104 BSERFJTIONS on the 



flruclion of triangles and parallelograms ; and when ever fuch 

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

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

 genius of Hipp arch us fuggefled the application of arithmetic 

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

 wliich pure geometry afforded no method of exprefTing. This 

 wnion of geometry and arithmetic did not happen, however, 

 till each of thefe fciences feparately had made great progrefs ; 

 for before the days of Hipparchus, Euclid, Archimedes, 

 and Appolonius, had all flourifhed in fuccefHon, 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 reflexion will convince xis, that he, who 

 firfb formed the idea of exhibiting, in aritlimetical tables, the ra- 

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

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

 of profovmd thought, and of extenfive knowledge. However 

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

 fyflem 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 mufl 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 

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

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

 nerally 



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