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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/290.jpg" pagenum="270"/>
              becauſe the angle B A D, conteined between the vertical lines, is
                <lb/>
              equal to the difference of the Polar altitudes, it ſhall be 4
                <emph type="italics"/>
              gr. </s>
              <s>40m.
                <emph.end type="italics"/>
                <lb/>
              which I note here apart; and I finde the chord of it by the Table
                <lb/>
              of Arches and Chords, and ſet it down neer unto it, which is 8142
                <lb/>
              parts, of which the ſemidiameter A B is 100000. Next, I finde
                <lb/>
              the angle B D C with eaſe, for the half of the angle B A D, which
                <lb/>
              is 2
                <emph type="italics"/>
              gr. </s>
              <s>20 m.
                <emph.end type="italics"/>
              added to a right angle, giveth the angle B D F 92
                <emph type="italics"/>
              gr.
                <emph.end type="italics"/>
                <lb/>
              20
                <emph type="italics"/>
              m.
                <emph.end type="italics"/>
              to which adding the angle C D F, which is the diſtance from
                <lb/>
              the vertical point of the greateſt altitude of the Star, which here is
                <lb/>
              62
                <emph type="italics"/>
              gr. </s>
              <s>15 m.
                <emph.end type="italics"/>
              it giveth us the quantity of the angle B D C,
                <lb/>
              154
                <emph type="italics"/>
              grad. </s>
              <s>45 min.
                <emph.end type="italics"/>
              the which I ſet down together with its Sine,
                <lb/>
              taken out of the Table, which is 42657, and under this I note
                <lb/>
              the angle of the Parallax B C D 0
                <emph type="italics"/>
              gr. </s>
              <s>2 m.
                <emph.end type="italics"/>
              with its Sine 58.
                <lb/>
              And becauſe in the Triangle B C D, the ſide D B is to the ſide
                <lb/>
              B C; as the ſine of the oppoſite angle B C D, to the ſine of the
                <lb/>
              oppoſite angle B D C: therefore, if the line B D were 58. B C
                <lb/>
              would be 42657. And becauſe the Chord D B is 8142. of thoſe
                <lb/>
              parts whereof the ſemidiameter B A is 100000. and we ſeek to
                <lb/>
              know how many of thoſe parts is B C; therefore we will ſay, by
                <lb/>
              the Golden Rule, if when B D is 58. B G is 42657. in caſe the
                <lb/>
              ſaid D B were 8142. how much would B C be? </s>
              <s>I multiply the
                <lb/>
              ſecond term by the third, and the product is 347313294. which
                <lb/>
              ought to be divided by the firſt, namely, by 58. and the quotient
                <lb/>
              ſhall be the number of the parts of the line B C, whereof the
                <lb/>
              midiameter A B is 100000. And to know how many
                <lb/>
              ters B A, the ſaid line B C doth contein, it will be neceſſary anew
                <lb/>
              to divide the ſaid quotient ſo found by 100000. and we ſhall have
                <lb/>
              the number oſ ſemidiameters conteined in B G. </s>
              <s>Now the
                <lb/>
              ber 347313294. divided by 58. giveth 5988160 1/4. as here you
                <lb/>
              may
                <lb/>
                <arrow.to.target n="table13"/>
              </s>
            </p>
            <table>
              <table.target id="table10"/>
              <row>
                <cell/>
                <cell>
                  <emph type="italics"/>
                gr.
                  <emph.end type="italics"/>
                </cell>
                <cell>
                  <emph type="italics"/>
                m.
                  <emph.end type="italics"/>
                </cell>
                <cell>Its chord 8142 of thoſe</cell>
              </row>
              <row>
                <cell>Ang. B A D</cell>
                <cell>4</cell>
                <cell>40</cell>
                <cell>parts, whereof the ſemid.</cell>
              </row>
              <row>
                <cell>B D F</cell>
                <cell>92</cell>
                <cell>20</cell>
                <cell>A B is an 100000.</cell>
              </row>
            </table>
            <table>
              <table.target id="table11"/>
              <row>
                <cell>B D C</cell>
                <cell>154</cell>
                <cell>45</cell>
                <cell>Sines</cell>
                <cell>42657</cell>
              </row>
              <row>
                <cell>B C D</cell>
                <cell>0</cell>
                <cell>2</cell>
                <cell/>
                <cell>58</cell>
              </row>
            </table>
            <table>
              <table.target id="table12"/>
              <row>
                <cell>58</cell>
                <cell>42657</cell>
                <cell>8142</cell>
              </row>
              <row>
                <cell/>
                <cell>8142</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>85314</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>170628</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>42657</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>341256</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>59</cell>
                <cell/>
              </row>
              <row>
                <cell>58</cell>
                <cell>3473</cell>
                <cell>13294</cell>
              </row>
              <row>
                <cell/>
                <cell>571</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>5</cell>
                <cell/>
              </row>
            </table>
            <table>
              <table.target id="table13"/>
              <row>
                <cell/>
                <cell>5988160 1/4</cell>
              </row>
              <row>
                <cell>58</cell>
                <cell>347313294</cell>
              </row>
              <row>
                <cell/>
                <cell>5717941</cell>
              </row>
              <row>
                <cell/>
                <cell>543</cell>
              </row>
            </table>
            <p type="main">
              <s>And this divided by 100000. the product is 59
                <lb/>
                <arrow.to.target n="table14"/>
              </s>
            </p>
            <table>
              <table.target id="table14"/>
              <row>
                <cell>1 |00000</cell>
                <cell>| 59 |</cell>
                <cell>88160.</cell>
              </row>
            </table>
            <p type="main">
              <s>But we may much abbreviate the operation, dividing the firſt
                <lb/>
              quotient found, that is, 347313294. by the product of the
                <lb/>
              plication of the two numbers 58. and 100000. that </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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