4922An ESSAY
of this laſt Line, and the Line E D G, which was
to be demonſtrated.
to be demonſtrated.
Remarks.
33.
By this Demonſtration it appears, that there
is no Neceſſity in taking G O exactly equal to
the Eye’s Diſtance, and O F equal to its Height:
But it is ſufficient if they have the ſame Propor-
tion, as the aforeſaid Diſtance has to the Height.
Likewiſe there is no Neceſſity in aſſuming the
Points G and F, in a Line parallel to the Baſe
Line; for any other Line paſſing through the
Eye O may be uſed at Pleaſure. For Example,
let g O f be a Line any how drawn through the
Eye O, and take the Point g at Pleaſure in this
Line, through which draw alſo the Line g N I
at Pleaſure, cutting the Horizontal Line in N,
and the Baſe Line in I; and draw the Line O N,
and through the Point I, draw the Line I f pa-
rallelthereto, cutting the Line g O f in f.
is no Neceſſity in taking G O exactly equal to
the Eye’s Diſtance, and O F equal to its Height:
But it is ſufficient if they have the ſame Propor-
tion, as the aforeſaid Diſtance has to the Height.
Likewiſe there is no Neceſſity in aſſuming the
Points G and F, in a Line parallel to the Baſe
Line; for any other Line paſſing through the
Eye O may be uſed at Pleaſure. For Example,
let g O f be a Line any how drawn through the
Eye O, and take the Point g at Pleaſure in this
Line, through which draw alſo the Line g N I
at Pleaſure, cutting the Horizontal Line in N,
and the Baſe Line in I; and draw the Line O N,
and through the Point I, draw the Line I f pa-
rallelthereto, cutting the Line g O f in f.
This being done, the Points g and f may be
uſed inſtead of G and F: for among all the
Lines that can be drawn (as G N I) it is mani-
ſeſt, that g N will always be to g I: : g O: g f,
which is ſufficient for the Demonſtration.
uſed inſtead of G and F: for among all the
Lines that can be drawn (as G N I) it is mani-
ſeſt, that g N will always be to g I: : g O: g f,
which is ſufficient for the Demonſtration.
If the Point f be firſt determin’d, the Point g
muſt be found by an Operation quite contrary
to that we have laid down.
muſt be found by an Operation quite contrary
to that we have laid down.
34.
When nothing is determinate, we
may (a Baſe Line being firſt drawn) take at
Pleaſure, in another Line any how drawn,
the three Points g O f; ſo that in this Caſe, there
is no Manner of Neceſſity to uſe Compaſſes, in
throwing any Figure whatſoever, which is on
the Geometrical Plane, into Perſpective. But
if after having thus work’d, the Point of Sight,
Height and Diſtance of the Eye be requir’d,
may (a Baſe Line being firſt drawn) take at
Pleaſure, in another Line any how drawn,
the three Points g O f; ſo that in this Caſe, there
is no Manner of Neceſſity to uſe Compaſſes, in
throwing any Figure whatſoever, which is on
the Geometrical Plane, into Perſpective. But
if after having thus work’d, the Point of Sight,
Height and Diſtance of the Eye be requir’d,