io6 THE POPULAR SCIENCE MONTHLY. 



MATHEMATICAL CURIOSITIES OF THE SIXTEENTH 



CENTURY. 



BY M. V. BRANDICOUET. 



IN the great intellectual revival of the sixteenth century, 

 mathematics as well as letters and the arts were recuperated 

 first from the pure sources of antiquity. Casting away poor 

 Latin translations, second-hand versions through the Arabic, on 

 which the Middle Ages had fed, geometricians emulated one an- 

 other in zeal for learning the Greek language, in order that they 

 might read in the original text the works of Euclid, Archimedes, 

 Ptolemy, and Diophantus. Most of the works published at this 

 epoch were only translations from Grecian authors. " The great 

 thought of that time," says Montucla, " was simply to refine the 

 minds of students and cause them to taste of a learning almost 

 unknown till then. This could not be done all at once, and the 

 human mind, like a weak stomach which too solid food would 

 tire out, had to be brought by degrees to considerations of a 

 higher order." 



One of the earliest translations of Euclid is found in the Mar- 

 garita philosophies of G. Reisch, prior of La Chartreuse at Fri- 

 borg a Latin book printed in Gothic characters at Heidelberg in 

 1496. It is a sort of encyclopaedia of the science of the beginning 

 of the sixteenth century, and certifies to the very extensive 

 knowledge of the author. Each of the scientific treatises con- 

 tained within it is adorned with very curious engravings of a 

 naive character. 



Memmius, a noble of Venice, made a translation of the works 

 of Apollonius in 1537, which was published after his death by one 

 of his sons. 



The mathematical sciences were then cultivated with most 

 success in Italy ; and when Francis I, of France, sent across the 

 Alps for architects, painters, and sculptors to construct and adorn 

 the magnificent chateaux of Chambord and Chenonceaux, he was 

 thus also able to ask for his colleges algebraists who were cer- 

 tainly the first mathematicians in Europe. Algebra was not then 

 what it has since become, a science employing only letters, signs, 

 and symbols, having a well-defined significance and serving as 

 the characters of a very clear and very precise language, which 

 the initiated could understand as well as they could their mother 

 tongue. The unknown quantity was then called " the thing " (res, 

 coser ; from which algebra was for some time named the art of the 

 thing), and it was often represented by R. The square of the un- 

 known quantity was called census (2). The signs + and = were 

 not known, but the initials of the words for which they stand 



