of Euler’s rule for isoperimetric problems. WEIERSTRASS- ERDMANN CONDITIONS. See Zentrulblutt 699(01012). (ACL) #18.4.31
DUGAC, PIERRE. See #18.4.23.
EDWARDS, A. W. F. 1991. A note on Waring’s rule. Historiu Muthemuticu 18(2), 177. The source of the rule attributed to EDWARD WARING that the person who first communicates an idea deserves to be called its inventor. (DEZ) #18.4.32
EFREMOV, Yu. N., AND PAVLOVSKAYA, E. D. 1989. Determination of the epoch of the Almugest star catalogue with respect to the analysis of the proper motion of the stars. Zstoriko-Astronomicheskie Zssledovuniyu 21, 175-192. On the problem of the authorship of PTOLEMY’S catalogue of stars. See Zentrulblutt 697(01001). (ACL) #18.4.33
EUCLIDE D’ALEXANDIUE. 1990. Les Z?lCments (truduits du texte de Heiberg): Volume I, Livres Z-IV: Gtomttrie plane. Paris: Presses Universitaires de France. 53 1 pp. Paperback. (Bibliothbque
HM 18 ABSTRACTS 397
d’Histoire des Sciences series.) General introduction by Maurice Caveing. Translation and commentary by Bernard Vitrac of EUCLID’S Elements based on the text by Heiberg. GEOMETRY. WU #18.4.34
FAUVEL, JOHN. See #18.4.82.
FISCHER, G., HIRZEBRUCH, F., SCHARLAU, W., AND T~RNIG, W. (Eds.) 1990. Ein Juhrhundert Mathematik 1890-1990. Festschrift zum Jubiliium der DMV. Braunschweig/Wiesbaden: Deutsche Mathematiker-Vereinigung. xii + 830 pp. DM 198. (Dokumente zur Geschichte der Mathematik, 6.) A collection of 19 articles commemorating the 100th anniversary of the DEUTSCHE MATHEMATIKER- VEREINIGUNG. Contents: Institutional history including the period of the Third Reich (by N. Schap- pacher and M. Kneser); DISCRETE MATHEMATICS (M. Aigner); COMPUTER SCIENCE (F. L. Bauer); PARTIAL DIFFERENTIAL EQUATIONS and CALCULUS OF VARIATIONS (J. Bemelmans, S. Hildebrandt, W. von Wahl); FOUNDATIONS OF GEOMETRY (W. Benz); NUMERICAL ANALYSIS (L. Collatz); DIFFER- ENTIAL GEOMETRY (P. Dombrowski); THEORY OF FUNCTIONS (D. Gaier); CONVEX GEOMETRY (P. M. Gruber); PROBABILITY THEORY (U. Krengel); MATHEMATICAL PHYSICS (R. Leis); FINITE SIMPLE GROUPS (G. 0. Michler); ALGEBRAIC NUMBER THEORY (J. Neukirch); ERICH HECKE and number theory (S. J. Patterson); QUADRATIC FORMS (A. Pfister); ALGEBRAIC TOPOLOGY (H.-W. Henn, D. Puppe); MATHEMATICAL LOGIC (K. Schtitte, H. Schwichtenberg); ANALYTIC NUMBER THEORY (W. Schwarz); MATHEMATICAL STATISTICS (H. Witting). (ACL) #18.4.35
FOLKERTS, MENSO. 1989. Euclid in medieval Europe. (Questio II de rerum natura.) Winnipeg: The Benjamin Catalogue for History of Science. 63 pp. Paperback; US $9, Can $10, DM 15, L 5. MEDIEVAL mathematics. EUCLID. GEOMETRY. (ACL) #18.4.36
FORD, CHARLES. 1991. DMITRII EGOROV: Mathematics and RELIGION in Moscow. The Muthemati- cal Intelligencer W(2), 24-30. An analysis of various charges made by the “Initiative Group” in 1930 against members of the Moscow MATHEMATICAL SOCIETY. The connections of the Society with the Russian religious-philosophical renaissance of the early 20th century are described, including the roles played by N. V. Bugayov, D. F. Egorov, N. N. Luzin, and P. A. Florensky. The “Initiative Group” consisted of L. A. Lyustemik, I. G. Shnirelman, A. Gelfond, L. Pontryagin, and P. A. Nekrasov. (DEW #18.4.37
F~~NGSMYR, TORE, HEILBRON, J. L., AND RIDER, ROBIN E. (Eds.) 1990. The quantifying spirit in the 28th century. Berkeley/Los Angeles/Oxford: Univ. of California Press. viii + 411 pp. 18~~ CENTURY. (ACL) #18.4.38
GABRIEL, G., GATZEMEIER, M., AND KAMBARTEL, E. F. (Eds.) 1989. Muthematisch-physikalische undphilosophische Schriften 1842-1843. Stuttgart: Frommann Verlag/Giinther Holzboog. 263 pp. DM 335. (Bernard Bolzano-Gesamtausgabe, Reihe I: Schriften, 18.) The mathematical and philosophical writings of Bernard Bolzano during 1842-1843. See Zentrulblutt 699(01035). (ACL) #18.4.39
GATZEMEIER, M. See #18.4.39.
