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

Table of figures

< >
[Figure 151]
Page: 916
[Figure 152]
Page: 917
[Figure 153]
Page: 919
[Figure 154]
Page: 922
[Figure 155]
Page: 923
[Figure 156]
Page: 924
[Figure 157]
Page: 926
[Figure 158]
Page: 927
[Figure 159]
Page: 927
[Figure 160]
Page: 928
[Figure 161]
Page: 929
[Figure 162]
Page: 930
[Figure 163]
Page: 932
[Figure 164]
Page: 938
[Figure 165]
Page: 941
[Figure 166]
Page: 942
[Figure 167]
Page: 944
[Figure 168]
Page: 945
[Figure 169]
Page: 948
[Figure 170]
Page: 949
[Figure 171]
Page: 950
[Figure 172]
Page: 952
[Figure 173]
Page: 953
[Figure 174]
Page: 955
[Figure 175]
Page: 956
[Figure 176]
Page: 958
[Figure 177]
Page: 959
[Figure 178]
Page: 961
[Figure 179]
Page: 962
[Figure 180]
Page: 970
< >
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/932.jpg" pagenum="239"/>
              Second Book. </s>
              <s>You muſt alſo know, that the point F which divi­
                <lb/>
              deth the Tangent E B in the middle, will many other times fall
                <lb/>
              above the point A, and once alſo in the ſaid A: In which caſes it is
                <lb/>
              evident of it ſelf, that the third proportional to the half of the Tan­
                <lb/>
              gent, and to B I (which giveth the Sublimity) is all above A. </s>
              <s>But
                <lb/>
              the Author hath taken a Caſe in which it was not manifeſt that the
                <lb/>
              ſaid third Proportional is alwaies greater than F A: and which
                <lb/>
              therefore being ſet off above the point F paſſeth beyond the Paral­
                <lb/>
              lel A G. </s>
              <s>Now let us proceed.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              It will not be unprofitable if by help of this Table we compoſe ano­
                <lb/>
              ther, ſhewing the Altitudes of the ſame Semiparabola's of Projects of
                <lb/>
              the ſame
                <emph.end type="italics"/>
              Impetus.
                <emph type="italics"/>
              And the Conſtruction of it is in this manner.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>PROBL. VI. PROP. XIII.</s>
            </p>
            <p type="main">
              <s>From the given Amplitudes of Semiparabola's in
                <lb/>
              the following Table ſet down, keeping the
                <lb/>
              common
                <emph type="italics"/>
              Impeius
                <emph.end type="italics"/>
              with which every one of
                <lb/>
              them is deſcribed, to compute the Altitudes of
                <lb/>
              each ſeveral Semiparabola.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Amplitude given be B C, and of the
                <emph.end type="italics"/>
              Impetus,
                <emph type="italics"/>
              which is
                <lb/>
              ſuppoſed to be alwaies the ſame, let the Meaſure be O B, to wit,
                <lb/>
              the Aggregate of the Altitude and Sublimity. </s>
              <s>The ſaid Altitude
                <lb/>
              is required to be found and diſtinguiſhed. </s>
              <s>Which ſhall then be done when
                <lb/>
              B O is ſo divided as that the Rectangle contained under its parts is
                <lb/>
              equal to the Square of half the Amplitude B C. </s>
              <s>Let that ſame divi­
                <lb/>
              ſion fall in F; and let both O B and B C be cut in the midſt at D and I.
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.932.1.jpg" xlink:href="040/01/932/1.jpg" number="163"/>
                <lb/>
                <emph type="italics"/>
              The Square I B, therefore, is equal to the
                <lb/>
              Rectangle B F O: And the Square D O is
                <lb/>
              equal to the ſame Rectangle together with the
                <lb/>
              Square F D. </s>
              <s>If therefore from the Square
                <lb/>
              D O we deduct the Square B I, which is equal
                <lb/>
              to the Rectangle B F O, there ſhall remain
                <lb/>
              the Square F D; to whoſe Side D F, B D be­
                <lb/>
              ing added it ſhall give the deſired Altitude
                <lb/>
              Altitude B F. </s>
              <s>And it is thus compounded
                <emph.end type="italics"/>
                <lb/>
              ex datis.
                <emph type="italics"/>
              From half of the Square B O known
                <lb/>
              ſubſtract the Square B I alſo known, of the remainder take the Square
                <lb/>
              Root, to which add D B known; and you ſhall have the Altitude ſought
                <lb/>
              B F. </s>
              <s>For example. </s>
              <s>The Altitude of the Parabola deſcribed at the
                <lb/>
              Elevation of 55 degrees is to be found. </s>
              <s>The Amplitude, by the follow­
                <lb/>
              ing Table is 9396, its half is 4698, the Square of that is 22071204,
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum