13967on PERSPECTIVE.
Line T B X;
which interſect in the Point X,
by a Perpendicular to the Baſe Line, in the
Point G; and then the Point X is the Appear-
ance ſought.
by a Perpendicular to the Baſe Line, in the
Point G; and then the Point X is the Appear-
ance ſought.
Demonstration.
In Fig.
44.
where V, S, T, and H, repreſent
the ſame Points as thoſe that are denoted with
the ſame Letters in this Figure; we have,
the ſame Points as thoſe that are denoted with
the ſame Letters in this Figure; we have,
T H:
H S:
: T V:
V O.
Compon.
and altern.
T H:
T V:
: T H + H S:
T V + V O.
This being apply’d to Fig.
45.
and it will be,
T H: T V: : T S: T V + V O.
T H: T V: : T S: T V + V O.
If now T X be continued, till it cuts the Ho-
rizontal Line in F; we ſhall have,
rizontal Line in F; we ſhall have,
T H:
T V:
: T B:
T F.
And conſequently,
T B:
T F:
: T S:
T V + V O.
Whence it follows, that if a Line be drawn
ſrom the Eye, to the Point F, it will be paral-
lel to S B A. Therefore the Perſpective 1113. B A, is a Part of B X; and ſo the Repreſenta-
tion of A is in the ſaid Line. The Perſpective
of a Line perpendicular to the Geometrical
Plane, in the Point A, paſſes thro’ the Perſpe-
ctive of the Point A, and thro’ the Point T ; 2213, 14. therefore it is a Part of T X. But the given Point
is in the aſoreſaid Perpendicular: And ſo its Per-
ſpective is in T X.
ſrom the Eye, to the Point F, it will be paral-
lel to S B A. Therefore the Perſpective 1113. B A, is a Part of B X; and ſo the Repreſenta-
tion of A is in the ſaid Line. The Perſpective
of a Line perpendicular to the Geometrical
Plane, in the Point A, paſſes thro’ the Perſpe-
ctive of the Point A, and thro’ the Point T ; 2213, 14. therefore it is a Part of T X. But the given Point
is in the aſoreſaid Perpendicular: And ſo its Per-
ſpective is in T X.
Again;
it is otherwiſe manifeſt, that the Per-
ſpective of C L, is a Part of C X; and 3341. quently, the Appearance of L is in this Line.
Now, if a Line be ſuppos’d to be drawn from
the Point L, thro’ the propos’d Point, it will be
parallel to the Vertical Line; and ſo its 446. ſpective is parallel to the Baſe Line. And
ſpective of C L, is a Part of C X; and 3341. quently, the Appearance of L is in this Line.
Now, if a Line be ſuppos’d to be drawn from
the Point L, thro’ the propos’d Point, it will be
parallel to the Vertical Line; and ſo its 446. ſpective is parallel to the Baſe Line. And