DOI Page / Citation link:
https://doi.org/10.11588/diglit.62828#0321
( M3 )
of the fquare D B. Make alfo A N equal to the fide of the
fquare; and draw N m, cutting at G; and iaftly, draw G V x, cut-
ting at B; and the fquare wall be completed as required.
Method fecond.—From A, fweep the arch k K, whofe radius
is equal to the fide of the fquare to be reprefented. Draw A u
equal to the angle of the inclined plane with the ground; and
from zz, draw u t parallel to the ground line; from t draw a vi-
fual to P; and from zz, draw u M, cutting at D; from A draw a
line through the interfebfion of u M with t P, and produce this
line till it find the vanifhing point V x in the perpendicular P V.
From D draw a line to v, as before; and Iaftly, from G, found
as before, draw G V zr, cutting at B, and the fquare will be
completed, as in the other method.
Obfervations.—If the original plane inclined to the ground
in an angle of forty-five degrees, the vifual line of the fide of
the fquare A D would pafs through the diagonal of the fquare
A, k, n, 8, and tend to the upper V, the vanifhing point in that
cafe; and V v would then be the vanifhing line, S would be the
center of the picture, m the meafuring point, and d 3 its diftance,
and % d 3, Q would be the angle of the inclined plane, which is
the diagonal of a fquare % d 3, Q, m. It is evident then, that
the true reprefentation of a fquare in any inclination, would
H h 2 defcribe
of the fquare D B. Make alfo A N equal to the fide of the
fquare; and draw N m, cutting at G; and iaftly, draw G V x, cut-
ting at B; and the fquare wall be completed as required.
Method fecond.—From A, fweep the arch k K, whofe radius
is equal to the fide of the fquare to be reprefented. Draw A u
equal to the angle of the inclined plane with the ground; and
from zz, draw u t parallel to the ground line; from t draw a vi-
fual to P; and from zz, draw u M, cutting at D; from A draw a
line through the interfebfion of u M with t P, and produce this
line till it find the vanifhing point V x in the perpendicular P V.
From D draw a line to v, as before; and Iaftly, from G, found
as before, draw G V zr, cutting at B, and the fquare will be
completed, as in the other method.
Obfervations.—If the original plane inclined to the ground
in an angle of forty-five degrees, the vifual line of the fide of
the fquare A D would pafs through the diagonal of the fquare
A, k, n, 8, and tend to the upper V, the vanifhing point in that
cafe; and V v would then be the vanifhing line, S would be the
center of the picture, m the meafuring point, and d 3 its diftance,
and % d 3, Q would be the angle of the inclined plane, which is
the diagonal of a fquare % d 3, Q, m. It is evident then, that
the true reprefentation of a fquare in any inclination, would
H h 2 defcribe