4trO GEOMETRT. 



CaS£ 2 — J^hen A is out of the Circumference. 



From the given point A 

 draw Ao to the centre, which 

 bisect in the point m. With 

 the centre w, and radius m A 

 or 771 o, describe ail arc, cut- 

 ting the given circle in n. 

 Through the points A and n 

 draw the tangent B C. 



TS^^ 



PROBLEM XV, 

 ^0 find a third ProportioJtal to two given Lines AB, AC. 



Place the two given lines, AB, 

 A C, making any angle at A, 

 and join BC. In AB take AD 

 equal to AC, and draw DE par- 

 allel to B C. So shall AE be 

 the third proportional to AB and 

 AC. 



That is, AB : AC :: AC : 



A. 

 A- 



.a: 



A^. 



^B 



PROBLEM XVl. 



To find a fourth Proportional to three given Lines AB, 

 AC, AD. 



Place two of them, A B, AC, A- 

 so as to make any an^lc at A, and '^' 

 join B C. Place AD on A B, and 

 draw D E parallel to BC. So shall 

 A £ be the fourth proportional re- 

 quired. 



That is, A^ ; AC ;; AD : AE. 



JV 



-D 



-B 



JB 



PROBLEM 



