themfelvcs will be in the fame proportion ; whence it 
will follow that, 
As d to r, fo the Angle at C to the Angle at D, 
and d^r will be as the Angle of incidence GAD ; and 
again as w to «, fo djkr to n 4 r *' which will be 
as the Angle GAH = CAp. This being taken from 
ACD which is as d } will leave m ~ n ^~~ n r analogous 
m 
to the Angle ApD, and the fides being in this cafe pro- 
portional -to the Angles they fubtend, it will follow, 
that as the Angle A? D is to the Angle A Dp, fo is the 
fide AD or BD to Ap or Bp: that is B p will be 
zs — m ^ r — which (hews in what point the beams pro 
ceeding from D would becollefredby means of the firft 
Reiradtion; but if nr cannot be fubftrachd from m — nd, 
it follows that the Beams after Refraction do ftill pafs on 
diverging, and the pom* p is on the fame fide of the 
■Lens beyond D. But if n r he equal to m—nd then, 
they proceed parallel tothe^xy, and the point p is in- 
finitely diflanr. 
The point p being found 'as before, and B p— B/3 
being given, which we will call %\ it follows by a pro- 
cefs like the former, that .$¥ or the focal diftance fought, 
3> p n 
is equal to — — And in the room of £ fub- 
w — n 6 -f-m p J 
/^•• n T>^ m d r . r « 
ftituting Bp~B/2 =s ■» t y putting/* for — — 
after due reduction this following Equation will anfe, 
m p d r p ^-n d p t -\- n p r p t 
wdr^-md^ — m p r ^~-m — nd t n r t 
Which Theorem , however it may feem operofe , 
is 
