41^ 



GEOMETRY. 



PROBLEM XLVr, 4 



To 77iah a Square equal to a given Rectangle ABGl). 



r 



Produce one side A B, till 

 B E be equal to the other side 

 B C. Bisect A E in o ; on; 

 which as a centre, with radius / 

 Ac, describe a semicircle, and [_ 

 produce B C to meet it at F. ^ 

 On B F make the square B F G H, and it will be equal, to 

 the rectangle A B G D, as required* 



R 



-a 



PROBLEM XLVIK 

 To make a Square equal to two given Squares P and Q. 



Set two sides AB, B C, of 

 the given squares perpendicular 

 fto each other. Join their ex- 

 tremities AC; so shall ths 

 square R, constructed on A C, 

 be equal to the two P and Q^ 

 taken together. 



Note. Circles, or any other similaY figures, are added 

 in the same manner. For if A B and B C be the diame- 

 ters of two circles, A C will be the diameter of a circle 

 equal to the other two. And if AB and B C be the like 

 sides of any two similar figures, then A C will be the like 

 side of another similar figure equal to the two for- 

 mer, and upon which the third figure may be constructed, 

 "by Problem rSiu 



PROBLEM 



