cf aefecled Equations. 4.75 
two angles are 10.3343832 and 10.0857536, which being re- 
fpe&ively increafed by 9.9208188 and 9.7446275, the two 
conftant logarithms, make 0.2552020 and 9.8304811, which 
are the logarithms of 1.7997079 and .6768323 ; and the dif- 
ference of thefe two numbers is 1.1228756, which is lefs than 
the difference of the log. co-tangents by .0954226. 
I next aflame the angles 30° and 52 0 45' ; and by pnrfiiing 
the fame fteps which have been deicribed above, I find the dif- 
ference of their co-tangents exceeds the difference of the pro- 
ducts by .0028987. Then, as 925239 (the difference of the. 
errors) is to 145' (the difference of fuppofitions), fo is the latter 
error 28987 to 4' which being added to 30°, gives 
30° 4' 33' v for the next affumption of the angle dCI ; but for 
eafe in the computation I fhall take 30° 5'' ; in which cafe the 
angle DCI will be 52 0 40' ; and by repeating the operation the 
difference of the co-tangents will be found lefs than the dif- 
ference of the products by .0002425. And 5 1412 (the fum of 
the two laid errors) is to 5' (the difference of the fuppofitions) 
as 2425 (the laid error) is to 23" ; which being taken from 
30° 5', the laft fuppofition, becaufe it was too great, leaves 
30° 4' 37" for the exact value of the angle dQl. 
This equation, like that in the fourth example, when the 
value of y is properly fubflituted, and the equation reduced in 
the ufual manner, will rife to four dimenfions with all the 
inferior ones ; and it does not appear, that either huygens, . 
slusxus, Mix robins, Dr. WILLSON, or. ProfeiTor sims.on, 
with all their artifice, have been able to deprefs it : but by this 
method of refolution the point of reflection is found, with the 
greateA exaCtnefs, in much lefs time than this fubftitution and 
reduction can be made. And this example farther fuggefls to 
us, that when the anfwer is fought by the method now under 
conib 
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