4iz 



GEOMETRY. 



In 



given 



PROBLEM XXXV. 



Circk io inscribe a Irigant a Hexngcn^ or 



Dodecagon. 



The radius is the side of the 

 hexagon. Therefore, from any 

 point A in the circumference, 

 with the distance of the radius, 

 describe the arc BoF. Then is 

 A B the side of the hexagon ; 

 and therefore, being carried 

 round six times, it will form, 

 the hexagon, or divide the cir- 

 cumference into six equal parta, 

 each containing 60 degrees. The second of these, C, 

 will give A C, the side of the trigon, or equilateral tri- 

 angle, and the arc A C one third of the circumference, or 

 120 degrees. Also the half of AB, or ^ ;|> is one twelfth 

 of the circumference, or 30 degrees, an|l gives the side pf 

 the dodecagon. 



Note. If tangents to the circle be drawn through ai' 

 the angular points of any inscribed figure, they will form 

 the $idcs of a like gircumscribing figure. 



PROBLEM XXXVI. 



In a given Circle io inscribe a Pentagon^ or a Decagon, 



Draw the two diame- 

 ters AP, w;/, perpendic- 

 ular to each other, and 

 bisect the radius on at q. 

 With the centre q^ and 

 radius q A, describe the 

 arc A r ; and with the 

 centre A, and radius Ar, 

 describe the arc rB. Then 

 is A B one £fth of the 



circumference \ 