GAUSS, CARL FRIEDRICH. 1990. Der cFiirst der Mathematiker~ in Briefen und Gesprachen. Munich: Veriag C. H. Beck. 231 pp; DM 29,80. Edited by Kurt-R. Biermann. (ACL) #18.4.40
GERICKE, HELMUTH. 1990. Mathematik im Abendland: Von den riimischen Feldmessern bis zu Descartes. Berlin/Heidelberg/New York: Springer Verlag. xiv + 352 pp. DESCARTES. (ACL)
#18.4.41
GLUSHKOV, S. S. 1982. Algebraic approach to geometric problems as the sources of De Moivre’s formula. Istoriya i Methodologiya Estestuennykh Nuuk 29,51-56. [In Russian with English summary.] It is shown that one of FERMAT’S methods could give DE MOIVRE’S THEOREM if applied to Vi&e’s case of van Roomen’s problem. See Zentrulblatt 699(01009). (ACL) #18.4.42
GLUSHKOV, S. S. See also #18.4.43.
398 ABSTRACTS HM 18
GLUSHKOVA, F. R., AND GLUSHKOV, S. S. 1982. On the geometrical part of PACIOLI’S Summa. Istoriya i Methodologiya Estestuennykh Nauk 2!&57-63. One of the oldest printed mathematical works. See Zentrulblutt W(O1005). (ACL) #18.4.43
GROSHOLZ, EMILY. 1991. Cartesian method and the problem of reduction. Oxford: Clarendon Press. x + 161 pp. Drawing primarily from the Geometry, the Principles, the Treatise of Man, and the Meditations, the author examines both the positive and negative impacts of DESCARTES’S reductive scientific method on his scientific and philosophical thought. (KVHP) #18.4.44
GURSHTEIN, A. A. See #l&4.22.
HAYES, ROBERT L. 1991. History-A way back to mathematics. Newsletter of the International Study Group on the Relations Between History and Pedagogy of Mathematics 2, 7-9. The author describes his use of history in motivating adult learners who have a deep-seated dislike of mathematics. PEDAGOGY. (VJK) #18.4.45
HEILBRON, J. L. See #18.4.38.
HEINZMANN, GERHARD. See #l&4.30.
HERB, REBECCA A. 1991. Harish-Chandra and his work. Bulletin of the American Mathematical Society 25(l), 1-17. Biographical remarks on the Indian mathematician HARISH-CHANDRA, whose career began in particle physics under Dirac and then switched to REPRESENTATION THEORY and HARMONIC ANALYSIS. He held positions at Columbia University (1950-1%3) and the Institute for Advanced Study (1%3-1983) after having graduated from Cambridge. (DEZ) #l&4.46
HILTON, PETER, AND PEDERSON, JEAN. 1991. Catalan numbers, their generalization, and their uses. The Mathematical Zntelligencer w(2), 64-75. A historical note (page 74) describes the role of EUGENE CHARLES CATALAN in defining the numbers named after him. (DEZ) # 18.4.47
HIRZEBRUCH, FRIEDRICH. 1991. One hundred years of the Deutsche Mathematiker-Vereinigung. The Mathematical Zntelfigencer W(2), 8-l 1. A sketch of the history of the MATHEMATICAL SOCIETY called the Union of German Mathematicians (DMV) from earlier failed efforts of ALFRED CLEBSCH and its founding by GEORG CANTOR in 1890 to the (literal) union of the two German Mathematical Societies in 1990. The account includes a discussion of some activities of the DMV in the era of National Socialism. (DEZ) #18.4.48
HIFUEBRUCH, FRIEDRICH. See also #l&4.35.
