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

Table of figures

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            <p type="main">
              <s>
                <pb xlink:href="040/01/894.jpg" pagenum="201"/>
                <emph type="italics"/>
              C O to the Square O F; foraſmuch as C D, D O, and O F are Propor­
                <lb/>
              tionals: And as C A is to A B, ſo is the Square C V to the Square
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              V B: Therefore C O hath greater proportion to O F, than C V to V B:
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              Therefore, by the foregoing Lemma, C O is greater than C V. </s>
              <s>It is
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              manifeſt moreover, that the Time along D C is to the Time along
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              D B C, as D O C is to D O together with C V.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>SCHOLIUM.</s>
            </p>
            <p type="main">
              <s>From theſe things that have been demonſtrated may evidently
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              be gathered, that the ſwifteſt of all Motions betwixt Term
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              and Term is not made along the ſhorteſt Line, that is by the
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              Right, but along a portion of a Circle.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              For in the Quadrat B A E C, whoſe Side B C is erect to the Hori­
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              zon, let the Arch A C be divided into any number of equal parts,
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              A D, D E, E F, F G, G C; and let Right-lines be drawn from C to
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              the Points A, D, E, F, G, H; and alſo by Lines joyn A D, D E, E F,
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              F G. and G C. </s>
              <s>It is manifest, that the Motion along the two Lines
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              A D C is ſooner performed than along the
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.894.1.jpg" xlink:href="040/01/894/1.jpg" number="141"/>
                <lb/>
                <emph type="italics"/>
              ſole Line A C, or D C out of Reſt in D:
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              But out of Reſt in A, D C is ſooner paſt
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              than the two A D C: But along the two
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              D E C out of Reſt in A the Deſcent is
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              likewiſe ſooner made than along the ſole
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              C D: Therefore the Deſcent along the
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              three Lines A D E C ſhall be performed
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              ſooner than along the two A D C. </s>
              <s>And
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              in like manner the Deſcent along A D E
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              preceding, the Motion is more ſpeedily con­
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              ſummated along the two EFC than along the ſole FC: Therfore along the
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              four A D E F C the Motion is quicklier accompliſhed than along the
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              three A D E C: And ſo, in the laſt place, along the two F G C after the
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              precedent Deſcent along A D E F the Motion will be ſooner conſumma­
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              ted than along the ſole F C: Therefore along the five A D E F G C
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              the Deſcent ſhall be effected in a yet ſhorter Time than along the four
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              A D E F C: Whereupon the nearer by inſcribed Poligons we approach
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              the Circumference, the ſooner will the Motion be performed between the
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              two aſſigned points A C.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              And that which is explained in a Quadrant, holdeth true likewiſe
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              in a Circumference leſſe than the Quadrant: and the Ratiocination is
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              the ſame.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
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