Gravesande, Willem Jacob 's
,
An essay on perspective
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of figures
<
1 - 30
31 - 60
61 - 82
[out of range]
>
<
1 - 30
31 - 60
61 - 82
[out of range]
>
page
|<
<
(53)
of 237
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
en
"
type
="
free
">
<
div
xml:id
="
echoid-div179
"
type
="
section
"
level
="
1
"
n
="
94
">
<
pb
o
="
53
"
file
="
0099
"
n
="
113
"
rhead
="
on PERSPECTIVE.
"/>
</
div
>
<
div
xml:id
="
echoid-div180
"
type
="
section
"
level
="
1
"
n
="
95
">
<
head
xml:id
="
echoid-head101
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Demonstration</
emph
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1284
"
xml:space
="
preserve
">If a Plane be conceiv’d to paſs thro’ the Eye,
<
lb
/>
perpendicular to the Geometrical Plane, and paral-
<
lb
/>
lel to the given Lines; </
s
>
<
s
xml:id
="
echoid-s1285
"
xml:space
="
preserve
">it is evident, that the ſaid
<
lb
/>
Plane will cut the Horizontal Plane in the Line
<
lb
/>
O D, and the perſpective Plane in D F. </
s
>
<
s
xml:id
="
echoid-s1286
"
xml:space
="
preserve
">It is,
<
lb
/>
moreover, manifeſt, that a Line drawn thro’ the
<
lb
/>
Eye, parallel to the given Line, is in the ſaid
<
lb
/>
Plane, and (with the Line O D) makes an An-
<
lb
/>
gle, equal to the Angle E C P, below the Hori-
<
lb
/>
zontal Plane, if the Lines be inclin’d towards
<
lb
/>
the perſpective Plane, and above it, if they in-
<
lb
/>
cline to the oppoſite ſide; </
s
>
<
s
xml:id
="
echoid-s1287
"
xml:space
="
preserve
">whence this laſt Line
<
lb
/>
makes a right-angled Triangle with O D and
<
lb
/>
D F, whoſe Angle at the Point O, is equal to
<
lb
/>
the Angle C E P. </
s
>
<
s
xml:id
="
echoid-s1288
"
xml:space
="
preserve
">But D G F is likewiſe a
<
lb
/>
right-angled Triangle, as having the Angle at the
<
lb
/>
Point G, equal to ECP; </
s
>
<
s
xml:id
="
echoid-s1289
"
xml:space
="
preserve
">therefore theſe two
<
lb
/>
Triangles are ſimilar. </
s
>
<
s
xml:id
="
echoid-s1290
"
xml:space
="
preserve
">And ſince the Side D G
<
lb
/>
is equal to the Side D O, the Triangles are alſo
<
lb
/>
equal: </
s
>
<
s
xml:id
="
echoid-s1291
"
xml:space
="
preserve
">Therefore the Line D F, being common
<
lb
/>
to theſe two Triangles; </
s
>
<
s
xml:id
="
echoid-s1292
"
xml:space
="
preserve
">the Point F, is the
<
lb
/>
Point wherein the Line, paſſing thro’ the Eye
<
lb
/>
parallel to the given Line, meets the Per-
<
lb
/>
ſpective Plane: </
s
>
<
s
xml:id
="
echoid-s1293
"
xml:space
="
preserve
">And this Point is the acciden- tal one ſought.</
s
>
<
s
xml:id
="
echoid-s1294
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1295
"
xml:space
="
preserve
">Note, This Demonſtration as well regards
<
lb
/>
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0099-01
"
xlink:href
="
note-0099-01a
"
xml:space
="
preserve
">13, 14.</
note
>
inclin’d Lines entirely ſeparate from the Geo-
<
lb
/>
metrical Plane, as thoſe that meet it in one of
<
lb
/>
their Extremes only.</
s
>
<
s
xml:id
="
echoid-s1296
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div182
"
type
="
section
"
level
="
1
"
n
="
96
">
<
head
xml:id
="
echoid-head102
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Problem</
emph
>
X.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1297
"
xml:space
="
preserve
">69. </
s
>
<
s
xml:id
="
echoid-s1298
"
xml:space
="
preserve
">To find the Repreſentation of one or more
<
lb
/>
Lines, inclin’d to the Geometrical Plane.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1299
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-0099-02
"
xlink:href
="
note-0099-02a
"
xml:space
="
preserve
">Fig. 36.</
note
>
</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1300
"
xml:space
="
preserve
">Let A be a Point given in the Geometrical
<
lb
/>
Plane; </
s
>
<
s
xml:id
="
echoid-s1301
"
xml:space
="
preserve
">whereon ſtands a Line, whoſe Length,
<
lb
/>
Direction, and Angle of Inclination is known.</
s
>
<
s
xml:id
="
echoid-s1302
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>