8638An ESSAY
there;
and finally e A here, E A in that Fi-
gure.
gure.
This being ſuppoſed, o f is parallel to e 1127.
and conſequently the Triangle o f a is ſimilar
to the Triangle a e A, and therefore we have this
Proportion.
to the Triangle a e A, and therefore we have this
Proportion.
o f:
f a:
: A e:
e o.
Comp.
Comp.
o f + a f:
f a:
: A e + e a:
e a.
Altern.
Altern.
o f + a f:
A e + e a:
: f a:
e a.
Comp. and Perm.
Comp. and Perm.
o f + f a + Ae + e a :
o f + f a :
: f a + e a :
f a.
This laſt Proportion being reduced to the pre-
cedent Figure, we ſhall have this,
cedent Figure, we ſhall have this,
O A :
o a :
:
F D :
F a.
Again, becauſe the Triangles O A L and O a G
are ſimilar, we ſhall have
are ſimilar, we ſhall have
O A:
O a :
:
A L :
a G.
And ſince the Triangle F E D and F a H are
ſimilar;
ſimilar;
F E :
F a :
:
D E :
H a.
And ſo if theſe three laſt Propoſitions be con-
ſider’d, we ſhall have
ſider’d, we ſhall have
A L :
a G :
:
D E :
H a.
But D E was made equal to A L, and there-
fore a G or a I is alſo equal to a H, which is 2256. qual to the Repreſentation ſought. Which was
to be demonſtrated.
fore a G or a I is alſo equal to a H, which is 2256. qual to the Repreſentation ſought. Which was
to be demonſtrated.
Method III.
58.
Near one of the Sides of the perſpective
33Fig. 25. Plane, raiſe the Perpendicular C B to the Baſe
Line, equal to the Height of the Eye, in which
take B L equal in length to twice the Perpen-
dicular, whoſe Perſpective is requir’d. Let S
33Fig. 25. Plane, raiſe the Perpendicular C B to the Baſe
Line, equal to the Height of the Eye, in which
take B L equal in length to twice the Perpen-
dicular, whoſe Perſpective is requir’d. Let S