Study of Dlophantine Analysis in the United States. 43 



can likewise be represented by rational numbers. He then 

 includes all equations for the six trigonometric functions in the 



symbolical form A = (P\ — | , — being called the "root of the 

 V n ^ n 



function." He then solves the three problems: (1) To find the 

 root of the function in terms of the angle; given the roots of 

 the function, (2) to find the root of their sum and (3) of their 

 difference. This occupies eleven pages in the book. The rest 

 of the work is devoted to the application of this notation to 

 indeterminate problems and to geometry. The thirtieth and 

 last problem on the former subject is "To find n square numbers 

 such that the sum of every n — 1 of them may be square num- 

 bers." As an example of the geometric pioblems solved we 

 quote this: "To find the sides of right angled triangles in rational 

 numbers, which have equal areas." 



The solution of a few difl&cult Diophantine problems was 

 communicated to SiUimari's American Journal of Science by 

 Theodore Strong, Professor at Rutgers College (died 1869). He 

 was one of the few men in this country who possessed some 

 knowledge of Gaussian methods in the theory of numbers, 

 which he employed in published articles, once or twice. 



All the mathematical periodicals, except two of our present 

 journals which are devoted to advanced mathematics exclusively, 

 have given a good share of their space to Diophantine analysis. 

 Men of a mathematical turn of mind liked to exercise their 

 ingenuity in this field. Eev. A. D. Wheeler discoursed " On 

 the Diophantine Analysis" in the Mathematical Monthhj of 

 August, 1861. Professor George R. Perkins wrote on it for the 

 Analijst of J. E. Hendricks. Dr. David S. Hart, of Stonington, 

 Conn., was a faithful follower of Diophantus. He wrote an 

 outline history of indeterminate analysis for the Mathematical 

 Magazine (Vol. I, No. 10), also articles entitled "Square Numbers 

 "Whose Sum is a Square" (Vol. I, No. 10), "Diophantine Solu- 

 tions" (Vol. 1, No. 3), "Consecutive Square Numbers Whose 

 Sum is a Square" (Vol. I, No. 8), "Cube Numbers whose Sum is 



