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(iii) Mahā-siddhānta (=MS), XV, 90, of Aryabhata II(c.950 A.D.)
as an approximate rules.
(iv) Tiloyasāra =(TS), gātha 760 (second half), of Nemicandra
(10th century) in the following Prakrit words?. bāņakadim chahi guņide tattha jude dhanukadi hodi || 760 // (bāņakrtim șadvih guņite tatra yute dhanuh kytih bhavati) ‘Six times the square of the bāņa (height of the segment) added there (to the square of the chord stated in the first half of the gāthā) becomes the square of the arc (of the segment).' That is, s2 =c2 +6 h
... (11)
(v) Jambū-paņņatti-samgaho (=JPS), II, 24, and VI, 10, of Pad
ma nadie.
The JPS, II, 28 (p. 13) gives the form (11) and states that it was said so by Jinendradeva.
If we use the relation (4) which was well-known to ancient Indians (including the authors mentioned above), then the formula (10) can be written as s=V [2 {(d+h)a=d2}]
... (12)
A rule which gives this formula is found in the Tiloya-paņņati (=TP), IV, 181, of Yativrsabha as follows:
• MS edited by Sudhakara Dvivedi, p. 171 (fasciculus II), Benares, 1910 (Benares
Sanskrit Series Nos. 148-150). ? The TS (Sanskrit, Trilokasara) edited by Manohar Lal Sastri, p. 303, Bombay,
1918 (Manik Chand Digambar Jain Granthamala No. 12). & JPS edited by A. N. Upadhye and Hiralal Jain, pp. 12 and 101 ; Sholapur 1958
(Jain Samskriti Samrakshaka Sangha). According to the editors (Introduction p. 14), Padmanandi might have composed the JPS about 1000 A.D. The present author has noted several other direct and indirect references to the formula (10) both in Jaina and non-Jaina works. But it seems unnecessary to quote them all here. TP (Sanskrit, Triloka-prajnapti), Part I, edited by A. N. Upadhye and Hiralal Jain, Second edition, Sholapur, 1956, p. 163; also Part II, 1951. According to Dr. Upadhye (TP, Vol. II, Introduction, p. 7) the TP is to be assigned to some date between 473 A.D. and 604 A.D. However, the work may have acquired its present form as late as about the beginning of the ninth century (TP, Vol. II, Hindi Introduction, p. 20).
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