Baudhayana Shrauta Sutra by Baudhayana (800BC) has detailed explanation of the Pythagorean theorem for an isosceles right triangle,Pythagorean triples discovered algebraically, and the statement of the Pythagorean theorem.
Baudhāyana Sulba Sutra says:
dīrghasyākṣaṇayā rajjuH pārśvamānī, tiryaDaM mānī,
cha yatpṛthagbhUte kurutastadubhayāṅ karoti.
A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.
Baudhayana also provides a non-axiomatic demonstration using a rope measure of the reduced form of the Pythagorean theorem for an isosceles right triangle: The cord which is stretched across a square produces an area double the size of the original square.
Apastamba Sulba Sutra (600BC) too has detailed explanation of the theorem.
Pythagoras is believed to have used algebraic methods to construct Pythagorean triples sometime during 569–475 BC.