JPHYSICAL AND LITERARY. 109 



CE, CF, meeting CE, CF in H, K ; and let 

 EL, FM, be tangents to the circle at the 

 points, E, F. 



Because the points, D, E, F, are given, 

 and the circle is given, the fedor DEF will 

 be given ; and, becaufe the fe6tor EDG is to 

 the fecftor GDF in the given ratio of tn to riy 

 the fedtors, EDG, GDF, will, each of them, 

 be given in magnitude. In the tangent EL 

 take the point L towards F ; fo that, joining 

 HL, the triangle HEL may be equal to the 

 fed:or EDG : again, in the tangent FM take 

 the point M towards E \ fo that, joining KM, 

 the triangle KFM will be equal to the feftor 

 FDG : it is evident, the points, L, M, will be 

 given. Join DL, DM, meeting the circle in 

 N, O ; the point G will fall between the 

 points, N, O. For, becaufe EL, FM, arc 

 tangents to the circle at E, F, the angles 

 HEL, KFM, will be right ; and therefore 

 DH, EL, will be parallel : likeways DK, FM, 

 will be parallel ; therefore the triangles, 

 DEL, HEL, will be equal, and likeways the 

 triangles, DFM, KFM, will be equal : and 

 therefore the triangle DEL will be equal to 

 the fedtor DEG, and the triangle DFM equal 



