384 Mathelnatieal CorrefpsnJdh-t. 



For, draw AD and CD.— Then the trlatigle GBE being fimllar to ABD, and GBF to 

 CBD, we have AB ( = FB) : j AB ( = FG) :: * : ^ :: BD : CD and BC ( = BE) : | BC 



( = EG) :: b :a :: BD : AD. Therefore AD, BD and CD being as a, b, and <: refpec- 

 tively, the point D is rightly found. Q^E. D. 



Hence alfo, if with AD ( : AB :: EG : BG) and CD ( : CB :: FG : BG) as rpdii, arcs 

 be defcribed about A and C, they will interfeft each other, and each of them will in- 

 terfcft GB produced in tlie required point. 



CALCULATION. 



FROM the values of FB, BE, FE, FG, and EG, find BG trigonometrically, and from 

 thence AD, BD, or CD. 



THIS quedion was anfwered In nearly the fame manner by Analtticus, who obferves, 

 that if the three ftations are at unequal diftances from the objea, its apparent altitude will 

 vary at each of them, according 10 the effeft of refraflion, and of courfe occafion a three- 

 fold error in the rcfult ; which may be avoided by taking the ftations fo that the angles of 

 elevation fhall be all equal, in which cafe a fingle refraftion only will be concerned, which 

 indeed is fufEcient to render this, or any other fimilar method of determining the heights of 

 terrenrial objeds, very inaccurate. If, befides the angles of elevation, thofe formed by the 

 bafe and hypothenufes drawn from each extremity of it, to the top of the objed, be taken, 

 there is no occafion for more than two ftations ; which being chofen in fets, in the way laft; 

 mentioned, will enable us to afcertain the difference of refradion at different diftances. 



