See2Learn Gaṇita

The Fact: In a rectangle, the sum of the squares of a side and of the height is equal to the square of the diagonal. The rationale as given in Gaṇita-yukti-bhāṣā of Jyeṣṭhadeva. History Manava śulva sūtra states: आयाममायामगुणं विस्तारं विस्तरेण तु । समस्य वर्गमूलं यत्तत्कर्णं तद्विदो विदुः | ಆಯಾಮಮಾಯಾಮಗುಣಂ ವಿಸ್ತಾರಂ ವಿಸ್ತರೇಣ ತು | ಸಮಸ್ಯ ವರ್ಗಮೂಲಂ ಯತ್ತತ್ಕರ್ಣಂ ತದ್ವಿದೋ ವಿದುಃ | āyāmamāyamaguṇah vistāram vistareṇa tu/ samasya vargamulam yattatkarṇam tadvido viduh. “Multiply the length by the length and the width by the width. It is known that adding them and taking the square root gives the diagonal of the rectangle.” The exposition here is seen to be focused on computing the size of the hypotenuse from the sizes of the sides, without specific reference to the underlying geometry.

  Two rectangles of equal area.

  A Visual or Demonstrational proof of a geometry fact. The Fact: In a right angled triangle the area of the square on a leg is equal to the area of the rectangle formed by the hypotenuse and the projection of the leg on the hypotenuse. Here is the proof of the above fact for the larger of the legs of a right angled triangle.