no ESSAYS and OBSERVATIONS 



to the fedor DFG; therefore the fedor DEG 

 will be greater than the fedor DEN, and the 

 fedlor DFG greater than the fedtor DFO ; 

 therefore the line DG will fall between the 

 lines, DN, DO j therefore the point G will 

 fall between the points, N, O. 



Again, Becaufe the points, L, M are 

 given, and the point D likeways given, thp 

 fedlors, DEN, DFO, will be given j and, be- 

 caufe the fedors, DEG, DFG, are given, 

 the fedors, DNG, DOG, will be given ; and 

 therefore the fedor NDG will be to the fe- 

 dor GDO in a given ratio, fuppofe that of 

 p to ij. The problem, therefore, will be re- 

 duced to this again. To divide the fedor 

 NDO by the line DG, fo that the fedor 

 NDG may be to the fedor GDO in the gi- 

 ven ratio of /> to q. And thus, repeating the 

 operation, the point G will be found withir^ 

 a very narrow limit. 



N. B. The limit ON might have been 

 found by taking in the tangents, EL, FM, 

 the point L towards F, and the point M to- 

 wards E i fo that, joining DL, DM, meeting 

 the circle in N, O, the triangle DEL would 

 be equal to the fedor EDG, and the triangle 



DFM 



