378

Appendix II.

And this will be the Cafe in every 1^"tance of an Object; for supposing the Oject A B were at some near Distance si 0111the Telescope, and subtended the s a ^Angle A N B, the only Consequence vroube, that its Image would be formed atgreater Distance from the Glass; supp 0 ^^

M P, it would still be contained under tfame Angle M N P, equal to N L O, aS ^fore, upon the Supposition that the Seg m ~

H I and B O produced meets A P in ^Point P, that is to- fay, suppose that tSegment H I is in such Position that tmoveable Image QJl, formed by it, exai jcoincides with the fixed Image M P,by the Segment E S G.

This likewise may be otherwise Ihe^ st

from Theorem Ali— — f. (See An* 10 ^'

d—r i

CXXV. Art. 27 .) For putting

N P =/, and NL = r, or Focus _ of P a 'rallel Rays, we have d r —f d — j r 5

thereby d : f :: d—r : r. Consequent )d +f : f :: d : r ; that is, A Qj IAN : NL; and by similar TrianglesQJB, N QJ3, we have A Qj Q^N -- ^ nN O ; therefore AN : N L :: A B : ^ '

Whence the Triangles A N B and N L °are similar, and the Angle at N m , et

o w hich