HOFMANN, JOSEPH EHRENFRIED. 1990. Ausgewiihlte Schriften. Hildesheim/Ztirich/New York: Georg Olms Verlag. Volume 1: 509 pp. Volume 2: 500 pp. Hardbound, DM 3% (for the set). Edited by Christoph J. Sqiba. This collection of selected works brings together some fifty papers by the distinguished historian of mathematics, J. E. HOFMANN (1900-1973). Although best remembered as a Leibniz specialist, Hofmann wrote on topics ranging from the mathematics of ApolIonius and Archi- medes to the work of Gauss and von Staudt. The editor has chosen articles which well reflect the breadth and depth of Hofmann’s scholarship. (KVHP) #18.4.49
HOGAN, EDWARD. 1991. “A proper spirit is abroad:” Peirce, Sylvester, Ward, and AMERICAN MATHEMATICS, 1829-1843. Historia Muthematica 18(2), 158-172. The twists in the mathematical careers of three friends during the period 1829 to 1843 in the United States. JAMES JOSEPH SYLVESTER’S high hopes in the new country never materialized and he returned to his native England. SAMUEL WARD abandoned a mathematical career. BENJAMIN PEIRCE did not produce significant mathematical research until the end of his career, some 30 years later. (DEZ) #18.4.50
HOMANN, FREDERICK A. 1991. Practical geometry [Pructica geometriae]: Attributed to Hugh of St. Victor. Milwaukee: Marquette Univ Press. iii + 96 pp. Paperback. A translation of the 12th-century Latin treatise Practica geometriue, attributed by Abbe Roger Baron in 1955 to HUGH OF ST. VICTOR
HM 18 ABSTRACTS 399
(1096-l 141). It provides a source reading of MEDIEVAL Latin mathematics, education, and scholastic thought. The translator’s introduction (pp. l-30) describes the mathematical content, quality, and place of the treatise in the history of mathematics. (DEZ) #18.4.51
HYMAN, ANTHONY. See #18.4.10.
KAMBARTEL, E. F. See #18.4.39.
KERZBERG, PIERRE. See #18.4.30.
KHAIRETDINOVA, N. G. 1982. Regiomontanus’ theory of ratios. Istoriya i Methodologiya Estestue- nnykh Nuuk 29,104-106. [In Russian with English summary.] The theory of REcIoMoNTANus (JOHANN MILLER) is close to that of Simon Stevin except that the former used only positive numbers. See Zentralblutt 699(01006). (ACL) #18.4.52
KIDWELL, PEGGY. 1990. American scientists and CALCULATING MACHINES-from novelty to com- monplace. Annals of the History of Computing 12, 31-40. Covers the period 1865 to 1920. Arith- mometers and comptometers. See the review by I. Grattan-Guinness in Zentrulblatt W&01017). (ACL) #18.4.53
KNORR, WILBUR R. 1991. On a medieval circle quadrature: De circulo quadrando. Historiu Mathe- matica 18(2), 107-128. A discussion of the MEDIEVAL text De circulo quadrando on circle quadrature. A comparison with an alternative version Quelibet media proportion&a suggests connections between the masters of GEOMETRY at Oxford and Paris in the 13th century. The question of authorship is investigated. (DEZ) #18.4.54
K~NIG, GERT (Ed.) 1990. Konzepte des mathematisch Unendlichen im 19. Jahrhundert. Gottingen: Vandenhoeck and Ruprecht. 273 pp. Paperbound. Revised texts of 10 papers read at a symposium at the University of the Ruhr in June 1986. The theme is the infinitely large and small in ANALYSIS, not Cantor’s theory of INFINITY. (DEZ) #18.4.55
KUZICHEVA, Z. A. 1982. Graphic methods of the logic of CLASSES. Zstoriya i Methodologiya Estes- tuennykh Nuuk 29, 57-85. [In Russian with English summary.] Review of 17th to 19th centuries graphical methods in MATHEMATICAL LOGIC. DE MORGAN’S diagrams. See Zentralblatt 699(01007). WL) #18.4.56
LI, JIMIN. 1989. Liu Hui’s exposition on IRRATIONAL NUMBERS. Journal ofNorthwest University. Natural Sciences 19,1-4. [In Chinese with English summary.] LIU Hur’s commentary on the Jiuzhang suanshu (Nine chapters on the mathematical art). Argues that the word “n&m” (literally “side”) has been hitherto mistranslated and should be taken as an equivalent of “gen,” i.e. “root.” See the review by J.-C. Martzloff in Zentrulblutt 699(01003). (ACL) #18.4.57
MAISTROV, L. E. See #18.4.12.
