Sridhara

He is known for two main treatises: Trisatika (300) and the Pāṭīgaṇita (পাটীগণিত). It was written in three hundred ślokas thus his major work Pāṭīgaṇitasāra was named Triśatika. The book discusses about counting of numbers, natural number, zero, measures, multiplication, fraction, division, squares, cubes, rule of three, interest-calculation, joint business or partnership and mensuration (the main part of geometry concerned with ascertaining sizes, lengths, areas, and volumes). Three other works have been attributed to him, namely the Bījaganita, Navasatī, and Bṛhatpati

• He gave an exposition on the zero. He wrote, "If zero is added to any number, the sum is the same number; if zero is subtracted from any number, the number remains unchanged; if zero is multiplied by any number, the product is zero".
• In the case of dividing a fraction he has found out the method of multiplying the fraction by the reciprocal of the divisor.
• He wrote on the practical applications of algebra
• He separated algebra from arithmetic
• He was the first person to give a formula for solving quadratic equations.

${\displaystyle ax^{2}+bx+c=0}$

Multiply both sides by 4a,

${\displaystyle 4a^{2}x^{2}+4abx+4ac=0}$

Subtract 4ac from both sides,

${\displaystyle 4a^{2}x^{2}+4abx=-4ac}$

Add ${\displaystyle b^{2}}$ to both sides,

${\displaystyle 4a^{2}x^{2}+4abx+b^{2}=-4ac+b^{2}}$

Since

${\displaystyle (m+n)^{2}=m^{2}+2mn+n^{2}}$

Complete the square on the left side,

${\displaystyle (2ax+b)^{2}=b^{2}-4ac={D}}$

Take square roots,

${\displaystyle 2ax+b=\pm {\sqrt {D}}}$

${\displaystyle 2ax=-b\pm {\sqrt {D}}}$

and, divide by 2a,

${\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac\ }}}{2a}}.}$

• O'Connor, John J.; Robertson, Edmund F., "Sridhara", MacTutor History of Mathematics archive, University of St Andrews.
• The Date of Sridharacharya by S. Srikanta Sastri, The Jaina Antiquary (Jan, 1948)