30 Colorado College Studies. 



only possible exception to this is his " Idea Trigonometriae 

 demonstrata in usum juventutis," 1654. His only other math- 

 ematical and astronomical writings, of which I have any knowl- 

 edge, are, "Astronomia Geometrica, London, 1656 " ; " Praelectis 

 de Cometis " ; " Inquisitio in Ismaelis Bulialdi Astronomiae 

 Philolaicae f undamenta " ; and a tract on Proportion. It is not 

 likely that mathematical books written in Latin were read in 

 our colleges at as late a date as " Ward's Mathematics " is known 

 to have been used. Let it be remembered, moreover, that Seth 

 Ward wrote the above works before the name of Newton had 

 become known to science. John Ward, on the other hand, 

 wrote his books half a century later and is, therefore, more 

 likely to be the author studied in this country. Wherever we 

 have seen this book mentioned in the curricula of American 

 colleges, it was always called " Ward's Mathematics." The bap- 

 tismal name of tlie author was never given. This shows that 

 there was only one Ward (either John or Seth) whose mathe- 

 matical works were known and studied in our colleges. Now, 

 Benjamin West, Professor of Mathematics in Brown University 

 from 1786 to 1799, published in the first volume of the American 

 Academy of Arts and Sciences a paper " On the Extraction o^. 

 Roots," in which he offers improvements on " Ward's " method. 

 I have seen a copy of the "Astronomia Geometrica " in the Ridg- 

 way Library in Philadelphia, but have found nothing in it on 

 root-extraction. One would hardly expect to find anything on 

 it in Seth's Trigonometry or Proportion. John Ward, on the 

 other hand, treats of the extraction of roots in his " Guide," and 

 gives a " general method of extracting the roots of all single 

 powers." West tak;es two examples (two numbers, one of 14, 

 the other of 18 digits) from "Ward" and shows how the re- 

 quired roots can be extracted by his method. Now, both these 

 examples are given in John Ward's " Young Mathematician's 

 Guide." This evidence in favor of John Ward's book may be 

 regarded conclusive. 



The first edition of the " Young Mathematician's Guide " 

 came out in London, in 1707.* The fourth edition, 1724, con- 



* An Essay upon Study, by John Clarke, London, 1731, p, 313. 



