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

INTRODUCTION xi
According to Brahmagupta there are twenty logistics
and eight determinations. He says :
"He who distinctly and severally knows the twenty
logistics, addition, etc., and the eight determinations ending
with shadow, is a mathematician."¹
The twenty logistics, according to Brahmagupta's com-
mentator, Pṛthûdakasvâmî, are : (1) saṅkalita (addition), (2)
vyavakalita (subtraction), (3) pratyutpanna (multiplication), (4)
bhâgahâra (division), (5) varga (square), (6) varga-mûla (square
root), (7) ghana (cube), (8) ghana-mûla (cube root), (9-13)
pañca-jâtayaḥ (five varieties of reduction of fractions), (14)
trairâśika (rule of three), (15) vyasta-trairâśika (inverse rule of
three), (16) pañca-râśika (rule of five), (17) sapta-râśika (rule
of seven), (18) nava-râśika (rule of nine), (19) ekâdaśa-râśika
(rule of eleven), and (20) bhâṇḍa-pratibhâṇḍa (barter of com-
modities). The eight determinations are : (1) miśraka
(mixtures), (2) śreḍhî (series), (3) kṣetra (plane figures), (4)
khâta (excavations), (5) citi (piles of bricks), (6) krâkacika
(saw problems), (7) râśi (heaps or mounds of grain), and (8)
châyâ (shadow).
More or less the same topics have been recognized by
the other writers also.
3. WORKS OF SRIDHARACARYA. Śrîdharâcârya
is the only author who wrote two works dealing exclusively
with arithmetic and mensuration, viz., the Pâṭîgaṇita and the
Pâṭîgaṇita-sâra (‘Abstract of the Pâṭîgaṇita’). These names
were given to those works by the author himself. For in the
opening stanza of the former, he says :
"Having paid obeisance to the Unborn God, the cause
of creation, preservation, and destruction of the worlds, I shall
briefly state the (pâṭî)gaṇita for the use of the people."
And in the opening stanza of the latter, he says :
¹ BrSpSi, xii. 1.