**Brahmagupta** (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 .

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

for some rational numbers *u*, *v*, and *w*.

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