358 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1747. 



secant, and versed sine of an arc; s\ t:,J\ the sine, tangent, secant of the com- 

 plement, and %), the versed sine of the supplement of that arc ; let z = \A -\- a, 



x^= :^A — a; or if z and x be put for the arcs, it will be ^ = z + jr, o = z x. 



Then will the terms in any column of the following table, be proportioned to 

 their corresponding ones in any other column. 



A Table of the Relations oj Goniomelrical Lines. 



Hence almost an infinite number of theorems may easily be derived ; some of 

 which are the following, given here as examples of the use of the table. 



I. J,z X s^ = ir X s'jO — s,Az=. J^r X s,z 



X- 





s ,z-\- X = T — rr=^ -pr-rr. 



*,x 

 s'x 



s\t X s\x = 4-r X s',a + * , A = -^r X s',z — x + s\z + x =z'-^rr=-^ rr. 



of a son, who being bom afterwards, was the late Sir Wm. Jones, chief judge in India, so justly ce- 

 lebrated for his eminent talents and learning. 



In all the works of our author, a remarkable neatness, brevity, and accuracy, every where pre- 

 vails. He seemed to delight in a very short and comprehensive mode of expression and arrangement j 

 in so much, that sometimes what he had contrived to express in two or three pages, would occupy a 

 little volume in the usual style of writing. It has been said that Mr. Jones possessed the best mathe- 

 matical library in England, there being scarcely a book of that kind but what was there to be found. 

 He had collected also a great quantity of manuscript papers and letters of former mathematicians, 

 which have often proved useful to writers of their lives, &-c. 



Many other curious particulars relating to Mr. Jones, with a catalogue of his works, may be seen 

 In Dr. Hutton's Dictionary of Mathematics, under the article Jones, and in the introduction prefixed 

 to the same author's work on Logarithms, p. 121. 



