PROBLEMS. 413 



circumference ; and A B, carried round five times, will 

 ^?0J the pentagon. Also the arc A B, bisected in S, wiU 

 give A S> the tenth part of the circumference, or the side 

 of the dcc:igon. 



Another Method, 



Inscribe the isosceles triangle ABC, -^- 



having each of the angles ABC, 

 A C B, double the angle B A C. Then 

 bisect the two arcs A D B, A E C, in 

 the points D, E ; and draw the chords 

 AD, DB, AE, EC ; so shall ADB 

 QE be the inscribed pentagon re- 

 quired. And the decagon is thence obtained as before. 



Note. Tangents, being drawn through the angular 

 points, will form the circumscribing pentagon or decagon. 



P ROLL EM XXXVII. 



STo divide the Circumferc7ice of a given Circle into tivdve equal 

 Parts y each being 30 D egret's. 



Or to iiiscribe a Dodecagon by another Method, 



Draw two diameters i 7 and 

 and 4 10 perpendicular to each 

 other. Then, with the radius of 

 the circle, and the four extremi- 

 ties I, 4, 7, 10, as centres, de- 

 scribe arcs through the centre of 

 the circle j and they will cut the 

 circumference in the points re- 

 quired, dividing it into 12 equal parts at the points marked 

 'Svith the numbers. 



PROBLEM 