MAUI, LAsz~6. 1991. Ott6 Steinfeld (1924-1990). Semigroup Forum 43(2), 127-134. Obituary of 0~~6 STEINFELD, who was the “first in Hungary to take up regular research in SEMIGROUP THEORY .” Includes a short account of his work. Photograph. (DEZ) #18.4.58
MARTINOVIC, IVICA. 1990. Theories and inter-theory relations in BoSkoviC. International Studies in the Philosophy of Science 4(3), 247-262. RUGJER BOSKOVIC explicitly used the concept of scientific theory during the period 1745-1755 to focus on the PROBLEM OF CONTINUITY AND INFINITY in three areas: the theory of forces, the theory of transformations of geometric loci, and the theory of INFINITESIMALS. The author describes the concept of a THEORY during BoSkoviC’s Roman period. WI #18.4.59
MASAHARU, UMETSU . 1988. Similar questions of “Sangaku” or mathematical tablet. Stigakushi Kenkyti 117, 31-40. [In Japanese.] See Zentralblutt 698(01006). (ACL) #18.4.60
400 ABSTRACTS HM 18
MAWHIN, JEAN. 1989. Louis-Philippe Gilbert: De l’analyse mathematique aux sources du Nil, en passant par la rotation de la Terre et le pro& de Galilee. Revue des Questions Scientifiques 160, 385-396. LOUIS-PHILIPPE GILBERT: From mathematical analysis to the sources of the Nile, by way of the rotation of the earth and the Galilean process. See Zentrulblutt 701(01008). (ACL) #18.4.61
MEDVEDEV, F. A. 1990. On the concept of mathematical infinity in ancient Greece as interpreted by D. D. Mordukhai-Boltovski. [In Russian.] Moscow: Academy of Science. Preprint 37. 24 pp. Paperback; 50 K. The author argues that the approach of D. D. MORDUKHAI-BOLTOVSKI, developed from the 1920s through the 1950s is erroneous, and that his interpretations are incorrect. Three examples drawing on the concept of INFINITY in ANCIENT GREECE are considered: infinitesimals in the form of angles of contact, use of infinity in the method of exhaustion, and the use of indivisibles in the research of Democritus and Archimedes. (DEZ) #18.4.62
MEHRTENS, HERBERT. 1990. Moderne Sprache Mathematik: Eine Geschichte des Streits urn die Grundlagen der Disziplin und des Subjekts formaler Systeme. Frankfurt am Main: Suhrkamp Verlag. 640 pp. DM 78. (ACL) #18.4.63
MILLER, ARTHUR I. See #18.4.30.
MITROPOLSKII, Yu. A. (Ed.) 1988. The Znstitute ofMathematics. Kiev: Naukova Dumka. 176 pp. R 1.70. [In Russian.] History of the Mathematical Institute of the UKRAINIAN ACADEMY OF SCIENCES from its founding in 1934. See the review by R. Cooke in Zentrulblatt 699(01034). (ACL) #18.4.64
NUNEMACHER, JEFFREY. 1991. Review of Mathematics and its history by John Stillwell. TheAmeri- can Mathematical Monthly 98(6), 569-574. The reviewer suggests ways in which this TEXTBOOK can be used as a capstone course for senior mathematics majors in American universities. He describes the book as “the first book concerned with the history of mathematics that I have found really captivating.” See #17.2.76. (DEZ) #18.4.65
OZHIGOVA, E. P. See #18.4.17.
