A treatise of algebra: wherein the principles are demonstrated ... To which is added, the geometrical construction of a great number of linear and plane problems .. (1809)
Simpson, Thomas, 1710-1761, Palmer (T. & G.) Philadelphia. (1809) bkp CU-BANC, Carey, Mathew, 1760-1839 · Philadelphia, Printed for M. Carey by T. & G. Palmer · leaf 404
D = MN%(^yconstruction) we have2AB X CP = 2AH XMN X ^•- MN2 ; but2AB X CP is = BH2— AH^ (by a knownproperty of triangles) ;therefore BH^ _ AH^ = 2AHxMN+MN% or BH^ = KW + 2AH x MN + MN^ = AH + U^Y{Euc. 4. 2.), consequently BH = AH + MN. ^ E. D. Method of Calculation.In the right-angled triangle ADE… … PROBLEM LXXVIL The base^ the perpendicular^ and the sum of the two sidesbeing given^ to describe the triangle* CONSTRUCTION. Bisect the base AB in C, and in it produced take CDa third proportional to 2AB, and the sum of the sides,MN ; erect DE equal to the given perpendicular, anddraw HE parallel…
Algebra · Geometry
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