16278An ESSAY
cauſe the Triangles THX and a F X are ſimilar,
TH — a F: a F : : Ta: a X.
TH — a F: a F : : Ta: a X.
And becauſe the Triangles T I x and ax L, are
alſo ſimilar, we have
TI + a L : : a L: Ta : ax.
alſo ſimilar, we have
TI + a L : : a L: Ta : ax.
Now let PM NR be the perſpective Plane,
11Fig. 54. O the Eye, A Q the Perpendicular, whoſe
Perſpective is requir’d, and O t a perpendicular
let fall from the Eye upon the perſpective Plane,
and ſo t will be the ſame, as the Point T in the
aforegoing Figure, Now if the Lines O Q be
drawn, it is manifeſt that A x, or A X, is the
Perſpective of A Q, according as this Line is
above or below the perſpective Plane in reſpect
to the Eye. Then becauſe the Triangles O t x
and Q A x are ſimilar, we have
O t — A Q: A Q : : t A: Ax.
11Fig. 54. O the Eye, A Q the Perpendicular, whoſe
Perſpective is requir’d, and O t a perpendicular
let fall from the Eye upon the perſpective Plane,
and ſo t will be the ſame, as the Point T in the
aforegoing Figure, Now if the Lines O Q be
drawn, it is manifeſt that A x, or A X, is the
Perſpective of A Q, according as this Line is
above or below the perſpective Plane in reſpect
to the Eye. Then becauſe the Triangles O t x
and Q A x are ſimilar, we have
O t — A Q: A Q : : t A: Ax.
And ſince the Triangles O t X and X A Q are
ſimilar,
O t + A Q: A Q : : t A: A X.
ſimilar,
O t + A Q: A Q : : t A: A X.
Now Ot is equal to TH or TI of the afore-
going Figure, and AQ to a F or a L of the
ſame Figure; as likewiſe At, Ta: Therefore
if theſe two laſt Proportions be compared with
the two precedent ones, we ſhall find A x = a X,
and A X = a x; which was to be demon-
ſtrated.
going Figure, and AQ to a F or a L of the
ſame Figure; as likewiſe At, Ta: Therefore
if theſe two laſt Proportions be compared with
the two precedent ones, we ſhall find A x = a X,
and A X = a x; which was to be demon-
ſtrated.
Remarks.
96.
When the two Circles interſect each other,
or fall within one another, and ſo this Way be-
comes uſeleſs; a Line muſt be drawn at Pleaſure,
through the Point T, equal to the Diſtance of
the Eye from the perſpective Plane; and then a
parallel equal to the given Perpendicular muſt be
drawn to the ſaid Line through the Point a, ei-
ther towards L or F, according as the
or fall within one another, and ſo this Way be-
comes uſeleſs; a Line muſt be drawn at Pleaſure,
through the Point T, equal to the Diſtance of
the Eye from the perſpective Plane; and then a
parallel equal to the given Perpendicular muſt be
drawn to the ſaid Line through the Point a, ei-
ther towards L or F, according as the
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