Indian Mathematics c7.32

c7.32

| | A | B | √(A²+B²) | Authorities. |
| i | n | (n²-1)/2 | (n²+1)/2 | Pythagoras (according to Proclus) |
| ii | √(m n) | (m n)/2 | (m+n)/2 | Plato (according to Proclus) |
| iii | 2 mn | m²-n² | m²+n² | Euclid and Diophantus. |
| iv | (m (n²-1))/(n²+1) | 2mn/(n²+1) | m | Diophantus. |
| v | 2 mn | m²-n² | m²+n² | Brahmagupta and Mahāvīra. |
| vi | √m | ½(m/n-n) | ½(m/n+n) | Brahmagupta, Mahāvīra, and Bhāskara. |
| vii | m | (2 mn)/(n²-1) | (m (n²+1))/(n²-1) | Bhāskara. |
| viii | (m (n²-1))/(n²+1) | (2 mn)/(n²+1) | m | Bhāskara. |
| ix | 2 l mn | l (m²-n²) | l (m²+n²) | General formula. |