TRlGONOMETRr of the BRAHMINS. 87 



name of the radius, or fine of 90°, viz. t-rijyn^ is alfo taken. 

 This regularity in their trigonometrical language, is a circum- 

 ftance not vmworthy of remark. But what is of more confe- 

 quence to be obferved, is, that the ufe of fines, as it was un- 

 known to the Greeks, who calculated by help of the chords, 

 forms a ftriking difference between the Indian trigonometry and 

 theirs. The ufe of the fine, inftead of the chord, is an iinprove- 

 ment which our modern trigonometry owes, as we have hither- 

 to been taught to believe, to the Arabs ; and it is certainly one 

 of the acquifitions which the mathematical fciences made, when, 

 on their expulfion from Europe, they took refuge in the Eaft. 

 But whether the Arabs are the authors of this invention, or 

 whether they themfelves received it, as they did the numerical 

 charadlers, from India, is a queflion, which a more perfedl 

 knowledge of Hindoo - literature will probably enable us to re- 

 folve. 



No mention is made in this trigonometry, of tangents or fe- 

 cants; a circumftance not wonderful, when we confider that the 

 ufe of thefe was introduced in Europe no longer ago thaji the 

 middle of the fixteenth century. It is, on the other hand, not 

 a little fmgular, that we fhould find a table of verfed fines in the 

 Surya Siddhanta ; for neither the Greek nor the Arabian ma- 

 thematicians, had any fuch, nor had we, in modern Europe, till, 

 after the time of Petiscus, who wrote about the end of the cen- 

 tury juft mentioned. 



5. Next, as to the extent and accuracy of thefe tables. The 

 firfl of them exhibits the fines to every twenty-fourth part of 

 the quadrant, that is, the fine of 3°. 45', and of all the multiples 

 of that arch, viz. 7°. 30', 11*. \^\l^c. up to 90°. The table of 

 verfed fines does the fame. In each, the fine, or verfed fine, is 

 expreffed in minutes of the circumference, but without any frac- 

 tions of a minute, either decimal or fexagefimal ; and^ agreeably 

 to the obfervation already made, when the fradion that ought 



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