GEORGIVM SIDUS. 319 



computation muft be exceedingly near the truth, becaufe the 

 ellipfe is very near the truth. But the trouble of this previous 

 conftrudlion may be avoided by means of the following confi- 

 derations : The triangles xFc, <?Gd, are nearly fimilarj and 

 therefore, cF : dG =. AE 1 : CE 2 nearly ; therefore the trian- 

 gle xcF : <?Gd = AE 4 : CE 4 nearly; alfo, Sc = Sd nearly; 

 therefore, Cc : Dd (or, ?F : ?G =) AE 4 : CE 4 nearly ; but AE 

 is nearly double of CE j therefore, ?F : y.G = 16 : i nearly ^ 

 alfo, ?F : X H 16 : i nearly. 



Now, CS : Cy Jin. y '-Jin. x r 



and Cy : Ey = Cy : Ey, 



and Ey : ES =.Jln.y :Jin.y, 



therefore, CS : ES = Cy xjin. y : Ey Xjin. x. 



Let ,CS : eS Jin.y '.Jin. x, 



then, ES : eS = Ey*: Cy, 



and ES : Ee - Ey : Cy Ey, = Ey : 2yG. 



IN like manner, make CS : aS Jin. u : fin. v, and we fhall 

 have AS : Aa AX ' 2 X H nearly, = Ey : 2yG nearly, "and 

 Ee : Aa = ES : AS nearly, and therefore Ee nearly equal to 

 Aa. 



Make AS : So ~Jin. z '.Jin. iv, 



then, (becaufe SE : AS E<pxjin. w : Apxjin. z) 



we have SE : So E^ : Af, 



and SE .: Eo = Ep : A^ Ef, =r. A^ : 2^F nearly, 



or SE : Eo = 2Ey : 32yG, = Ey : i6yG nearly^ 



Hence it follows that Eo is nearly equal to eight times Ee, 



Lajlly, Make aS : St Jin. z \fin. iv, then we fhall have 

 aS : S = AS : So, and Aa : o = AS : SE, and therefore o 

 nearly equal to Aa, or to Ee j therefore e is nearly fix times 



HENCE 



