The Elements of Geometry in General Terms With Notes C C Also a Variety O

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The diagonals (OC and CD) of the squares described on the sides of a right angled triangle, which terminate in the vertex of the triangle, lie in directum.

94 Fig. 69.

Because, in the triangle LOC, the side LO is ga to LC, and the angle OLC a right angle, the angle LCO is half a right angle ; for the same reason the angle FCD is half a right angle, and the angle LCF is a right angle ; . -. The three LCO, LCF, and FCD are = to two right angles;, \ (prop. 14, 1 Elr. ) the right lines OC an

PROP. 151. THEOR.

In figure sixty -nine, the diagonal (CV) of the parallelo- gram (LCFV), formed by producing the sides (DF and L V) of the squares described on the sides of a right an- gled triangle, is in directum with the perpendicular (CT) let fall from the vertical angle on the hypotenuse. Because, in the triangles CLV, and BCA, the side CL is = to BC, the side LV (= CF) = CA, and the angle CLV zz BCA, the angle ABC shall be zz to VCL ; but the angle ABC with BCT is zz to a right angle ; /.

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