PROPERTIES of the CIRCLE. 37 
equal to the fum of the fquares on the three parts, into which 
the other is cut. 
SoLUTION. 
Wirn 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 rit, the perpendiculars drawn to 
the 3d and sth 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 {quares of the other three. And if they 
be drawn from a point in the circumference equally diftant 
from two points of contact, the 1ft = the 6th, the 2d = the sth, 
and 3d = the 4th. 
Acatn, 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 
fu of the {quares.of the parts of the one fhall be equal to the 
fum of the fquares of the parts ofthe 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. ebay 
SOLUTION. 
