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9. 1, Roma, 1, 12, 1
68
The Jaina Antiqury
(Vol. XVII
355 TIS
The value -= which is the third convergent has been very rarely used by Hindu mathematicians and astronomers. This value has been called the Chinese value of as it occurs in the works of Chinese scholars about the seventh century A. D.
Virasena the author of the Dhavala completed his work on 8th October, 816 A. D. He uses the volue == and in support quotes the following from a previous author:
Vyasam sodasagunitam sodasasahitali
tri rupa-rupairbhaktam |
Vyasam trigunitasahitam sukṣmadapi
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113
16 D+16
113
tadbhavetsük şmali I
The literal translation of the above, according to modern sanskrit usage, will run as follows:
"The diameter multiplied by sixteen added by sixteen (and) divided by three one-one, together with three times the diameter is finer than the fine (value of the circumference)"
This gives
C=3D+
wher C stands for the circumference and D the diameter of a circle. Virasena, however, interprets the above as
C = 3D+
-
16 D 355 D 113 16. 835
113
113
ic.as 3
Virasena's interpretation, however. cannot be correct unless "Soday asahitam" in the first line is interpreted to mean "added sixteen times". so that the translation of the couplet would run as follows:
"The diameter multiplied by sixteen, (that is) added sixteen times (and) divided by three-one-one together with three times the diameter is finer than the fine (value of the circumference)."
Now, the term "Sahitam" was used in the sense of addition as well as "multiplication", i. e. "repeated addition a number of times” in the Velanga jyotiga but has not been used in that double sense by Aryabhata (499) and suceeding mathematicians. This leads one to conclude that the above quotation is from some work written before the fifth century A. D., when "Sahilah" was being used in hoth the senses of multiplication as well as addition. It would appear,
