Gravesande, Willem Jacob 's, An essay on perspective

Table of figures

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[Figure 1]
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[2] fronting page 8Plate 1.Fig. 1.C A D B e E
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[3] Fig. 2.M T O V R L A N D F S I H B G C
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[4] Fig. 3.O b B F a A G
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[5] Fig. 4.c C b d F B D a A G
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[6] Plate 2.page 16.Fig. 5.@ O H F c d E D C G
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[7] Fig. 6.E D O @ c F a b A C B G
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[8] Fig. 7.D F H V C X a I B G E Z A
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[9] Plate. 3.page 20Fig. 8.O Y D C X æ B E Z A
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[10] Fig. 9.O I Y H G D V X a B E F C Z L A
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[11] Plate 4.Page 24.Fig. 10.f F O G g V D N L a P E H I M A
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[12] Plate 5.page 26.Fig. 11.O Y b X a E Z A B
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[13] Fig. 12.M O Y F S C L D X a E B Z A
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[14] Plate 6.page 28.Fig. 13.O D c b a g E G B A C
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[15] Fig. 14.O b 1 2 3 a c 1 2 3 g D A C 3 1 2 2 1 3 B G
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[16] page 28.Plate. 7Fig. 16Fig. 15O G F I Vl d c e m n b a h B A H M N C E P D L
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[17] page 36.Plate 8Fig. 17O G F c d b a A B D C
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[18] Page 36.Plate 9Fig. 18.G F C S V I E B A
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[19] Fig. 19.O i M X L D @ b a
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[20] Fig. 20.S x G n H S V D l R f Q m P t
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[21] Fig. 21.I X f T L B N A C l M E F
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[22] page 38Plate 10.Fig. 22.V F I N a G H M P D E B C L A
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[23] Fig. 23.O F I H a G D E B C L A M
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[24] Fig. 24.@ o f X a e A
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[25] page 42Plate 11.Fig. 25.S F V M I N P H a L D E G C A B
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[26] Fig. 26.Fig. 27.S V P Q R n l g h G H B N I A C M L
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[27] page 46Plate 12.Fig. 28.
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[28] Fig. 29.F S V q q q E L p p p I G H q D P n n n T R m m m C B Q A
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[29] Fig. 30.O X E L N M G Z Y D
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[30] Fig. 31.f 3 c l n m g 4
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9645on PERSPECTIVE. and conſequently to V P. Therefore if the before-
mentioned Plane be ſuppoſed to revolve upon the Line
V I, as an Axis, until it coincides with the Per-
ſpective Plane, the Center of the Sphere will meet
the Perſpective Plane in Q, and the Eye in F;
whence the Part G E of the Line I V is the tranſ-
verſe Diameter of the Ellipſis.
Again let G D E in Figure 30, and g e f, in
11Fig. 30,
31. Figure 31 repreſent the Points denoted with the ſame
Letters in the foregoing Figure. Now if the Cone,
whoſe Profile is denoted by the Lines f g and fe be ſup-
poſed to be compleated, and to be cut by a Plane paſ-
ſing through the Line g e perpendicular to the Plane
of the Figure; we ſhall have an Ellipſis g 4 e 3
ſimilar to that which is the ſought Repreſentation
of the Sphere. Further if the ſaid Cone be conceived
to be cut by a Plane 14 m 3 parallel to its Baſe,
and biſecting g e in n, it is manifeſt, that 3 4, the
common Section of the Circle 14 m 3, and the Ellip-
ſis g 4 e 3, is the conjugate Axis of the Ellip-
ſis. And therefore this conjugate Axis is equal
to the Line 3 4, Perpendicular in the Point n to the
Diameter 1 m of the Circle 14 m 3. Now draw
the Lines E O and G Y in Figure 30, parallel to
L M, then the Triangles E G Y and E N M are
ſimilar, whence
EG: EN:: GY: NM.
But E G is twice E N; wherefore G Y is alſo the
double of N M, and ſo N M equal to G Z. After
the ſame manner we demonſtrate, that L N is equal
to X E; whence it follows, that G D is equal to
L M, and is ſo cut in z as L M is in N; and there-
fore R L or G T of Figure 29, is equal to 34 in
Figure 31; and conſequently equal to the conjugate
Axis of the Ellipſis to be drawn. On the other
Hand, it is manifeſt by Conſtruction, that ſome one
of the Perpendiculars m n, Figure 29, viz. that
which paſſes through the Center of the

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