A ̄ryabhat.a I was one of the most influential mathematicians and astronomers
in India through his two works, A ̄ryabhat.ı ̄yaandA ̄ryabhat.asiddha ̄nta.The latter
work is not extant but has been referred to by many later scholars. The work
mainly influenced northwestern India. It is also known to have had some influ-
ence upon the Sasanian and Islamic astronomy. The A ̄ryabhat. ̄yaı , on the other
hand, mainly influenced south India.
A ̄ryabhat.a I was born in ad476. This is known from his own statement in
theA ̄ryabhat.ı ̄ya(3.10): “When sixty of sixty years and three quarters of the
Yuga had passed, then twenty-three years had passed here from my birth.” That
is, he was 23 years old in ad499 (= 3600 - 3101, since the last quarter, called
Kaliyuga, of the current Yuga began in 3102 bc). The year mentioned here, ad
499, is usually taken to refer to the date of the composition of the A ̄ryabhat. ̄ya.ı
TheA ̄ryabhat.ı ̄yais divided into four “quarters” (pa ̄das), that is,
1 Quarter in Ten Gı ̄ti verses,
2 Quarter for Mathematics (gan.ita, in 33 A ̄rya ̄ verses),
3 Quarter for Time-Reckoning (ka ̄lakriya ̄, in 25 A ̄rya ̄ verses), and
4 Quarter for Spherics (gola, in 50 A ̄rya ̄ verses).
Chapter 1 consists of 13 verses. The first verse contains the author’s salute to
God Brahma ̄ and refers to the three fields to be treated in the next three chap-
ters. The second verse defines an alphabetical notation of numbers. The next ten
verses (the words, “ten Gı ̄ti verses,” in the title of this chapter refer to this part)
contain tables of astronomical parameters and of sine-differences expressed in
that notation. For example, the number of the sun’s revolutions in a yuga,
4320000, is expressed as khyughr.=(2+30)¥ 104 + 4 ¥ 106.
Chapter 2 of the A ̄ryabhat. ̄yaı is the oldest extant mathematical text in San-
skrit after the S ́ulbasu ̄tras. Although the chapter does not have a clear division
into sections, it may be divided into four parts:
i. Rules for basic computations (vv. 2–5),
ii. Rules for geometric figures (vv. 6–18),
iii. Rules for both figures and quantities (vv. 19–24), and
iv. Rules for numerical quantities (vv. 25–33).
A ̄ryabhat.a gives the names of the first 10 decimal places, and says: “·EachÒ
place shall be ten times greater than ·the previousÒplace.”
Problems of proportion were solved by means of the traira ̄s ́ika or “the ·com-
putationÒrelated to three quantities.” The traira ̄s ́ika was not only indispensable
for astronomy but also essential for monetary economy. The first of the seven
examples for the traira ̄s ́ika supplied by the commentator, Bha ̄skara I, is this: “Five
palasof sandal-wood were bought by me for nine ru ̄pakas.Then, how much of
sandal-wood can be obtained for only one ru ̄paka?” The palaand the ru ̄pakaare
units of weight and money, respectively.
The last rule provides a general solution called kut.t.akaor “pulverizer” to an
indeterminate system of linear equations of the following type: “When a certain
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