PARIKH, CAROL. 1991. The unreal life of Oscar Zariski. San Diego: Academic Press. xvii + 264 pp. Hardbound, $32.95. An account of the life of OSCAR ZARISKI based on interviews with family, col- leagues, and students, and on tape-recorded interviews with Zariski before his death in 1986. There is a foreword by David Mumford, a survey of Zariski’s mathematical work, and a complete bibliography. Family photographs abound. [Adapted with permission from The American Mathematical Monthly 98(6) (1991), 575.1 (LAS) #18.4.66
PAVLOVSKAYA, E. D. See #18.4.33.
PECKHAUS, VOLKER. 199011991. Ernst Schroder und die “pasigraphischen Systeme” von Peano und Pierce, Modern Logic 1(2/3), 174-205. ERNST SCHR~DER shifted his attitudes concerning the nature and tasks of LOGIC in foundations of mathematics toward LOGICISM as a result of his study of the logic of relatives of CHARLES S. PEIRCE. Evidence is cited from Schriider’s correspondence with PAUL CARUS and with FELIX KLEIN. (IA) #18.4.67
PEDERSON, JEAN. See #18.4.47.
PETRILLI, SUSAN. See #18.4.29.
POINCAR~, JULES HENRI. 1990. Suifondumenti della geometriu. Brescia: Editrice La Scuola. xliv + 60 pp. Paperback; L 10.000. (11 Pensiero classici della filosofia comentati.) Edited by Ubaldo Sanzo. The foundations of GEOMETRY. (ACL) #18.4.68
PETROVA, S. S. 1982. G. BOOLE and the development of the CALCULUS OF OPERATIONS in EN- GLAND. Zstoriya i Methodologiya Estestvennykh Nauk 29,98-103. [In Russian with English summary.] See Zentralblatt 699(01014). (ACL) #18.4.69
HM 18 ABSTRACTS 401
RAINS, DIMITRIS K. 1989. Archimede, Menelaos d’Alexandrie et le ‘Carmen de ponderibus et mensuris’: Contributions d l’histoire des sciences. Jannina, Greece: (no publisher). 256 pp. Paperback. ANCIENT GREECE. ARCHIMEDES. MENELAUS. (ACL) #18.4.70
RANSOM, PETER. See #18.4.82.
REICH, KARIN. 1990. Die Beziehung Martin Luthers zu Michael Stifel. Esslinger Studien 29,17-36. A detailed account of the relationship between MARTIN LUTHER and his friend MICHAEL STIFEL based mainly on the 16 letters Luther wrote Stifel between 1525 and 1533. Topics include Stifel’s fascination with numerology and their mutual interest in the date of the end of the world. (ACL) #18.4.71
RIDER, ROBIN E. See #18.4.38.
ROZHANSKAYA, M. M. See #18.4.1.
SANZO, UBALDO. See #18.4.68.
SCHARLAU, W. See #18.4.35.
SCIMONE, ALDO. 1989. The mathematical circle of CATANIA. Bollettino di Storia delle Scienze Matematiche 9,171-192. [In Italian.] Describes the work of mathematicians such as G. Scorza and M. Cipolla, the founding of the journal Esercitazioni matematiche, and the mathematical seminar. See the review by I. Grattan-Guinness in Zentralblatt 699(01033). (ACL) #18.4.72
SCRIBA, CHRISTOPH J. See #18.4.49.
SHENITZER, ABE. 1991. The Cinderella career of projective geometry. The Mathematical Intelli- gencer 13(2), 50-55. An essay on the devious route by which projective geometry moved from its origins with Apollonius through its apotheosis with Arthur Cayley to its culmination with Felix Klein. (DEZ) #18.4.73
SOROKINA, L. A. 1982. On the works of E. MINDING dedicated to the theory of ABELIAN INTE- GRALS. Zstoriya i Methodologiya Estestvennykh Nauk29,144-151. [In Russian with English summary.] See Zentralblatt 699(01013). (ACL) #18.4.74
TAKAO, HAYASI. 1987. MAGIC SQUARES of Moschopoulos. Sugakushi Kenkyu 114,46-52. [In Japa- nese.] See Zentralblatt 698(01014). (ACL) #18.4.75
TAKAO, KURODA. 1987. Babylonian algebra and “kokoho” or three-squares theorem in China. Stigakushi Kenkyu 115,43-65. [In Japanese. J ALGEBRA. CHINA. See Zentralblatt 698(01002). (ACL)
#18.4.76
TATSUHIKO, KOBAYASHI. 1988. On ‘Tetsujutsu’ in the annotated ancient laws. [In Japanese.] Sziga- kushi Kenkyti 116, 44-47. See Zentralblatt 698(01005). (ACL) #18.4.77
THOM, REN& See #18.4.30.
