Gravesande, Willem Jacob 's, An essay on perspective

List of thumbnails

< >
131
131 (62)
132
132 (63)
133
133 (64)
134
134
135
135
136
136
137
137 (65)
138
138 (66)
139
139 (67)
140
140 (68)
< >
page |< < (78) of 237 > >|
16278An ESSAY cauſe the Triangles THX and a F X are ſimilar,
TH — a F:
a F : : Ta: a X.
And becauſe the Triangles T I x and ax L, are
alſo ſimilar, we have
TI + a L :
: a L: Ta : ax.
Now let PM NR be the perſpective Plane,
11Fig. 54. O the Eye, A Q the Perpendicular, whoſe
Perſpective is requir’d, and O t a perpendicular
let fall from the Eye upon the perſpective Plane,
and ſo t will be the ſame, as the Point T in the
aforegoing Figure, Now if the Lines O Q be
drawn, it is manifeſt that A x, or A X, is the
Perſpective of A Q, according as this Line is
above or below the perſpective Plane in reſpect
to the Eye.
Then becauſe the Triangles O t x
and Q A x are ſimilar, we have
O t — A Q:
A Q : : t A: Ax.
And ſince the Triangles O t X and X A Q are
ſimilar,
O t + A Q:
A Q : : t A: A X.
Now Ot is equal to TH or TI of the afore-
going Figure, and AQ to a F or a L of the
ſame Figure;
as likewiſe At, Ta: Therefore
if theſe two laſt Proportions be compared with
the two precedent ones, we ſhall find A x = a X,
and A X = a x;
which was to be demon-
ſtrated.
Remarks.
96. When the two Circles interſect each other,
or fall within one another, and ſo this Way be-
comes uſeleſs;
a Line muſt be drawn at Pleaſure,
through the Point T, equal to the Diſtance of
the Eye from the perſpective Plane;
and then a
parallel equal to the given Perpendicular muſt be
drawn to the ſaid Line through the Point a, ei-
ther towards L or F, according as the

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index