PII: 0315-0860(80)90011-7 HM7 Reviews 449 REVIEWS EDITED BY JUDY V. GRABINER All books monographs, journal articles, and other publica- tions (including films and other multi-sensory materials) relat- ing to the history of mathematics are abstracted in the Abstracts Department. The Reviews Department prints extended reviews of selected publications. Materials for review should be sent for abstracting as indi- ------ -- cated in the heading of the Abstracts Department. Publishers --- -- who wish to accelerate the process of abstracting and subsequent reviewing may send a second copy directly to the editor of the Book Review Department: Professor Judy V. Grabiner, 424 West 7th Street, Claremont, CA 91711 USA. Most reviews are solicited. However, colleagues wishing to review a book are invited to make known their wishes. Comments on books, articles, or reviews should be submitted to the Cor- respondence Department. We also welcome retrospective reviews of older books. Colleagues interested in writing such reviews should consult first with the editor to avoid duplication. PIER0 DELL FRANCESCA'S MATHEMATICAL TREATISES: THE "TRATTATO D'ABACO" AND "LIBELLUS DE QUINQUE CORPORIBUS REGULARIBUS." By Margaret Daly Davis. Ravenna (Long0 Editore). 1977 xxii + 135 pp., 36 plates. Lit 8000 Reviewed by Warren Van Egmond Institut fiir Geschichte der Naturwissenschaften Deutsche Museum, 8 Miinchen 26, West Germany The connections between art and mathematics in the Italian Renaissance have long been recognized by both historians of art and historians of mathematics. George Sarton devoted a page to the development of the theory of perspective in painting in 14th- century Italy in his Introduction to the History of Science (Vol. III, p. 1105), while Rudolf Wittkower and P.H. Scholfield have carefully studied the mathematical principles used in Renaissance architecture. But with these exceptions, the barriers presented by modern disciplinary boundaries have long prevented any real interchange between the two fields. Except for Lon Shelby's article, "The Geometrical Knowledge of Mediaeval Master Masons" (Speculum 47 (19721, 395-421) and Diane Finiello Zervas' study, "The Trattato dell'abaco and Andrea Pisano's Design for the Florentine Baptistery Door" (Renaissance Quarterly 28 (1975), 483-503), there has been little recent interaction between the Copyright 0 1980 by Academic Press, Inc. All rights of reproduction in any form reserved. 450 Reviews HM7 two disciplines. Margaret Daly Davis' book thus constitutes one of the first major studies to concentrate on the links between art and mathematics, connected historically yet separated in scholarly activity. Its focus is a personage no less important than Piero Della Francesca, one of the foremost artists of the Italian Renaissance, whose paintings have long been recognized for their mathematical precision. This precision is not surprising since Piero based his paintings on sound mathematical principles of optics and perspective, and composed three theoretical treatises outlining these principles for those who wished to follow them: a treatise on perspective, De prospectiva pinyendi; a treatise on the five regular bodies, De corporibus regularibus; and Trattato d'abaco, a general treatise on commercial arithmetic, algebra, and geome- try which was probably written first and served as the mathemati- cal foundation for the other two. Yet despite his great fame as a painter, Piero's written works passed into an early obscurity and were not even printed until within the last century, De pro- spectiva in 1899 and again in 1942, De corporibus in 1916 and the Trattato d'abaco only within the last decade. Mrs. Davis' book is an analysis of the last two. It should be pointed out that, in spite of its perhaps slightly misleading title, this is a work in the history of art, not the history of mathematics. Only five pages are devoted to the first two parts of Piero's treatise on commercial mathematics and alge- bra, and these draw on sources no more recent than Libri, Cantor, and Zeuthen, yet still manage to make some minor errors within this small compass, such as saying that the solution of the cu- bic equation "was probably due to Niccolo Tartaglia" (p. 231, neglecting to mention the first successful solution made by Scipione de1 Ferro of Bologna. Mrs. Davis' primary attention is devoted to an analysis of the geometrical section of the abaco and the book on the five regular bodies, with particular concern for how they relate to the construction of perspective drawings of the regular bodies as they appear in Luca Pacioli's De divina proportione of 1509 and numerous treatises on perspective written after that date. A short preliminary chapter is devoted to the application of mathematics to art and its study before Piero; one chapter each is devoted to the Trattato and the Libellus; and a final chapter studies the influence they had on the artists of the 16th century, particularly Albrecht Diirer and Daniele Barbaro, mediated pri- marily by Luca Pacioli's uncredited publication of the major por- tion of the Libellus and part of the abaco in his Summa and De divina proportione. Perhaps the greatest direct interest the book holds for his- torians of mathematics is its very careful, detailed study of the connections between Piero and Pacioli, showing precisely which works Pacioli used and how he altered them. Two appendixes sum- HM7 Reviews 451 marize the results of these studies,and two tables of concordances list the corresponding problems in the Trattato d'abaco, the Libellus de corporibus regularibus, and Pacioli's Summa. Overall, the book is very well organized and well written. It is brief, clear, and nontechnical and does not demand any previous knowledge of the history of art or its voluminous lit- erature. Since it also includes a very well selected bibliography, it is a particularly good point of entry for any historian of mathematics who is interested in pursuing this subject in greater detail. Mrs. Davis has not built the bridge between Renaissance art and mathematics we have all been looking for (to be fair we must realize that this was not her intent), but she has surely laid one of the principal foundation stones on which any such bridge will eventually be built. WOMEN AND MATHEMATICS, SCIENCE AND ENGINEERING. A PARTIALLY ANNOTATED BIBLIOGRAPHY WITH EMPHASIS ON MATHEMATICS AND WITH REFERENCES ON RELATED TOPICS. By Else B#yrop. Roskilde University Library, Denmark. 1978. Reviewed by Dr. Louis L. Bucciarelli Program in Science Technology and Society M. I. T. Cambridge, Mass. 02139 Else H$yrup is a Danish mathematician who has turned her attention to the study of the sociology and psychology of mathe- matics and the individual--especially women and mathematics. Her bibliography contains approximately 400 items drawn primarily from contemporary journals in the fields of education, mathe- matics, and psychology and gathers citations under the headings "Women and Engineering," Women and Problem Solving," "Sex-dif- ferences in Cognition," and "Creativity," as well as "Women and Mathematics." Most of the entries are annotated with a brief comment, e.g., "important," "prejudiced," "very technical," "good bibliography,"etc. This slender paperback is described by the author as a work in progress. It is well worth perusing and could serve as the basis for a coherent and more comprehensive bibliography. Else H@yrup would be pleased to receive comments and references on this subject. Her address is Bdgerej 8, DK 3500 Voerlase, Den- mark. Copyright 0 1980 by Academic Press, Inc. AN rights oJ reproduction in any form reserved.