Text-Book of Last Century. 33 



moving one of the parallel linos toward the other the figure for 

 the former theorem reduces to that of the latter. The next 

 section contains the algebraic solution of 20 geometric problems. 



Part IV, on Conic Sections, gives a semi-empirical treatment 

 of the subject. Starting with the definition of a cone, it shows 

 how the three sections are obtained from the cone and then 

 gives some of their principal properties. In this as in all Eng- 

 lish books of the 18th century, analytical geometry was 

 neglected. The Conic Sections were then studied in England 

 and America only by the synthetic method. It was not till the 

 close of the first quarter of this century that analytical geometry 

 began to be introduced into our American colleges. 



The part on " Arithmetick of Infinites " is interesting, for 

 it constitutes a sort of integral calculus, such as was employed 

 by Wallis, Cavalieri, Format, and Koberval before the inven- 

 tion of the Differential and Integral Calculus of Newton and 

 Leibniz. Ward seems to have known nothing of Fluxions. 

 The first edition of Ward's book appeared in 1707. Newk)n 

 published the first edition of his Principia in 1687, but his 

 Method of Fluxions was not published till 1736, though written 

 in 1671. 



Were those half-developed, pre-Newtonian methods ever 

 studied in American colleges? It is possible that they were on 

 some rare occasions, but we have no evidence to that effect. 



In the essay on the history of logarithms we look in vain for 

 any statement pointing out the difference between natural loga- 

 rithms and those invented and published by Napier. The two 

 have been considered identical by many English and Ameri- 

 can writers, down to the present day, and it is probable that 

 text-book compilers will persist in this error for many years to 

 come. 



Though Ward's Mathematics treated of five broad subjects, 

 ■ it covered only 475 pages, or not quite so much as is given now- 

 a-days to the elementary presentation of any one of these sub- 

 jects. The type in this old book was coarse. From this we 

 may judge how meagre the kuowledge to be derived from 

 Ward's Mathematics really was. 

 3 



