Gravesande, Willem Jacob 's
,
An essay on perspective
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 237
>
Scan
Original
31
10
32
11
33
12
34
13
35
14
36
15
37
16
38
39
40
41
17
42
18
43
19
44
20
45
46
47
48
21
49
22
50
23
51
24
52
53
54
55
25
56
26
57
58
59
60
27
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 237
>
page
|<
<
(40)
of 237
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
en
"
type
="
free
">
<
div
xml:id
="
echoid-div144
"
type
="
section
"
level
="
1
"
n
="
78
">
<
pb
o
="
40
"
file
="
0078
"
n
="
88
"
rhead
="
An ESSAY
"/>
<
p
>
<
s
xml:id
="
echoid-s1052
"
xml:space
="
preserve
">Now we have proved, that F G is the half of
<
lb
/>
F B, therefore G N is likewiſe equal to the half
<
lb
/>
of B L, and conſequently equal to the Height
<
lb
/>
of the ſuppoſed Perpendicular.</
s
>
<
s
xml:id
="
echoid-s1053
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1054
"
xml:space
="
preserve
">Again, the ſimilar Triangles F G N and F a I
<
lb
/>
give</
s
>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1055
"
xml:space
="
preserve
">F G : </
s
>
<
s
xml:id
="
echoid-s1056
"
xml:space
="
preserve
">F a : </
s
>
<
s
xml:id
="
echoid-s1057
"
xml:space
="
preserve
">: </
s
>
<
s
xml:id
="
echoid-s1058
"
xml:space
="
preserve
">G N : </
s
>
<
s
xml:id
="
echoid-s1059
"
xml:space
="
preserve
">a I.</
s
>
<
s
xml:id
="
echoid-s1060
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1061
"
xml:space
="
preserve
">But F G : </
s
>
<
s
xml:id
="
echoid-s1062
"
xml:space
="
preserve
">F a : </
s
>
<
s
xml:id
="
echoid-s1063
"
xml:space
="
preserve
">: </
s
>
<
s
xml:id
="
echoid-s1064
"
xml:space
="
preserve
">G D : </
s
>
<
s
xml:id
="
echoid-s1065
"
xml:space
="
preserve
">a H; </
s
>
<
s
xml:id
="
echoid-s1066
"
xml:space
="
preserve
">becauſe the Tri-
<
lb
/>
angles F G D and F a H are ſimilar.</
s
>
<
s
xml:id
="
echoid-s1067
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1068
"
xml:space
="
preserve
">Whence</
s
>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1069
"
xml:space
="
preserve
">G N : </
s
>
<
s
xml:id
="
echoid-s1070
"
xml:space
="
preserve
">a I : </
s
>
<
s
xml:id
="
echoid-s1071
"
xml:space
="
preserve
">: </
s
>
<
s
xml:id
="
echoid-s1072
"
xml:space
="
preserve
">G D : </
s
>
<
s
xml:id
="
echoid-s1073
"
xml:space
="
preserve
">a H.</
s
>
<
s
xml:id
="
echoid-s1074
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1075
"
xml:space
="
preserve
">Now becauſe G N has been proved to be e-
<
lb
/>
qual to the Perpendicular, whoſe Perſpective is
<
lb
/>
requir’d and D G is ſuppoſed equal to that Per-
<
lb
/>
pendicular; </
s
>
<
s
xml:id
="
echoid-s1076
"
xml:space
="
preserve
">it follows, that G N and G D are
<
lb
/>
equal; </
s
>
<
s
xml:id
="
echoid-s1077
"
xml:space
="
preserve
">and therefore a I and a H are alſo equal.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1078
"
xml:space
="
preserve
">Q E D.</
s
>
<
s
xml:id
="
echoid-s1079
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div146
"
type
="
section
"
level
="
1
"
n
="
79
">
<
head
xml:id
="
echoid-head85
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Scholium</
emph
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1080
"
xml:space
="
preserve
">I might have aſſumed C P equal to the Perpen-
<
lb
/>
dicular, and uſed the Points C and P inſtead of
<
lb
/>
B and L. </
s
>
<
s
xml:id
="
echoid-s1081
"
xml:space
="
preserve
">But uſing the ſaid Points B and L is
<
lb
/>
better: </
s
>
<
s
xml:id
="
echoid-s1082
"
xml:space
="
preserve
">For when the Points C and P are uſed,
<
lb
/>
the Horizontal Line muſt almoſt always be con-
<
lb
/>
tinued, that ſo a Line drawn through the Points
<
lb
/>
c and a may cut it; </
s
>
<
s
xml:id
="
echoid-s1083
"
xml:space
="
preserve
">moreover this Interſection
<
lb
/>
will ſometimes be at an infinite Diſtance; </
s
>
<
s
xml:id
="
echoid-s1084
"
xml:space
="
preserve
">where-
<
lb
/>
as in uſing the Point B, M N can never be
<
lb
/>
greater than thrice the Breadth of the Deſign to
<
lb
/>
be drawn.</
s
>
<
s
xml:id
="
echoid-s1085
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div147
"
type
="
section
"
level
="
1
"
n
="
80
">
<
head
xml:id
="
echoid-head86
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Corollary</
emph
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1086
"
xml:space
="
preserve
">The ſixth Problem may be ſolv’d by this;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1087
"
xml:space
="
preserve
">for a Point elevated above the Geometrical
<
lb
/>
Plane, may be conceived as the Extremity of a
<
lb
/>
Perpendicular to the Geometrical Plane.</
s
>
<
s
xml:id
="
echoid-s1088
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>