Baudhāyana Sulba Sūtra says:
dīrghasyākṣaṇayā rajjuḥ pārśvamānī, tiryaḍam mānī,
cha yatpṛthagbhūte kurutastadubhayāṅ karoti.
A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.
This appears to be referring to a rectangle, although some interpretations consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides. If restricted to right-angled isosceles triangles, however, it would constitute a less general claim, but the text seems to be quite open to unequal sides.
If this refers to a rectangle, it is the earliest recorded statement of the Pythagorean theorem.
Baudhāyana 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.
dīrghasyākṣaṇayā rajjuḥ pārśvamānī, tiryaḍam mānī,
cha yatpṛthagbhūte kurutastadubhayāṅ karoti.
A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.
This appears to be referring to a rectangle, although some interpretations consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides. If restricted to right-angled isosceles triangles, however, it would constitute a less general claim, but the text seems to be quite open to unequal sides.
If this refers to a rectangle, it is the earliest recorded statement of the Pythagorean theorem.
Baudhāyana 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.
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