PROPERTIES of the CIRCLE. 37 



equal to the fum of the fquares on the three parts, into which 

 the other is cut. 



Solution. 



With radius equal to one-third part of either of the given 

 lines defcribe a circle. If a regular hexagon circumfcribe it, per- 

 pendiculars drawn from the point where any fide of the hexagon 

 touches the circle, to the other five fides, are refpectively equal 

 to the parts into which the two given equal right lines are requi- 

 red to be divided. Calling the fide, from a point in which the 

 perpendiculars are drawn, the ift, the perpendiculars drawn to 

 the 3d and 5th are the parts, into which one of the two equal gi- 

 ven right lines is cut, and thofe drawn to the 2d, 4th, and 6th 

 fides, the three parts into which the other given line is cut. 



N. B. If the perpendiculars be drawn from any point in the 

 circumference, that is not one of the points of contact, three of 

 them taken alternately, are together equal to the other three, and 

 equal to either of the given lines, and the fum of their fquares 

 equal to the fum of the fquares of the other three. And if they 

 be drawn from a point in the circumference equally diflant 

 from two points of contact, the ift zr the 6th, the 2d — the 5th, 

 and 3d = the 4th. 



Again, let it be required to divide each of two equal given 

 right lines into four unequal parts, fo that none of the parts of 

 the one fhall be equal to any of the parts of the other, but the 

 fum of the fquares of the parts of the one mail be equal to the 

 fum of the fquares of the parts o£ the other, and alfo the fum 

 of the cubes of the parts of the one equal to the fum of the cubes 

 of the parts of the other* 



Solution. 



