Harriot, Thomas, Mss. 6782

List of thumbnails

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741 (370v) 		742
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745 (372v) 		746
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747 (373v) 		748
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page |< < (365) of 1011 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="bundle" level="1" n="1">
          <pb file="add_6782_f365" o="365" n="730"/>
          <head xml:space="preserve" xml:lang="lat"> De
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On ]</head>
          <p>
            <s xml:space="preserve"> That in a finite time an infinite space
              <lb/>
            may be </s>
          </p>
          <p>
            <s xml:space="preserve"> It is now convenient
              <lb/>
            that
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            be in this </s>
          </p>
          <p>
            <s xml:space="preserve"> Suppose the
              <emph style="st">the</emph>
            line
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>e</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
              <foreign xml:lang="lat">et ultra</foreign>
              <lb/>
            to be infinite, & the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            suppose
              <lb/>
            to revolve & describe a circle
              <lb/>
            in a finite time, fro
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            towards
              <lb/>
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            .
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            doth first respect
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            , then
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <lb/>
            after
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            , & so forth successively no poynt
              <lb/>
            in the infinite line is
              <emph style="st">not</emph>
            unrespected by that time the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            cometh
              <lb/>
            to
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            where then the line is parallel & cutteth not the former
              <lb/>
            line </s>
            <s xml:space="preserve"> Now seing that a motion may be of any thing
              <lb/>
            according
              <emph style="super">to</emph>
            the continuall succession of a poynt, as well in respect
              <lb/>
            of
              <emph style="st">[???]</emph>
              <foreign xml:lang="lat">mobile ab motus</foreign>
            </s>
            <s xml:space="preserve"> Whatsoever may be or not be in
              <lb/>
            respect of the moment, it maketh no matter: the purpose is
              <lb/>
            </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Consequentia
              <lb/>
            Accidentis quædam huius </s>
          </p>
          <p>
            <s xml:space="preserve"> The line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            having moved till he comes to be
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            that is
              <lb/>
            parallel to
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            . & so that continuing his motion of </s>
          </p>
          <p>
            <s xml:space="preserve"> The lines are parallel but in one </s>
            <lb/>
            <s xml:space="preserve"> They never cut at an infinite distance but at that instant
              <lb/>
            they are </s>
            <lb/>
            <s xml:space="preserve"> And if they cut then, they must
              <foreign xml:lang="lat">ad utrasque partes</foreign>
            & then
              <lb/>
            being right lines there must be no space betwixte them, but
              <lb/>
            there distance by supposition is more than the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> Which
              <lb/>
            implies </s>
          </p>
          <p>
            <s xml:space="preserve"> And yet there must be a cutting at an infinite distance or else all
              <lb/>
            the poyntes of the infinite line could not have been respected. &</s>
            <s xml:space="preserve"> if
              <lb/>
            that be not some part of the infinite line, that is some quantity
              <emph style="st">which</emph>
              <lb/>
              <emph style="st">it is</emph>
            finite is only & that is at a finite distance; & then it maketh an
              <lb/>
            angle
              <emph style="super">of quantity</emph>
            at the greatest distance of such cutting: from that cutting the line
              <lb/>
            by motion came to be parallel: That motion is made in an instant or
              <lb/>
            in </s>
            <s xml:space="preserve"> If in time, then in half the time the cutting must be further
              <lb/>
            than the supposed </s>
            <s xml:space="preserve"> If in an instant, our line wilbe in
              <emph style="st">two places</emph>
              <lb/>
            two places in one
              <emph style="st">[???]</emph>
              <foreign xml:lang="lat">quæ implicant</foreign>
            </s>
          </p>
          <p>
            <s xml:space="preserve"> The lines therefore must cut at an infinite distance before they come to
              <lb/>
            be </s>
            <s xml:space="preserve"> And that must be in time before or in an instant before.
              <lb/>
            </s>
            <s xml:space="preserve"> If in time, then in half the time they cut at greater distance than infinite or
              <lb/>
            are parallel before they are </s>
            <s xml:space="preserve"> Which both do imply contradiction.
              <lb/>
            </s>
            <s xml:space="preserve"> If in an instant before; the two instants are one or </s>
            <s xml:space="preserve"> If one,
              <foreign xml:lang="lat">implicat</foreign>
            .
              <lb/>
            </s>
            <s xml:space="preserve"> If two there must be no other betwixt </s>
            <s xml:space="preserve"> And then there [???] be a time greater
              <lb/>
            than an instant & lesse than any time of quantity that is indivisible, that is
              <lb/>
            agayne, indivisible into partes of quantity. & so also like of poyntes &</s>
          </p>
        </div>
      </text>
    </echo>
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