PII: 0315-0860(77)90049-0 HM4 Reviews 105 marginalia, giving the reader most welcome help, especially in understanding the subtleties of infinitesimals in geometry and dynamics . A list of passages in the Principia that Leibniz underlined or otherwise marked and a conclusion complete the book. It is a rich edition; preface, introduction, commentary and conclusion are given both in German and in French (and hence the title page in Latin). The Academic Internationale d’Histoire des Sciences of whose Collection des Travaux the edition forms a part, explains the decision for a bilingual edition by the interest of the subject and the honour of the memory of Leibniz who wrote so much in French--but one hopes the argument will not be taken over by other editors of Leibnitiana, as there are already enough delays in that venture. The printing is beauti- fully done (by Vrin)--apart from a rather large number of mis- prints. The copy I saw was provided with a loose sheet of Corrigenda on which however was not mentioned the misprint that mars the dedication (“victimis omnium saeculorum intolerantia cuiuscunque generis oppressis dedicatum,” but it says quiuscunque). Nevertheles a gem, and as a true gem it has its hidden mysteries which it refuses to reveal. We will not know what Leibniz thought on reading the passages on the deduction of Kepler’s law of areas or on the law of gravity in the solar system; his comments to the first were cut off when the volume was rebound some 75 years ago, and the second was crossed out immediately by Leibniz himself, and this so rigorously that even the most modern optical techniques could not disclose them! The book conveys the excitement, the craftmanship and the fascination which history of science can offer--it is a pleasure to own, to browse and to use it. HISTOIRE DES MATHiMATIQUES. By Jean-Paul Collette. Montreal (Editions du Renouveau Pedagogique). 1973. 238 p. Reviewed by Guy A. R. Guillotte Polyvalente J. H. Leclerc, Granby, Quebec, Canada It is a pleasure to welcome and review a new French book on the history of mathematics. The author is a native of Quebec who has been teaching history of mathematics at the University of Quebec in Trois Rivisres, Quebec, Canada. The work is a manual rather than a treatise, The author presents historical notions widely accepted by historians in a way that is readable for the layman. In his preface he warns his reader that a good background in college or CEGEP level or in O-level mathematics is sufficient to understand his book with profit. This volume initiates the reader into the history of mathe- matics from primitive times up to the beginning of the 17th 106 Reviews HM4 century. It is the desire of Professor Collette to present later a second volume (of a projected series of four volumes) which will deal with the 17th century. At the end of this first book is a list of thirty-two sources of research and a bibliography classified under specific topics. This arrangement may incite the reader, whether he is a student, a professor or a simple layman, to have direct contact with these sources for his own research, There is an index to the principal names cited, a list of illustrations, and finally a general index. Each chapter ends with a brief r&ume’, followed by a bibliography of works or articles from scientific journals, giving the pages referring directly to the content of the chapter. Exercises are provided to facilitate the synthesis of the context or to complete cer- tain notions already presented in previous chapters. In this instructive and well-written book, the author se- lected the following periods: the prehistory of mathematics, the Babylonian civilization, the Egyptian civilization, the birth of Greek mathematics, the period from Plato to Euclid, Archimedes and the School of Alexandria, the Chinese and Hindu civilization, Islamic mathematics, the mathematics of Europe during the Middle Ages, 500-1400 A.D., the European Renaissance, and finally the beginning of the 17th century. The main mathe- matical topics discussed--numbers, fractions, geometry, elemen- tary algebra, infinite series, co-ordinate geometry and elemen- tary calculus--may lead both professors and teachers to a better understanding of the learning techniques of mathematics. Finally, although the author obtained his information from secondary sources, his book consists of an honest synthesis of the principal mathematical contribution of the great civiliza- tions that preceded us. This book is to be recommended to all lovers of mathematics and to teachers at all levels. Professor Collette has presented his manual admirably. Bravo! THE ITALIAN RENAISSANCE OF MATHEMATICS. By Paul Lawrence Rose. Geneva (Librairie Droz) . 1975. xiii + 316 pp. Reviewed by Stillman make University of Toronto, Toronto M5.S 1Al European mathematics from the invention of printing with movable type to the close of the sixteenth century constitutes a topic of special interest socially as well as technically. The universities remained almost the sole repository of mathe- matics during the Middle Ages, and the chief text was Euclid. Printed books made it possible for talented persons outside the main stream of education to take part in the development of mathematics and to communicate their contributions on a scale