Page:Indian mathematics, Kaye (1915).djvu/20

 9. The Pañcha Siddhāntikā contains material of considerable mathematical interest and from the historical point of view of a value not surpassed by that of any later Indian works. The mathematical section of the Pauliśa Siddhānta is perhaps of the most interest and may be considered to contain the essence of Indian trigonometry. It is as follows:— "(1) The square-root of the tenth part of the square of the circumference, which comprises 360 parts, is the diameter. Having assumed the four parts of a circle the sine of the eighth part of a sign [is to be found]. "(2) Take the square of the radius and call it the constant. The fourth part of it is [the square of] Aries. The constant square is to be lessened by the square of Aries. The square-roots of the two quantities are the sines. "(3) In order to find the rest take the double of the arc, deduct it from the quarter, diminish the radius by the sine of the remainder and add to the square of half of that the square of half the sine of double the arc. The square-root of the sum is the desired sine." [The eighth part of a "sign" (=30°) is 3° 45' and by "Aries" is indicated the first "sign" of 30°.] The rules given may be expressed in our notation (for unit radius) as They are followed by a table of 24 sines progressing by intervals of 3° 45' obviously taken from 's table of chords. Instead, however, of dividing the radius into 60 parts, as