पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

84 PAÑCASIDDHĀNTIKĀ IV. 15 ‘मनुविषयतिथिरसा:’ स्युस्त्रिगुणाः पञ्चाष्टकं ‘स्वरोपेतम्’ | सप्तदशनवपञ्चकं षोडश चेति क्रमान्मिथुने || १५ || 15. The seconds of the intervals in the third sign, are, 3 × 14, 3 × 5, 3 × 15, 3 × 6, 5 × 8 + 7, 17, 9 × 5 and 16. The intervals can be got by deducting the previous sines from the succeeding ones, and com- pared with the author’s concern for correctness, they are correct. It is to be noted that the intervals of TS also come correct in the third sign, because there is a uniform error of 1″ in all sines. The intervals are as tabulated:

No.	0	1	2	3	4	5	6	7
Int.		7′ 51″	7′ 49″	7′ 45″	7′ 39″	7′ 30″	7′ 22″	7′ 9″
No.	8	9	10	11	12	13	14	15
Int.	6′ 55″	6′ 40″	6′ 23″	6′ 4″	5′ 44″	5′ 22″	4′ 59″	4′ 34″
No.	16	17	18	19	20	21	22	23
Int.	4′ 9″	3′ 42″	3′ 15″	2′ 45″	2′ 18″	1′ 47″	1′ 17″	0′ 45″
No. 24
Int. 0′ 16″
These intervals are useful for interpolation. The method of interpolation has not been given by
the author, as being obvious. The intervals being increments in the series for successive increments
in the arcs (or angles) of 3° 45′, we can find the value for what is left over after taking the tabular
value, by proportion, and adding it to the tabular value find the value wanted, whether it is arc for
sine, or sine for arc.
Further, the author has given the sines of arcs upto 3 signs, as usually given in tables. But the
method to compute the sines of arcs greater than three signs, has not been mentioned by him.
We shall find a method. The circle is divided into four quadrants (Fig. 3), AOB, BOC, COD and
DOA, each quadrant being three signs. Arcs AE = HC = CK = GA, from which their sines, EF =
HJ = JK = GF. But, since the sines increase in the first quadrant from O at A to BO (= 120′) and
then decrease in the second quadrant from 120′ to O at C and again increase in the third quadrant
to DO (= 120′) and then again decrease in the fourth quadrant to O at A, sine AE = sine AH = sine
15a. B. मुनि विषय. A.om स्यु c. B. ०दशन्वपञ्चकके
b. B. त्रिगुणा पञ्चाष्टक d. A. ०मिने (i.e. on थु)