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

Table of figures

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      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/930.jpg" pagenum="237"/>
            <p type="head">
              <s>PROBL. V. PROP. XII.</s>
            </p>
            <p type="main">
              <s>To collect by Calculation of the Amplitudes of all
                <lb/>
              Semiparabola's that are deſcribed by Projects
                <lb/>
              expulſed with the ſame
                <emph type="italics"/>
              Impetus,
                <emph.end type="italics"/>
              and to make
                <lb/>
              Tables thereof.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              It is obvious, from the things demonſtrated, that Parabola's are de­
                <lb/>
              ſcribed by Projects of the ſame
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              then, when their Subli­
                <lb/>
              mities together with their Altitudes do make up equal Perpendicu­
                <lb/>
              lars upon the Horizon. </s>
              <s>Theſe Perpendiculars therefore are to be com­
                <lb/>
              prehended between the ſame Horizontal Parallels. </s>
              <s>Therefore let the
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              Horizontal Line C B be ſuppoſed equal to the Perpendicular B A, and
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              draw the Diagonal from A to C. </s>
              <s>The Angle A C B ſhall be Semi­
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              right, or 45 Degrees. </s>
              <s>And the Perpendicular B A being divided into
                <lb/>
              two equal parts in D, the Semiparabola D C ſhall be that which is de­
                <lb/>
              ſcribed from the Sublimity A D together with the Altitude D B: and
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              its
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              in C ſhall be as great as that of the Moveable coming out of
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              Reſt in A along the Perpendicular A B is in B. </s>
              <s>And if A G be drawn
                <lb/>
              parallel to B C, the united Altitudes and Sublimities of all other re­
                <lb/>
              maining Semiparabola's whoſe future
                <emph.end type="italics"/>
              Impetus's
                <emph type="italics"/>
              are the ſame with thoſe
                <lb/>
              now mentioned muſt be bounded by the Space between the Parallels
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.930.1.jpg" xlink:href="040/01/930/1.jpg" number="162"/>
                <lb/>
                <emph type="italics"/>
              A G and B C. Farthermore, it having
                <lb/>
              been but now demonſtrated, that the Am­
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              plitudes of the Semiparabola's whoſe
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              Tangents are equidiſtant either above or
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              below from the Semi right Elevation are
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              equal, the Calculations that we frame
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              for the greater Elevations will likewiſe
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              ſerve for the leſſer. </s>
              <s>We chooſe moreover
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              a number of ten thouſand parts for the
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              greateſt Amplitude of the Projection of
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              the Semiparabola made at the Elevation
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              of 45 degrees: ſo much therefore the Line
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              B A, and the Amplitude of the Semipa­
                <lb/>
              rabola B C, are to be ſuppoſed. </s>
              <s>And we
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              make choice of the number 10000, becauſe we in our Calculation uſe
                <lb/>
              the Table of Tangents, in which this number agreeth with the Tangent
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              of 45 degrees. </s>
              <s>Now, to come to the buſineſs, let C E be drawn, contain­
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              ing the Angle E C B greater (Acute nevertheleſs,) than the Angle
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              A C B; and let the Semiparabola be deſcribed which is touched by the
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              Line E C, and whoſe Sublimity united with its Altitude is equal to
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              B A. </s>
              <s>In the Table of Tangents take the ſaid B E for the Tangent at the
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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