History of Hindu Mathematics: A Source Book v2.c17.s18.t2.41

v2.c17.s18.t2.41

**Juxtaposition of Right Triangles.** It will be noticed that the device employed by Brahmagupta and Mahâvîra to find the above solutions is to juxtapose two rational right triangles—equal in this case—so as to have a common leg. It is indeed a very powerful device. For, every rational triangle or quadrilateral may be formed by the juxtaposition of two or four rational right triangles. So, in order to construct such rational figures, it suffices to know only the complete solution of x² + y² = z² in integers. The beginning of this principle is found as early as the *Baudhâyana Śulba*¹ (800 B.C.) wherein is described the formation of a kind of brick, called *ubhayî* (born of two), by the juxtaposition of the eighths of two suitable rectangular bricks of the same breadth (and thickness) but of different lengths.