Gravesande, Willem Jacob 's
,
An essay on perspective
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An ESSAY
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Line G E, in the Points p, from every of which
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raiſe Perpendiculars p q, each of which muſt
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be continued on each Side the Line G E, equal
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to m n the Part of the correſpondent Line p m.
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">Now if a great Number of the Points q be thus
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found, and they are joyn’d by an even Hand,
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you will have a Curve Line which will be the
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Repreſentation ſought.</
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">The Rays by which we perceive a Sphere, do form
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an upright Cone, whoſe Axis paſſes through the Cen-
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ter of the Sphere, and whoſe Section made by the
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Perſpective Plane, is the Repreſentation ſought: </
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whence it follows, that I is the Point in the Perſpe-
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ctive Plane, through which the Cone’s Axis paſſes.
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</
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">But when an upright Cone is ſo cut by a Plane, that
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the Section is an Ellipſis, as in this Caſe, the tranſ-
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verſe Diameter of this Ellipſis, will paſs through
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the Point of Concurrence of the ſaid Plane, and
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Axis of the Cone, and that Point wherein a Per-
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pendicular drawn from the Vertex of the Cone, cuts
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the ſaid Plane. </
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<
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">This will appear evident enough
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to any one of but mean Knowledge in Conick Secti-
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ons. </
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<
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">Therefore the tranſverſe Axis of the Ellipſis,
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which is the Repreſentation of the Sphere, is ſome
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Part of V I; </
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">for the Eye is the Vertex of the Cone
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formed by the viſual Rays of the Spbere.</
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">Now let us conceive a Plane to paſs through the
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Eye, and the Line I V; </
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Center of the Sphere: </
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">And if a Perpendicular be
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let fall from the Center upon the principal Ray con-
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tinued, that Part of the ſaid Ray included between
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the Point of Sight, and the Point wherein this Per-
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pendicular falls, which is always parallel to the Per-
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ſpective Plane, will be equal to the Diſtance from
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the Center of the Sphere to the Perſpective </
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