Harriot, Thomas, Mss. 6782

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501
501 (251) 		502
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      <text xml:lang="eng" type="free">
        <div type="bundle" level="1" n="1">
          <pb file="add_6782_f369" o="369" n="738"/>
          <head xml:space="preserve" xml:lang="lat"> De
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On ]</head>
          <p>
            <s xml:space="preserve"> Now will I propound some dfficultyes to be
              <lb/>
            considered </s>
            <s xml:space="preserve"> Seing that every line is compounded
              <lb/>
            of atomes, & therefore the periphery of a circle.
              <emph style="st">that
                <lb/>
              is to say</emph>
              <foreign xml:lang="lat">atomus</foreign>
            is succeeding one an other
              <lb/>
            infinitely in such manner as
              <emph style="it">that</emph>
            the perifery is at
              <lb/>
            last compounded and </s>
          </p>
          <p>
            <s xml:space="preserve"> Now also seing that the whole
              <foreign xml:lang="lat">periferies</foreign>
            is compounded of
              <foreign xml:lang="lat">atomis undiquaque
                <lb/>
              sitis</foreign>
            about the poynt
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            . so many times infinitely, & to that number of them
              <lb/>
            infinitely, till the circle supposed be </s>
          </p>
          <p>
            <s xml:space="preserve"> I demand
              <emph style="st">therefore</emph>
              <emph style="super">then</emph>
            what wilbe the nomber of
              <foreign xml:lang="lat">atomi</foreign>
            that are
              <foreign xml:lang="lat">deinceps</foreign>
            about the
              <lb/>
            point
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> Infinite they must needes be, or else infinite lines could not
              <lb/>
            be
              <emph style="st">dra</emph>
            supposed actually from the point
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            to the </s>
            <s xml:space="preserve"> And infinite also
              <lb/>
            are
              <emph style="super">also</emph>
            in the </s>
            <s xml:space="preserve"> But now I demande whether they are aequally infinite
              <lb/>
            or </s>
            <s xml:space="preserve"> If about the center are lesse infinite then there cannot from the
              <lb/>
            center
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            to every poynt in the perifery be understood a right line but
              <lb/>
            we must understand those
              <emph style="super">
                <foreign xml:lang="lat">atomi</foreign>
              about the center</emph>
            that we supposed indivisible, divisble
              <emph style="super">which were absurd</emph>
            </s>
            <s xml:space="preserve"> and
              <lb/>
            if they be æqually infinite: then
              <emph style="st">the same nomber
                <foreign xml:lang="lat">atomi</foreign>
              </emph>
            in a great
              <lb/>
            place, (where the nomber, although infinite, yet in them selves definite; because
              <lb/>
            they being supposed to have
              <emph style="st">[???]</emph>
            acte there is not one more nor </s>
            <s xml:space="preserve"> Neither
              <lb/>
            can there be more because
              <emph style="st">[???]</emph>
            they being
              <foreign xml:lang="lat">deinceps</foreign>
            one more cannot
              <lb/>
            be between there being no distance: & if there
              <emph style="st">be supposed</emph>
              <emph style="super">might be</emph>
            one lesse; there
              <lb/>
            lacketh of the supposed actaull, & definite & positive number although infinite.
              <lb/>
            </s>
            <s xml:space="preserve"> Then I say in a greate place where there could be no more or lesse,
              <lb/>
            in a lesse place there are an æquall nomber; which seemeth to </s>
          </p>
          <p>
            <s xml:space="preserve"> An other difficulty riseth from the </s>
            <s xml:space="preserve"> If a line
              <lb/>
            be compounded of
              <foreign xml:lang="lat">atomis</foreign>
            , the diametrall line wilbe
              <lb/>
            found to be aæquall to the </s>
            <s xml:space="preserve"> ffor suppose the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
              <lb/>
            to be drawne
              <emph style="st">from the poynt[???]</emph>
            from the point
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
              <emph style="super">of the line
                <math>
                  <mstyle>
                    <mi>a</mi>
                    <mi>d</mi>
                  </mstyle>
                </math>
              ,</emph>
            to
              <lb/>
            the point
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            , of
              <emph style="st">th</emph>
            the line
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            . Then from the next point
              <lb/>
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            , which is
              <foreign xml:lang="lat">deinceps</foreign>
            to
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            in the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , draw a line
              <lb/>
            to
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            the next point to
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            in the line
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> So likewise from every
              <lb/>
            next point in the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            , to every next point in the line
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            </s>
            <s xml:space="preserve"> Now the lines so drawne must needs be the least & most that may be,
              <lb/>
            because they are
              <foreign xml:lang="lat">deinceps</foreign>
            & & they all cut the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            & of the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            there can be
              <emph style="st">between</emph>
            no point
              <emph style="st">the</emph>
            two of the former
              <emph style="super">because they
                <foreign xml:lang="lat">deinceps</foreign>
              </emph>
            </s>
            <s xml:space="preserve"> And therefore
              <lb/>
            the nomber of the poynts of the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <emph style="super">are</emph>
            aequally infinite to the poynts of
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            &
              <lb/>
              <foreign xml:lang="lat">per</foreign>
            consequence the lines
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            &
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            </s>
            <s xml:space="preserve"> But this difficulty wilbe made more
              <lb/>
            playne by the next following, which
              <emph style="st">[???]</emph>
            wilbe found the meanes for the solution
              <lb/>
            of </s>
          </p>
          <p>
            <s xml:space="preserve"> An other question is. where
              <foreign xml:lang="lat">atomi</foreign>
              <foreign xml:lang="lat">deinceps</foreign>
            . whether an other
              <lb/>
            (the
              <emph style="st">other</emph>
              <emph style="super">first two</emph>
            not disioyned) may either passe or have situation betwixt </s>
          </p>
        </div>
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