Harriot, Thomas, Mss. 6782

List of thumbnails

< >
501
501 (251) 		502
502 (251v)
503
503 (252) 		504
504 (252v)
505
505 (253) 		506
506 (253v)
507
507 (254) 		508
508 (254v)
509
509 (255) 		510
510 (255v)
< >
page |< < (368) of 1011 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="bundle" level="1" n="1">
          <pb file="add_6782_f368" o="368" n="736"/>
          <head xml:space="preserve" xml:lang="lat"> Ratio
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          The ratio of ]</head>
          <p>
            <s xml:space="preserve"> Let Achilles be
              <math>
                <mstyle>
                  <mi>A</mi>
                </mstyle>
              </math>
            </s>
            <lb/>
            <s xml:space="preserve"> Testudo
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The tortoise
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            . </s>
            <s xml:space="preserve"> The Motion of Achilles from
              <math>
                <mstyle>
                  <mi>A</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
              <lb/>
            in the time
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            . of Testudo from
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>C</mi>
                </mstyle>
              </math>
              <lb/>
            in the
              <emph style="super">same</emph>
            time
              <emph style="st">fg</emph>
            </s>
            <s xml:space="preserve">
              <emph style="st">Which let be the</emph>
              <lb/>
              <emph style="st">half parte of the time ef</emph>
            </s>
            <s xml:space="preserve"> Which
              <lb/>
            space of
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            let be the tenth parte
              <lb/>
            of
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> Now the quaestion is,
              <lb/>
            both these motions being continued in the same proportion as 10 to 1.
              <lb/>
            where & when shall
              <math>
                <mstyle>
                  <mi>A</mi>
                </mstyle>
              </math>
            overtake
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            .
              <emph style="st">Suppose at d</emph>
            .
              <lb/>
            </s>
            <s xml:space="preserve"> At some point or other it must really </s>
            <s xml:space="preserve"> Suppose that
              <emph style="super">X</emph>
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> There must be
              <lb/>
              <math>
                <mstyle>
                  <mi>A</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            ,
              <emph style="st">[???]</emph>
            at the same instant of </s>
            <s xml:space="preserve"> And therefore the time wherein
              <lb/>
              <emph style="st">that</emph>
              <math>
                <mstyle>
                  <mi>A</mi>
                </mstyle>
              </math>
            hath moved to
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            must be the same wherein
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            hath moved to
              <lb/>
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> But the space
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            must be as 10 to </s>
            <lb/>
            <s xml:space="preserve"> Now by the supposition it must follow (because these motions be proportionall
              <emph style="super">(as 10 to 1)</emph>
            )
              <lb/>
            * As
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            . so:
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            . which same termes
              <lb/>
            proportionall call by these
              <emph style="st">same</emph>
            letters & in the same </s>
          </p>
          <p>
            <s xml:space="preserve"> As
              <math>
                <mstyle>
                  <mi>β</mi>
                </mstyle>
              </math>
            is known to be 1.
              <math>
                <mstyle>
                  <mi>γ</mi>
                </mstyle>
              </math>
            is
              <math>
                <mstyle>
                  <mfrac>
                    <mrow>
                      <mn>1</mn>
                    </mrow>
                    <mrow>
                      <mn>1</mn>
                      <mn>0</mn>
                    </mrow>
                  </mfrac>
                </mstyle>
              </math>
              <math>
                <mstyle>
                  <mi>β</mi>
                  <mo>+</mo>
                  <mi>α</mi>
                </mstyle>
              </math>
            is unknown. & so is
              <math>
                <mstyle>
                  <mi>α</mi>
                </mstyle>
              </math>
            .
              <lb/>
            yet this is known that.
              <emph style="st">is æquall to
                <math>
                  <mstyle>
                    <mi>ɛ</mi>
                  </mstyle>
                </math>
              .</emph>
            </s>
          </p>
          <p>
            <s xml:space="preserve"> * Now what other proportion is this than if a man
              <lb/>
            should say as
              <emph style="st">all</emph>
            the first to the second so
              <lb/>
            all the antecedents to all the consequents which
              <lb/>
            in this be infinite in </s>
          </p>
          <p>
            <s xml:space="preserve"> X To find that poynt geometrically is set downe
              <lb/>
            in my other papers
              <foreign xml:lang="lat">de infinitis</foreign>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            on ]</s>
          </p>
        </div>
      </text>
    </echo>
Impressum