4^4 



PROBLEM XXXVIII. 



To divide a given Circle into any proposed Numher of Parts hy 

 equal LineSy so thai those Parts shall he piutually eqtmly both 

 in Area a:;d Perimeter. 



Divide the diameter Ah into 

 the proposed number of equal 

 parts at the points ^, by r, &c. 

 Thenon Afl, hb, Ar, &c. as diam- 

 eters, describe semicircles on one 

 side of the diameter A B ; and 

 on Vtd, Br, B^, &c. describe 

 semicircles on the other side of 

 the diameter. So shall the corresponding joining semi- 

 circles divide the given circle in the manner proposed. 

 And in like manner we may proceed, when the spaces are 

 to be in any given proportion. As to the perimeters, 

 they are always equal, whatever may be the proportion o( 

 the spaces. 



PROBLEM XXXIX. 



On a given Line AV> to describe the Segment of a Circl^^ 

 capable of containing a given Angle, 



Draw AC and BC, making the 

 angles BAG and ABC each equal 

 to the given angle. Draw A D 

 perpendicular to AC, and BD per- 

 pendicular to B C. With centre 

 D, and radius D A, or D B, de- 

 scribe the segment AEB. Then 

 any angle', as E, made in that seg- 

 ment, will be equal to the given 

 angle. 



PROBLEM 



