Gravesande, Willem Jacob 's, An essay on perspective

Table of Notes

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            Line G E, in the Points p, from every of which
              <lb/>
            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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            <s xml:id="echoid-s1130" xml:space="preserve">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.</s>
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            <emph style="sc">Demonstration</emph>
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            <s xml:id="echoid-s1132" xml:space="preserve">The Rays by which we perceive a Sphere, do form
              <lb/>
            an upright Cone, whoſe Axis paſſes through the Cen-
              <lb/>
            ter of the Sphere, and whoſe Section made by the
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            Perſpective Plane, is the Repreſentation ſought: </s>
            <s xml:id="echoid-s1133" xml:space="preserve">from
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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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            </s>
            <s xml:id="echoid-s1134" xml:space="preserve">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
              <lb/>
            the Point of Concurrence of the ſaid Plane, and
              <lb/>
            Axis of the Cone, and that Point wherein a Per-
              <lb/>
            pendicular drawn from the Vertex of the Cone, cuts
              <lb/>
            the ſaid Plane. </s>
            <s xml:id="echoid-s1135" xml:space="preserve">This will appear evident enough
              <lb/>
            to any one of but mean Knowledge in Conick Secti-
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            ons. </s>
            <s xml:id="echoid-s1136" xml:space="preserve">Therefore the tranſverſe Axis of the Ellipſis,
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            which is the Repreſentation of the Sphere, is ſome
              <lb/>
            Part of V I; </s>
            <s xml:id="echoid-s1137" xml:space="preserve">for the Eye is the Vertex of the Cone
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            formed by the viſual Rays of the Spbere.</s>
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            <s xml:id="echoid-s1139" xml:space="preserve">Now let us conceive a Plane to paſs through the
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            Eye, and the Line I V; </s>
            <s xml:id="echoid-s1140" xml:space="preserve">this will paſs through the
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            Center of the Sphere: </s>
            <s xml:id="echoid-s1141" xml:space="preserve">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
              <lb/>
            the Center of the Sphere to the Perſpective </s>
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Impressum