( ,i6o y 
TbeUoots of thefe cubic Equations ate found by 
feeking the firft of two mean Proportionals, between 
each of the verfed Sines appertaining to the Arches 
C G, A G, and the Sine of thofe Arches, counting 
from the verled Sines ; for the Sum of thele two mean 
Proportionals is the Root of the former Equation, and 
the difference between them the Root of the latter ; 
as may be colledfed from Cardan's Rules. 
And hence likewife if the fird: and laft of the five 
mean Proportionals, between the Sine and Cofine of 
half the Angle under C M G be found, twice the Sum 
of the Squares of thefe mean Proportionals applied to 
the Radius exceeds the Sine of the Angle of In- 
cidence by the Sine of the Angle under C M G ; and 
twice the difference of the Squar es of the fame mean 
Proportionals applied to the Radius is equal to the 
Sine of double the refracSIed Angle. Moreover this 
double of the refraded Angle exceeds the Angle of 
Incidence by the Angle under CM G. 
In the latter Determination of the fecond Propofi- 
tion draw K Y, and A Y being parallel to M N, the 
Angle under CKY will be equal to twice the Angle 
under 
