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 Notes
<
1 - 3
[out of range]
>
[Note]
Page: 130
[Note]
Page: 131
[Note]
Page: 132
[Note]
Page: 133
[Note]
Page: 133
[Note]
Page: 133
[Note]
Page: 137
[Note]
Page: 138
[Note]
Page: 138
[Note]
Page: 138
[Note]
Page: 139
[Note]
Page: 139
[Note]
Page: 139
[Note]
Page: 139
[Note]
Page: 140
[Note]
Page: 140
[Note]
Page: 140
[Note]
Page: 140
[Note]
Page: 140
[Note]
Page: 144
[Note]
Page: 144
[Note]
Page: 144
[Note]
Page: 144
[Note]
Page: 144
[Note]
Page: 144
[Note]
Page: 145
[Note]
Page: 145
[Note]
Page: 145
[Note]
Page: 146
[Note]
Page: 146
<
1 - 3
[out of range]
>
page
|<
<
(64)
of 237
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
en
"
type
="
free
">
<
div
xml:id
="
echoid-div224
"
type
="
section
"
level
="
1
"
n
="
118
">
<
pb
o
="
64
"
file
="
0116
"
n
="
133
"
rhead
="
An ESSAY
"/>
<
p
>
<
s
xml:id
="
echoid-s1530
"
xml:space
="
preserve
">Whence</
s
>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1531
"
xml:space
="
preserve
">G I: </
s
>
<
s
xml:id
="
echoid-s1532
"
xml:space
="
preserve
">G C:</
s
>
<
s
xml:id
="
echoid-s1533
"
xml:space
="
preserve
">: G F: </
s
>
<
s
xml:id
="
echoid-s1534
"
xml:space
="
preserve
">G O.</
s
>
<
s
xml:id
="
echoid-s1535
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1536
"
xml:space
="
preserve
">Again, becauſe the Triangles G I E and G C D
<
lb
/>
are ſimilar, we have</
s
>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1537
"
xml:space
="
preserve
">G I: </
s
>
<
s
xml:id
="
echoid-s1538
"
xml:space
="
preserve
">G C:</
s
>
<
s
xml:id
="
echoid-s1539
"
xml:space
="
preserve
">: G E: </
s
>
<
s
xml:id
="
echoid-s1540
"
xml:space
="
preserve
">G D.</
s
>
<
s
xml:id
="
echoid-s1541
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1542
"
xml:space
="
preserve
">And conſequently</
s
>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1543
"
xml:space
="
preserve
">G F: </
s
>
<
s
xml:id
="
echoid-s1544
"
xml:space
="
preserve
">G O:</
s
>
<
s
xml:id
="
echoid-s1545
"
xml:space
="
preserve
">: G E: </
s
>
<
s
xml:id
="
echoid-s1546
"
xml:space
="
preserve
">G D.</
s
>
<
s
xml:id
="
echoid-s1547
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1548
"
xml:space
="
preserve
">And ſo the Triangles G F E, and G O D are
<
lb
/>
ſimilar; </
s
>
<
s
xml:id
="
echoid-s1549
"
xml:space
="
preserve
">and the Line F E A is parallel to O D:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1550
"
xml:space
="
preserve
">Whence it follows , that the Perſpective
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0116-01
"
xlink:href
="
note-0116-01a
"
xml:space
="
preserve
">13.</
note
>
E A, is a Part of E a D. </
s
>
<
s
xml:id
="
echoid-s1551
"
xml:space
="
preserve
">We demonſtrate in
<
lb
/>
the ſame Manner, that B a is the Perſpective
<
lb
/>
of B A, and ſo the Perſpective of the Point A,
<
lb
/>
the common Section of E A and B A, is a, the
<
lb
/>
Interſection of the Appearances of the ſaid two
<
lb
/>
Lines.</
s
>
<
s
xml:id
="
echoid-s1552
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div227
"
type
="
section
"
level
="
1
"
n
="
119
">
<
head
xml:id
="
echoid-head125
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Prob</
emph
>
. IV.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1553
"
xml:space
="
preserve
">80. </
s
>
<
s
xml:id
="
echoid-s1554
"
xml:space
="
preserve
">To find the Repreſentation of a Line, per-
<
lb
/>
pendicular to the Geometrical Plane, when the per-
<
lb
/>
ſpective Plane is above the Eye.</
s
>
<
s
xml:id
="
echoid-s1555
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1556
"
xml:space
="
preserve
">In the Baſe Line B E, aſſume the Line E D,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0116-02
"
xlink:href
="
note-0116-02a
"
xml:space
="
preserve
">Fig. 43.</
note
>
equal in Length to the propoſed Perpendicular;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1557
"
xml:space
="
preserve
">and draw C L, parallel to the Baſe Line, and
<
lb
/>
diſtant therefrom (for Example) {1/4} of the Height
<
lb
/>
of the Eye; </
s
>
<
s
xml:id
="
echoid-s1558
"
xml:space
="
preserve
">make F L equal to {3/4} of D E, and
<
lb
/>
draw the Lines E L and D F. </
s
>
<
s
xml:id
="
echoid-s1559
"
xml:space
="
preserve
">Note, if the
<
lb
/>
Diſtance from C L to B E, had been aſſumed
<
lb
/>
equal to a fifth Part of the Height of the Eye,
<
lb
/>
F L muſt have been aſſumed equal to {4/5} Parts of
<
lb
/>
E D. </
s
>
<
s
xml:id
="
echoid-s1560
"
xml:space
="
preserve
">Now let a be the Perſpective of the Foot
<
lb
/>
of the propoſed Perpendicular; </
s
>
<
s
xml:id
="
echoid-s1561
"
xml:space
="
preserve
">through which
<
lb
/>
draw a H parallel to the Baſe Line, and a I per-
<
lb
/>
pendicular to the ſaid Line; </
s
>
<
s
xml:id
="
echoid-s1562
"
xml:space
="
preserve
">then make a I equal
<
lb
/>
to G H, and the propoſed Perſpective will be
<
lb
/>
had. </
s
>
<
s
xml:id
="
echoid-s1563
"
xml:space
="
preserve
">The Demonſtration of this Operation is
<
lb
/>
manifeſt , in conſidering that D F and E
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0116-03
"
xlink:href
="
note-0116-03a
"
xml:space
="
preserve
">56.</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>