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 |< < (364) of 1011 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="bundle" level="1" n="1">
          <pb file="add_6782_f364" o="364" n="728"/>
          <head xml:space="preserve" xml:lang="lat"> De
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On ]</head>
          <p>
            <s xml:space="preserve"> Seing that any finite line will
              <lb/>
            subtend an angle at summe distance;
              <lb/>
            as let
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            subtend the
              <emph style="st">the</emph>
            angle
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            </s>
            <lb/>
            <s xml:space="preserve"> Then a line double to
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , which let be
              <lb/>
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            , will subtend the same angle at a
              <lb/>
            double distance, so that
              <emph style="it">
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mi>b</mi>
                  </mstyle>
                </math>
              </emph>
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            will be
              <lb/>
            aequall to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            </s>
          </p>
          <p>
            <s xml:space="preserve"> In those subtensions I understand that the poynt
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            be
              <emph style="super">in a</emph>
            perpendicular
              <emph style="super">line</emph>
            to the
              <lb/>
            middle of the subtendent </s>
            <s xml:space="preserve"> as also in all the others which </s>
          </p>
          <p>
            <s xml:space="preserve"> Now I suppose
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            to be removed to a further distance from the poynt
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            .
              <lb/>
            </s>
            <s xml:space="preserve"> Then the angle
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            subtended must be lesse than </s>
            <s xml:space="preserve"> And
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            .
              <lb/>
            shall
              <emph style="st">[???]</emph>
            subtend the same angle at a double distance as </s>
          </p>
          <p>
            <s xml:space="preserve"> And this is true
              <emph style="st">generally</emph>
            continually that the
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            is removed
              <lb/>
            the lesse angle it subtendeth &
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            always must subtend the same
              <lb/>
            angle at a double </s>
          </p>
          <p>
            <s xml:space="preserve"> Then I suppose
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            to be removed to an infinite distance; at which
              <lb/>
            distance the supposition altereth not the quantity of
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . but
              <emph style="st">quantity </emph>
            consequence
              <lb/>
            is of the </s>
            <s xml:space="preserve"> Which wilbe, that the angle
              <emph style="st">wh</emph>
            then subtended
              <emph style="it">[???]</emph>
            to be
              <lb/>
            of an infinite quantity in litleness in respecte of the former </s>
            <s xml:space="preserve"> Yet it
              <lb/>
            cannot be sayd to be no angle negatively because it is positive. & it
              <lb/>
            must also follow that the line
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            must subtend the same positive angle
              <lb/>
            at a double </s>
            <s xml:space="preserve"> Which is Double to the former infinite </s>
          </p>
          <p>
            <s xml:space="preserve"> Also, let the distance of the subtendents be nearer
              <emph style="st">[???]</emph>
              <emph style="super">to</emph>
              <emph style="st">[???]</emph>
            it cannot be
              <lb/>
            otherwise inferred but that the lines
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
              <emph style="st">being infinit</emph>
            though infinite,
              <lb/>
            be
              <foreign xml:lang="lat ">ad diversas partes, & in diversis locis</foreign>
            , because
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            are betweene them,
              <lb/>
            & have agreement or concurrence but only in the poynt
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
              <emph style="st">[???]</emph>
              <emph style="super">or</emph>
            in no distance
              <lb/>
            out of the poynt
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            </s>
          </p>
          <p>
            <s xml:space="preserve"> And yet the nearness of there congruence &con
              <emph style="super">cu</emph>
            rrence in all other partes
              <lb/>
            [???] at the utmost is such, that although they be remote; the angle
              <lb/>
            is of no proportion explicable by nomber finite, but [¿]unknown[?], to any
              <lb/>
              <emph style="st">angles</emph>
            other angle which we call </s>
            <s xml:space="preserve"> The like inexplicable proportion
              <lb/>
            is of the
              <emph style="super">subtendent</emph>
            lines
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , to there infinite distance position from
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            </s>
            <lb/>
            <s xml:space="preserve"> And yet the sayd lines
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . as also that infinite litle or improportio-
              <lb/>
            nable angle is divisible still
              <foreign xml:lang="lat">in infinitum</foreign>
            . & still, although improportionable
              <lb/>
            yet in an other respect, that is to say of his owne partes, is </s>
          </p>
        </div>
      </text>
    </echo>
Impressum