Indian Mathematics c7.46

c7.46

This figure is sometimes termed "Brahmagupta's trapezium." From the triangles (3, 4, 5) and (5, 12, 13) a commentator obtains the quadrilateral (39, 60, 52, 25), with diagonals 63 and 56, etc. He also introduces a proof of Ptolemy's theorem and in doing this follows Diophantus (*iii*, 19) in constructing from triangles (a, b, c) and (α, β, γ,) new triangles (aγ, bγ, cγ,) and (ac, β c, γ c,) and uses the actual examples given by Diophantus, namely (39, 52, 65) and (25, 60, 65).