400 A ‘Treatise of Algebra.

Regard being had, at the same Time, to the Methodobserved in the Construction of the preceding Problem.

PROBLEM LXXXI.

The Sum of the Legs of any right-angled Triangle, and theSum of the Hypothenuse and Perpendicular falling fromthe right-angle upon the Hypothenuse , being given ; todescribe the Triangle.

CONSTRUCTION.

Make AC and AD perpendicular to one another, andeach equal to the given Sum of the Legs, and upon the

M

Right Line, CD, joining their Extremities, describe theCircle DCB; also upon D, as a Center, with an Intervalequal to the Sum of the Hypothenuse and Perpendicular,let an Arch be described, cutting AC in n j draw ABperpendicular to CD intersecting the Periphery of theCircle in B, and draw which produce to r, so thatnr may be equal to An, and inscribe the Subtense DE— DR; join A, E and B, E and produce AE to M,so that EM may be equal to EB ; join B, M, and in AEtake Aa — AC, and draw ab parallel to BM, meetingAB in b j also draw ^Q. parallel to AE, intersecting

EB