y20 ESSAYS Anp OBSERVATIONS 
Because the points, D, FE, F, are givert, 
and the circle is given, the feGtor DEF wilk 
be given ; and, becaufe the fe€tor EDG is 
to the fector GDF in the given ratio of m 
to n, the fectors 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 fector EDG: Agaia, 
in the tangent FM take the point M to- 
wards E, fo that, joining KM, the trian- 
‘ gle KFM will be equal to the feCtor 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, are 
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 trian- 
gles DEL, HEL, will be equal, and like- 
ways the triangles DFM, KFM, will be 
equal: And therefore the triangle DEL 
will be equal to the fector DEG, and the 
triangle DFM equal to the fe@tor DFG; 
therefore the fector DEG will be greater 
than 
