पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

vi INTRODUCTION
mathematics and is called Gaṇita-pâda, but this is too brief
and does not give a clear idea of the state of mathematical
knowledge in India in those times. According to Bhâskara I,
the most competent scholiast of Âryabhaṭa I, the subject-
matter discussed by Âryabhaṭa I in his Gaṇita-pâda hardly
deserves the name mathematics (gaṇita). He has preferred to call
it 'a bit of mathematics.' He writes : "In the Gaṇita-pâda
the Âcârya (Âryabhaṭa) has dealt with the subject of mathe-
matics (gaṇita) by indications only, whereas in the Kâlakriyâ-
pâda and Gola-pâda¹ he has discussed 'reckoning with time'
(kâlakriyâ) and 'spherical astronomy' (gola) in detail. So by
the word gaṇita (used by Âryabhaṭa) one must understand 'a
bit of mathematics.' Otherwise, the subject of mathematics is
vast. There are eight vyavahâras (determinations), miśraka
(mixtures), śreḍhî (series), kṣetra (plane figures), khâta (excava-
tions), citi (piles of bricks), krâkacika (saw problems) and châyâ
(shadow). The miśraka is that which involves the mixture of
several things. The śreḍhî is that which has a beginning (i.e.,
first term) and an increase (i.e., common difference). The
kṣetra tells us how to calculate the area of a figure having
several angles. The khâta enable us to know the volumes of
excavations. The citi tells us the measure of a pile in terms
of bricks. The krâkacika : The krâkaca (saw) is a tool which
saws timber ; that which relates to the sawing of timber, i.e.,
that which tells the measure of the timber sawn, is called
krâkacika (vyavahâra). The râśi tells us the amount of a heap
of grain, etc. The châyâ tells us the time from the shadow of
a gnomon, etc. Of the vyavahâra-gaṇita (practical or commer-
cial mathematics, i.e., pâṭîgaṇita), which is thus of eight
varieties, there are four bîjas, viz., first, second, third, and
fourth, i.e., yâvattâvat ('theory of the simple equation'), vargâvarga
('theory of the quadratic equation'), ghanâghana ('theory of the
cubic equation'), and viṣama ('theory of the equations with
several unknowns'). Rules and examples pertaining to each
one of these have been compiled (in independent works) by
¹ These are the names of chapters three and four of the Âryabhaṭîya.