Pāṭīgaṇitam of Śrīdharācārya

Śrīdharācārya's Pāṭīgaṇitam deals with arithmetic and mensuration to cater the needs of both students and businessmen and is the author's bigger work on the subject.

Contents

Pāṭīgaṇitam is divided into two main sections viz., logistics and determinations.

These are as follows:

Logistics

Here are the 29 parikarmas (logistics) arranged as follows:

(1) saṅkalita (addition), (2) vyavakalita (subtraction), (3) pratyutpanna (multiplication), (4) bhāgahāra (division), (5) varga (square), (6) varga-mūla (square root), (7) ghana (cube), (8) ghana-mūla (cube root), (9-16) the same operations for fractions,

(17-22) reduction of fractions (kalā-savarṇa) of six varieties, viz.

(i) bhāga (fractions connected by + or - ),

(ii) prabhāga (fractions connected by "of "),

(iii) bhāga-bhāga (a whole number divided by a fraction),

(iv) bhāgānubandha (a whole number increased by a fraction, or a fraction increased by a fraction of itself),

(v) bhāgāpavāha (a whole number diminished by a fraction, or a fraction diminished by a fraction of itself), and

(vi) bhāgamātā (a blending of two or more fractions of previous forms),

(23) trairāśika (rule of three), (24) vyasta-trairāśika (inverse rule of three), (25) pañca-rāśika (rule of five), (26) sapta-rāśika (rule of seven), (27) nava-rāśika (rule of nine), (28) bhāṇḍa-prati-bhāṇḍa (barter of commodities), and (29) jīva-vikraya (sale of living beings).

Determinations

The nine vyavahāras (determinations) arranged as follows:

(1) miśraka (mixtures), (2) śreḍhī (series), (3) kṣetra (plane figures), (4) khāta (excavations), (5) citi (piles of bricks), (6) krākaca (sawn pieces of timber), (7) rāśi (heaps or mounds of grain), (8) chāyā (shadow), and (9) śūnya-tatva (the mathematics of zero).

In mixtures of things (miśraka), Śrīdharācārya deals with (i) simple interest, (ii) alligation of gold, (iii) partnership, (iv) purchase and sale, (v) meeting of two travellers, (vi) wages and payments, (vii) the well-known cistern problem, (viii) wages paid out of the commodity, (ix) combination of savours, and (x) certain special problems reducing to the solution of simple and quadratic equations. In series (śreḍhī) he deals with arithmetic and geometric series as well as with series of squares, cubes, and successive sums of series in arithmetic progression. In the surviving part of the section dealing with plane figures, he gives rules for finding the areas of triangles and quadrilaterals.

Special Features

The following are the special features of the Pāṭīgaṇita:

(1) Rule for reducing a chain of measures. (Rule 42)

(2) A special rule for finding the time in which a sum lent out on simple interest will be paid back by equal monthly installments. (Rule 49-50). Also the example set on this rule. (Ex. 55-56).

(3) Interpretation of arithmetic series both geometrically and symbolically. (Rules 79-93)

(4) Rule telling us how two travellers starting at different times with different speeds and accelerations would meet two times on the way. (Rule 97-98)

See Also

श्रीधराचार्य की 'पाटीगणितम्'