Śrīdhara

Śrīdhara, Śrīdharācārya or Śrīdhara Acharya ( c. 870 CE – c. 930 CE) was an Indian mathematician, Sanskrit pundit and philosopher. Śrīdhara was an Indian mathematician who wrote on practical applications of algebra and was one of the first to give a formula for solving quadratic equations.

Śrīdhara is the author of two mathematical treatises, namely the Trisatika (Pāṭīgaṇitasara ) and the Pāṭīgaṇita. Bījagaṇita, Navaśati, and Bṛhatpāṭī  are the other works from Śrīdhara.

Pāṭīgaṇita
Pāṭīgaṇita aims at providing a complete course of arithmetic and mensuration. Logistics and determinations are the two main sections in Pāṭīgaṇita.

Logistics: (1) saṅkalita (addition), (2) vyvakalita (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) kalāsavarṇa (reduction of fractions of six varieties), (23) trairāśika (rule of three), (24) vyasta-trairāśika(inverse rule of three), (25) pañcarāśika (rule of five), (26) sapta-rāśika (rule of seven), (27) nava-rāśika (rule of nine), (28) bhāṇḍa-pratibhāṇḍa (barter of commodities), and (29) jīva-vikraya (sale of living beings).

Determinations: (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.

Pāṭīgaṇitasara (Trisatika )
Pāṭīgaṇitasara is an abstract of the Pāṭīgaṇita.

It gives the important rules and examples of the Pāṭīgaṇita with slight modifications, alterations and additions here and there, and provides a short course of arithmetic and mensuration.

Appreciation of Śrīdharācārya
The works of Śrīdharācārya were so popular which brought a great name to Śrīdharācārya. The following verse which is in appreciation of him both by the Hindus and Jainas gives an idea of the unique position attained by him as a mathematician.

उत्तरतो सुरनिलयं दक्षिणतो मलयपर्वतं यावत् ।

प्रागपरोदधिमध्ये नो गणकः श्रीधरादन्यः ॥

"Up to the abode of the gods (Himalayas) towards the north and up to the Malaya mountain towards the south and between the eastern and western oceans, there is no mathematician except Śrīdhara."