T~~RNIG, W. See #18.4.35.
TSUTOMU, KANEKO. 1987. On KITAME SEIGETSU and his followers after he returned to Sado. Sugakushi Kenkyli 114, 53-59. [In Japanese.] See Zentralblatt 698(01012). (ACL) #18.4.78
TWEDDLE, IAN. 1988. James Stirling. ‘This about series and such things.’ A discussion of the later work of the Scottish mathematician James Stirling (1692-1770), based mainly on material from his notebooks, one of which is inscribed with the above title. Edinburgh: Scottish Academic Press. viii + 208 pp. f25.00. Biographical sketch of JAMES STIRLING with excerpts from his manuscripts. See Zentralblatt 701(01003). (ACL) #18.4.79
402 ABSTRACTS HM 18
VALL~E, ROBERT. 1990. blurt 699(01022). (ACL)
LOUIS DE BROGLIE and CYBERNETICS. Kybernetics 19,32-33. See Zentral- #18.4.80
VITRAC, BERNARD. See #18.4.34.
VOLKOV, ALEXEI. 1991. Dissertation on “Matematika v drevnem Kitaie (3-7vv.)” (Mathematics in ANCIENT CHINA during the 3rd-7th centuries A.D.). Historia Muthematicu M(2), 185-187. A description of the author’s 323-page dissertation on various commentaries on the CHINESE treatise “Jiu Zhang Suan Shu,” especially those of Lru HUI and LI CHUNFENG. There is a list of the seven principal findings in the dissertation. (DEZ) #18.4.81
WALLIS, PETER, WALLIS, RUTH, RANSOM, PETER, AND FAUVEL, JOHN. 1991. Mathematical trudi- tion in the North of England. NEBMA, 12 Annasi de Mews, leadgat, Consett, Durham DH86HL. 66 pp. Detailed catalogue for an exhibition held in Newcastle for the annual conference of the Mathematical Association. Many portraits and title pages shown, with descriptions. Emphasis on the “philomath” tradition, book subscription lists, and various societies and universities in the area. WILLIAM EMERSON. CHARLES HUTTON. Bibliography of secondary literature. (IGG) #18.4.82
WALLIS, RUTH. See #18.4.82.
WANG, QINGXIANG. 1987. On a comparative study of “Suan-Fa tong zong” with “Jin-Kou-Ki.” An attempt to study mathematical history comparatively. SPgukushi Kenkyti, Part I, ll3, l-53; Part II, 114, l-40. [In Japanese.] See Zentrulblutt 6!&01009) and 6!@(01010). (ACL) #18.4.83
WANG, QINGXIANG. 1987. On the writings of Japanese.] See Zentrulblutt 698(01008). (ACL)
WATERHOUSE, WILLIAM. 1991. An elementary interpretation of entry 12 in Gauss’ Tugebuch. Historiu Muthemuricu 18(2), 173-176. An interpretation that differs from the usual one due to Bachmann on Entry 12 in GAUSS’ diary. The time, and the placement of that entry, suggest a result on NUMBER THEORY about the sum of numbers less than, and relatively prime to, a given number. (DEZ)
#18.4.85
WEINER, JOAN. 1990. Frege in perspective. Ithaca, N.Y.: Cornell Univ. Press. xx + 307 pp. $32.50. FOUNDATIONS. GOTTLOB FREGE. (ACL) #18.4.86
WILKES, M. V. 1990. HERSCHEL, PEACOCK, BABBAGE and the development of the CAMBRIDGE curriculum. Notes and Records of the Royal Society of London 44, 205-219. Early 19th century mathematical reform at Cambridge. The ANALYTICAL SOCIETY. See Zentrulblutt 701(01004). WL) #18.4.87
WILSON, ROBIN. 1991. Nineteenth-century analysis. The Mathematical Zntelligencer W(2), 80. Stamps commemorating the 200th anniversaries of the births of BERNARD BOLZANO and AUGUSTIN- LOUIS CAUCHY. (DEZ) #18.4.88
