On the figure of the EARTH. 315 



FCA is a nghc angle, the angles FAC and AFC will each 

 be half of a right angle. LOT will alfo be half of a 

 right angle, became LO is parallel to AF, and confe- 

 quently LTO is half of a right angle. If then the 

 cllipfis reprefent a meridian of the earth lA and HO vv'ill 

 reprefent the common fedions ot that meridian and the 

 horizons of two places ; and AT, LT two perpendicu- 

 lars to the horizons, and the angle ATL will be the dif- 

 ference of the latitude, (equal to 45°). But A is at the 

 end of one of the axes of the cUipils, and therefore the 

 point L will reprefent a place in the latitude of 45°. 



Since all the degrees of latitude increafe in length as 

 we approach to the pole, it is evident that the arch of 

 450 between the latitude of 45" and^ the pole, will be 

 longer than the arch between the equator and the latitude 

 of 45°. Now draw TS and LN parallel to BC and AC. 

 Make BC = ^, AC = r, LS = r, LN =y, LS=NC, and 

 LN = CS. Then becaufe LOT is half of a right angle, 

 and OSL is a right angle, OLS is alfo half of a right 

 angle, therefore OS is equal to LS. I11 the lame manner 

 we prove HN equal to LN and confequently HC equal 

 to OG, put OC {= X + y) = 6. 



Then by conies y : c : : c : 6 and y = -r and 6 = — 



by 



X : aw a\b and .v = — and h =■ — 



b X 



x = 



