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

Table of figures

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            <p type="main">
              <s>
                <pb xlink:href="040/01/892.jpg" pagenum="199"/>
                <emph type="italics"/>
              pendicular to the Diameter A I: Wherefore alſo A I toucheth the Cir­
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              cle B O E in I. And, becauſe the Angle A I C is greater than the An­
                <lb/>
              gle A B C, as inſiſting on a larger Periphery: Therefore the Angle
                <lb/>
              S I N ſhall be alſo greater than the ſame A B C: Therefore the Portion
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              I E S is greater than the Portion B O; and the Line C S, nearer to the
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              Center, greater than C B: Therefore alſo C O is greater than C I;
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              for that S C is to C B, as O C is to C I.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              And the ſame alſo would happen to be greater, if (as in the other
                <lb/>
              Figure) the Quadrant B I C were
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.892.1.jpg" xlink:href="040/01/892/1.jpg" number="139"/>
                <lb/>
                <emph type="italics"/>
              leſſer: For the Perpendicular D B
                <lb/>
              will cut the Circle C I B: Wherefore
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              D I alſo is equal to the ſaid D B; and
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              the Angle D I A ſhall be Obtuſe, and
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              therefore A I N will alſo cut B I N:
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              And becauſe the Angle A B C is leſſe
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              than the Angle A I C, which is equal
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              to S I N; and this now is leſſe than that
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              which would be made at the Contact in
                <lb/>
              I by the Line S I: Therefore the Porti­
                <lb/>
              on S E I is much greater than the Por­
                <lb/>
              tion B O: Wherefore,
                <emph.end type="italics"/>
              &c.
                <emph type="italics"/>
              Which was
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              to be demonſtrated.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>THEOR.
                <emph type="italics"/>
              XXII.
                <emph.end type="italics"/>
              PROP.
                <emph type="italics"/>
              XXXVI.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>If from the loweſt point of a Circle erect unto
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              the Horizon a Plane ſhould be elevated ſub­
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              tending a Circumference not greater than a
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              Quadrant, from whoſe Terms two other
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              Planes are Inflected to any point of the Cir­
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              cumference, the Deſcent along both the Infle­
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              cted Planes would be performed in a ſhorter
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              Time than along the former elevated Plane
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              alone, or than along but one of the other two,
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              namely, along the lower.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let C B D be the Circumference not greater than a Quadrant of a
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              Circle erect unto the Horizon on the lower point C, in which let
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              C D be an elevated Plane; and let two Planes be inflected from the
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              Terms D and C to any point in the Circumference taken at pleaſure,
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              as B. </s>
              <s>I ſay, that the Time of the Deſcent along both thoſe Planes D B C
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              is ſhorter than the Time of the Deſcent along the ſole Plane D C, or
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              along the other only B C
                <emph.end type="italics"/>
              ex quiete
                <emph type="italics"/>
              in B. </s>
              <s>Let the Horizontal Line M D A
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
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