4821on PERSPECTIVE.
Method. IV.
31.
Draw the Line F O G through the Eye O,
parallel to the Baſe Line, then aſſume F O in
11Fig. 10. this Line, equal to the Height of the Eye, and
O G equal to the Length of the principal Ray.
A is the given Point.
parallel to the Baſe Line, then aſſume F O in
11Fig. 10. this Line, equal to the Height of the Eye, and
O G equal to the Length of the principal Ray.
A is the given Point.
Operation,
Without Compaſſes.
Without Compaſſes.
From the given Point A, draw the Lines AO,
A F, to the Points O and F, and from the
Point E, wherein A F cuts the Baſe Line, draw
the Line E G to the Point G; then the Point a,
the Interſection of A O, and E G, is the Repre-
ſentation ſought.
A F, to the Points O and F, and from the
Point E, wherein A F cuts the Baſe Line, draw
the Line E G to the Point G; then the Point a,
the Interſection of A O, and E G, is the Repre-
ſentation ſought.
Demonstration.
Let fall the perpendicular G M from the Point
G, upon the Baſe Line, and through the Eye O,
draw the Line O D to the Point D, the Inter-
ſection of the Horizontal Line, and the Line G E.
G, upon the Baſe Line, and through the Eye O,
draw the Line O D to the Point D, the Inter-
ſection of the Horizontal Line, and the Line G E.
Then becauſe the Triangles G D L, G E M are
fimilar,
G D: G E: : G L: G M.
But G O is equal to G L, and G F to L M.
whence
G D: G E: : G O: G F.
fimilar,
G D: G E: : G L: G M.
But G O is equal to G L, and G F to L M.
whence
G D: G E: : G O: G F.
And conſequenely the Triangles G O D:
and
G F E, are ſimilar, and the Lines O D, and
A E F, are parallel between themſelves; and
therefore the Appearance of A E, is a 2213 of the Line E D G. It has alſo been 3327. that the Repreſentation of the Point A, is in the
Line A O; therefore i@ is in a the
G F E, are ſimilar, and the Lines O D, and
A E F, are parallel between themſelves; and
therefore the Appearance of A E, is a 2213 of the Line E D G. It has alſo been 3327. that the Repreſentation of the Point A, is in the
Line A O; therefore i@ is in a the