C 557 ] 
Proposition II. 
The di fiance H E of the objeti from the glafs, is to 
E F, the focal di fiance of parallel rays , as the 
di/lance H G of the objehifrom its image is to E G, 
the diflance oj the image from the glafs : That is, 
HE : EF : : HG : EG. 
The demonftration of this proportion may be ga- 
thered from any treatife of dioptrics ; it being a ge- 
neral rule for finding the respective focus to any given 
diftance, when the focus of parallel rays is known. 
Proposition III. 
The angle fubt ended by the diameter of the object , 
from the glafs , is equal to that fubt ended , by the 
opening of the centres of the fegments , from the 
focus of parallel rays. That is , the angle AEB 
equal to the angle C F D. 
\ 
Demonftration. 
It appears, by infpedtion of the figure, that 
AB : CD:: HG: EG. 
And by the laft proportion H E : E F : : H G : 
EG. 
Then, as the two laft terms of thefe two analogies 
are alike • the two f rft terms of one will be in the 
fame proportion as the two f rft terms of the other • 
which gives the following proportion : A B:C D : : 
HE : EF. Whence the truth of the proportion is 
evident. 
From 
