Harriot, Thomas, Mss. 6787

List of thumbnails

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731
731 (366v) 		732
732 (367)
733
733 (367v) 		734
734 (368)
735
735 (368v) 		736
736 (369)
737
737 (369v) 		738
738 (370)
739
739 (370v) 		740
740 (371)
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page |< < (378) of 1155 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6787_f378" o="378" n="754"/>
          <head xml:space="preserve" xml:lang="lat"> 1.) De
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          1) On the ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Datis tribus punctis
              <lb/>
            quorum unum ponitur in
              <lb/>
            centro de et caetera
              <lb/>
            duo in parabola:
              <lb/>
            Invenire
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Given three points of which one is supposed in the centre
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            and the other two on the parabola, find the parabola. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sint tria puncta,
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            , centroidis.
              <lb/>
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            , in
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let there be three points
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            ;
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            the focus,
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            on the parabola. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> fiat circulus cuius
              <lb/>
            diameter
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            et fit
              <lb/>
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>h</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            fiat alter circulus cuius semidiameter
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            et
              <lb/>
            fit
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            .
              <lb/>
            punctum
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            est in infini-
              <lb/>
            tis parabolis et locus
              <lb/>
            omnium verticum est
              <lb/>
            in spirali quaedam propria
              <lb/>
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            quae fit ex medijs
              <lb/>
            punctis inter periferias
              <lb/>
            circulorum
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Make the circle whose diameter is
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            and construct
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>h</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Make another circle whose semidiameter is
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            and construct
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            .
              <lb/>
            The point
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            is on an infinite parabola and the locus of all vertices is on the spiral through
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            , which is constructed from the midpoints between the circumferences of the described circles. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Deinde fiat circulus
              <lb/>
            cuius diameter
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            et fit
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>k</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Fiat alter circulus cuius
              <lb/>
            semidiameter
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            et fit
              <lb/>
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Then make the circle whose diameter is
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            and construct
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>k</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Make another circle whose semidiameter is
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            and construct
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>f</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> punctum
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            est in infinitis
              <lb/>
            parabolis, et locus omnium
              <lb/>
            vertica, est similis
              <lb/>
            altera spiralis
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            quae fit ex medijs punctus
              <lb/>
            inter periferias ultimo
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The point
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            is on an infinite parabola, and the locus of all vertices is another spiral
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , which is constructed from the midpoints between the circumferences last described. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Et ubi secant duae spralis
              <lb/>
            ut in puncto
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            , ibi est
              <lb/>
            vertex parabola in qua sint
              <lb/>
            duo puncta
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            And where the two spirals cut, as in point
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            , there is the vertex of the parabola in which lie the two points
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Iugantur puncta
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            .
              <lb/>
            linea
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            producatur,
              <lb/>
            et secabit periferias in
              <lb/>
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            . et reliqus peri-
              <lb/>
            ferias in
              <math>
                <mstyle>
                  <mi>k</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
            , secabat.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let the points
              <math>
                <mstyle>
                  <mi>a</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            be joined, and the line
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            extended cut the circumferences in
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            . And it will cut the other circumference in
              <math>
                <mstyle>
                  <mi>k</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
            . * </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> * Agantur rectam
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>k</mi>
                </mstyle>
              </math>
            , quae faciunt
              <lb/>
            angulos rectos cum
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            . Et sint
              <lb/>
            lineae ordinatim applicatam.
              <lb/>
            Si agatur recta
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            , tanget parabolam
              <lb/>
            in puncto
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Si agatur recta
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            , tanget parabolam
              <lb/>
            in puncto
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Nam
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            est medium punctum inter
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            .
              <lb/>
            et inter
              <math>
                <mstyle>
                  <mi>k</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            * Take the lines
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>k</mi>
                </mstyle>
              </math>
            , which make right angles with
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>g</mi>
                </mstyle>
              </math>
            . And these lines are ordinates.
              <lb/>
            If the line
              <math>
                <mstyle>
                  <mi>d</mi>
                  <mi>b</mi>
                </mstyle>
              </math>
            is taken, it touches the parabola at the point
              <math>
                <mstyle>
                  <mi>b</mi>
                </mstyle>
              </math>
            .
              <lb/>
            If the line
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            is taken, it touches the parabola at the point
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            For
              <math>
                <mstyle>
                  <mi>g</mi>
                </mstyle>
              </math>
            is the midpoint between
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            and between
              <math>
                <mstyle>
                  <mi>k</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>f</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Constructio geometrica
              <lb/>
            fit
              <emph style="super">per</emph>
            poristica
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The geometric construction is by the following ]</s>
          </p>
        </div>
      </text>
    </echo>
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