Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

Table of figures

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          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/886.jpg" pagenum="193"/>
                <emph type="italics"/>
              demonſtrated, and the Motions thorow them ſhall be performed in equal
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              Times ſeeing that they terminate in A unto the Circumference of the
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              Circle A G O from the higheſt point of it A.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>PROBL. XII. PROP.
                <emph type="italics"/>
              XXXIII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>A Perpendicular and Plane inclined to it being
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              given, whoſe height is one and the ſame, as al­
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              ſo the higheſt term, to find a point in the Per­
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              pendicular above the common term, out of
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              which if a Moveable be demitted that ſhall
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              afterwards turn along the inclined Plane, the
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              ſaid Plane may be paſt in the ſame Time in
                <lb/>
              which the
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              erpendicular
                <emph type="italics"/>
              ex quiete
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              would be
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              paſſed.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Perpendicular and inclined Plane, whoſe Altitude is the
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              ſame, be A B and A C. </s>
              <s>It is required in the Perpendicular B A,
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              continued out from the point A to find a Point out of which a
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              Moveable deſcending may paſſe the Space A C in the ſame Time in
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              which it will paſſe the ſaid Perpendicular A B out of Reſt in A. </s>
              <s>Draw
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              D C E at Right-Angles to A C, and let C D be cut equal to A B, and
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              draw a Line from A to D: The Angle A D C ſhall be greater than the
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              Angles C A D: (for C A is greater than A B or C D:) Let the
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              Angle D A E be equal to the Angle A D E; and to A E let E F an in­
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              clined Plane be Perpen-
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.886.1.jpg" xlink:href="040/01/886/1.jpg" number="132"/>
                <lb/>
                <emph type="italics"/>
              dicular, and let both be­
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              ing prolonged meet in F,
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              and unto both A I and
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              A G ſuppoſe C F to be
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              equal, and by G draw
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              G H equidiſtant to the
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              Horizon. </s>
              <s>I ſay, that H
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              is the point which is
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              ſought. </s>
              <s>For ſuppoſing the
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              Time of the Fall along
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              the Perpendicular A B
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              to be A B, the Time along
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              A C ex quiete in A ſhall be the ſame A C. </s>
              <s>And becauſe in the Right­
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              angled Triangle A E F, from the Right Angle E unto the Baſe A F,
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              E C is a Perpendicular, A E ſhall be a Mean-Proportional betwixt F A
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              and A C, and C E a Mean betwixt A C and C F, that is, betwixt C A
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              and A I: and foraſmuch as the Time of A C out of A is A C, A E
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
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