104 OBSER TACTIONS on the 



ilruclion of triangles and parallelograms ; and when ever fuch 

 comparifons are to be made, fome other method muft be fought 

 for. It was precifely in fuch circumflances, that the inventive 

 genius of Hipp arch us fuggefled the application of arithmetic 

 to alcertain thofe ratios among the fides and angles of figures, 

 which pure geometry afforded no method of exprefTmg. This 

 union of geometry and arithmetic did not happen, however, 

 till each of thefe fciences feparately had m.ade great progrefs j 

 for before the days of Hipparchus, Euclid, Archimedes, 

 and Appolon lus, had all flourifhed in fucceflion, and had pro- 

 duced thofe immortal works, of which the luftre has not been ob- 

 fcured by the highefl improvements of later ages. In the progrefs 

 of fcience, therefore, the invention of trigonometry is to be confi- 

 dered as a flep of great importance, and of confiderable diffi- 

 culty. It is an application of arithmetic to geometry, with 

 which we are now too familiar, to perceive all the merit of the 

 inventor ; but a little reflecflion will convince us, that he, who 

 firfl formed the idea of exhibiting, in arithmetical tables, the ra- 

 tios of the fides and angles of all poflible triangles, and contrived 

 the means of conflru6ling fuch tables, muft have been a man 

 of profound thought, and of extenfive knowledge. However 

 ancient, therefore, any book may be, in which we meet with a 

 fyftem of trigonometry, we may be affured, that it was not 

 written in the infancy of fcience. 



12. As we cannot therefore fuppofe the art of trigonometri- 

 cal calculation to have been introduced till after a long pre- 

 paration of other acquifitions, both geometrical and aftro- 

 nomical, we muft reckon far back from the date of the Surya 

 Siddhanta, before we come to the origin of the mathemati- 

 cal fciences in India. In Greece, the conftellations were 

 firft reprefented on the fphere, if we take a medium between 

 the chronology of Newton, and that which is now ge- 

 nerally 



