Indian Mathematician and astronomer Brahmagupta

BrahmaguptaBrahmagupta (598–.670 CE)Triangles

Brahmagupta dedicated a substantial portion of his work to geometry. One theorem gives the lengths of the two segments a triangle’s base is divided into by its altitude:

12.22. The base decreased and increased by the difference between the squares of the sides divided by the base; when divided by two they are the true segments. The perpendicular [altitude] is the square-root from the square of a side diminished by the square of its segment. Thus the lengths of the two segments are    sq1.

He further gives a theorem on rational triangles. A triangle with rational sides a, b, c and rational area is of the form:

sq2

 

for some rational numbers u, v, and w.

 

 

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