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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 



HM4 Reviews 107 

previously unmatched. At the same time, printing and other as- 
pects of Renaissance culture encouraged the translation and cir- 
culation of neglected mathematical works from classical antiquity. 
This book deals with the Italian and foreign mathematicians who 
drew primarily on Greek manuscript treasures in Italy, especially 
at Venice and Rome, to revive neglected sources, reopen lines 
of mathematical research, and begin new conquests in the domains 
of algebra and trigonometry. 

Unlike most historians of mathematics, Professor Rose has 
concerned himself with the patrons of mathematicians, individual 
and institutional, as well as the contributors to knowledge 
during the fifteenth and sixteenth centuries. A vast amount of 
information about mathematical source materials and their rela- 
tion to Renaissance books is presented, not previously brought 
together to my knowledge, and here woven in with biographical 
data concerning scores of writers, editors, and translators of 
mathematical works. Emphasis is placed on the social rather 
than the technical aspect of history of mathematics in the 
Italian Renaissance, providing us with a dimension of history 
lacking in older conventional accounts of particular theorems, 
problems, and notations that emerged in stated epochs. The 
notes accompanying each chapter are invaluable for their bibli- 
ographical references alone, the work having required study of 
a vast and scattered literature as well as of a great many still 
unpublished letters and manuscripts in Italian libraries. 

The book is attractively and accurately printed as volume 
145 in the publisher’s series Travaux d'Humanisme et enaissance. 
The few misprints noted are unlikely to mislead anyone, as the 
date 1300 for 1400 on p. 84, the word “this” for “his” on p. 283, 
and “These” for “There” on p. 285. The same may be said of 
occasional infelicitous expressions such as “comet of 1604-05” 
on p. 229, in which a mistaken opinion of an early writer might 
be taken as a statement by the author about an astronomical 
event, Though it may be that some of the author’s evaluations 
and convictions will be modified as others pursue the rich field 
he has opened up, this monograph will, in the reviewer’s opinion, 
remain of permanent value to the history of the mathematical 
Renaissance.