12057on PERSPECTIVE.
The Operation of Prob.
VII.
muſt be uſed
here, but with this Difference (ſee Fig. of the
ſaid Prob.) that whereas a I in the ſaid Problem
is perpendicular to the Baſe Line, here it muſt
make an Angle with the Baſe Line, equal to the
Angle of Inclination of the given Lines.
here, but with this Difference (ſee Fig. of the
ſaid Prob.) that whereas a I in the ſaid Problem
is perpendicular to the Baſe Line, here it muſt
make an Angle with the Baſe Line, equal to the
Angle of Inclination of the given Lines.
For the Demonſtration of this, ſee n.
7, and 10.
Prob. XIV.
73.
To throw a Body into Perſpective, having
ſome one or all of its Sides inclined to the Geometri-
cal Plane.
ſome one or all of its Sides inclined to the Geometri-
cal Plane.
The Appearances of the Lines forming the
Angles of the propoſed Body muſt be found: And
this may be eaſily done by Prob. 10. 1169. takes in all the Caſes. And in this Manner the
Appearance of a Pyramid, an inclined Priſm,
& c. may be found. But nevertheleſs, it hap-
pens ſometimes, that the Operations of the pre-
cedent Problem may be abbreviated; as when
the Extremity of ſeveral Lines are found in one
and the ſame Line, or when inclined Lines, that
have difficult accidental Points, interſect one
another, and ſo mutually determine each other.
This will appear manifeſt by the following Ex-
amples.
Angles of the propoſed Body muſt be found: And
this may be eaſily done by Prob. 10. 1169. takes in all the Caſes. And in this Manner the
Appearance of a Pyramid, an inclined Priſm,
& c. may be found. But nevertheleſs, it hap-
pens ſometimes, that the Operations of the pre-
cedent Problem may be abbreviated; as when
the Extremity of ſeveral Lines are found in one
and the ſame Line, or when inclined Lines, that
have difficult accidental Points, interſect one
another, and ſo mutually determine each other.
This will appear manifeſt by the following Ex-
amples.
Example I.
To throw ſeveral parallel Shores which ſtrengthen a
Wall, into Perſpective.
Wall, into Perſpective.
I ſuppoſe here that the Baſes of theſe Shores,
22Fig. 38. which are the Places where they meet the Sur-
face of the Ground, are all in a right Line, pa-
rallel to the Side of the Wall; and then the
faid Shores may be thrown into Perſpective in
the following Manner: Having firſt found 3368.
22Fig. 38. which are the Places where they meet the Sur-
face of the Ground, are all in a right Line, pa-
rallel to the Side of the Wall; and then the
faid Shores may be thrown into Perſpective in
the following Manner: Having firſt found 3368.