Harriot, Thomas, Mss. 6784

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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f352" o="352" n="703"/>
          <div type="page_commentary" level="0" n="0">
            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> On this page Harriot investigates Proposition 15 from
                <emph style="it">Supplementum geometriæ</emph>
                <ref id="Viete_1593c" target="http://www.e-rara.ch/zut/content/pageview/2684119"> (Viète 1593c, Prop </ref>
              . </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Proposition XV.
                  <lb/>
                Si e circumferential circuli cadant in diametrum perpendiculares duæ, una in centro, altera extra & ad perpendicularem in centro agatur ex puncto incidentiæ perpendicularis alterius, linea recta faciens cum diametro angulum æqualem trienti recti; a puncto autem quo acta illa secat perpendiculare in centro, ducatur alia linea recta ad angulum semicirculi: triplum quadratum huius, æquale est tam quadrato perpendicularis quae incidit extra centrum, quam quadratis segmentorum diametri, inter quæ perpendicularis illa media est </s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> If from the circumference of a circle there fall two perpendiculars onto the diameter, one to the centre, the other off-centre; and to the perpendicular to the centre there is drawn from the point of incidence of the other perpendicular a straight line making an angle equal to one-third of a right angle to the diameter; moreover from the point where that line cuts the perpendicular to the centre, there is drawn another line to the angle of the semicircle, then three times the square of it is equal to the square of the perpendicular which falls off-centre and the squares of the segments of the diameter between which the perpendicular is the mean </s>
              </quote>
              <lb/>
              <s xml:space="preserve"> The working contains a reference to Euclid's
                <emph style="it">Elements</emph>
              , Proposition
                <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookII/propII4.html"/>
              . </s>
              <lb/>
              <quote>
                <s xml:space="preserve">
                  <ref target="http://aleph0.clarku.edu/~djoyce/java/elements/bookII/propII4.html"/>
                If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the parts, together with twice the rectangle contained by the parts. </s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve"> prop. 15.
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Proposition 15 from the ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si e circumferential circuli cadant in
              <lb/>
            diametrum perpendiculares duæ; una in
              <lb/>
            centro; altera extra centrum: et ad per-
              <lb/>
            pendicularem in centro agatur ex puncto
              <lb/>
            incidentiæ perpendicularis alterius, linea
              <lb/>
            recta faciens cum diametro angulum æqualem
              <lb/>
            trienti recti, a puncto autem quo acta illa secat
              <lb/>
            perpendiculare in centro, ducatur alia
              <lb/>
            linea recta ad angulum semicirculi; Triplum
              <lb/>
            quadratum huius, æquale est tam quadrato perpendicularis quae incidit extra centrum,
              <lb/>
            quam quadratis segmentorum diametri, inter quæ perpendicularis illa media est
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If from the circumference of a circle there fall two perpendiculars onto the diameter, one to the centre, the other off-centre; and to the perpendicular to the centre there is drawn from the point of incidence of the other perpendicular a straight line making an angle equal to one-third of a right angle to the diameter; moreover from the point where that line cuts the perpendicular to the centre, there is drawn another line to the angle of the semicircle, then three times the square of it is equal to the square of the perpendicular which falls off-centre and the squares of the segments of the diameter between which the perpendicular is the mean ]</s>
            <lb/>
            <s xml:space="preserve"> Sit diameter circuli
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            , a cuius circumferentia cadat perpendiculariter
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            et fit
              <lb/>
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            minus segmentum,
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            maius,
              <math>
                <mstyle>
                  <mi>E</mi>
                </mstyle>
              </math>
            verum centro. Sed et cadat quoque e circumferentia
              <lb/>
            perpendiculariter
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            , et ex
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            ducatur recta
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            ita ut angulus
              <math>
                <mstyle>
                  <mi>G</mi>
                  <mi>B</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            sit æqualis trienti
              <lb/>
            recti, unde fiat
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            dupla ipsius
              <math>
                <mstyle>
                  <mi>G</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            ; et iungatur
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            . Dico triplum quadratum ex
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
              <lb/>
            æquari quadrato ex
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            , una cum quadrato ex
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            et quadrato ex
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            be the diameter of a circle, from whose circumference there falls perpendicularly
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            , and let
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            be the lesser segment,
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            the greater, and
              <math>
                <mstyle>
                  <mi>E</mi>
                </mstyle>
              </math>
            the centre. But there also falls perpendicularly from the circumference
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            , and from
              <math>
                <mstyle>
                  <mi>B</mi>
                </mstyle>
              </math>
            there is drawn a line
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            so that the angle
              <math>
                <mstyle>
                  <mi>G</mi>
                  <mi>B</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            is equal to a third of a right angle, whence
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            is twice
              <math>
                <mstyle>
                  <mi>G</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            ; and
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            is joined. I say that three times the square on
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            is equal to the square on
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            together with the square on
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            and the squareon
              <math>
                <mstyle>
                  <mi>B</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            . </s>
            <lb/>
            <s xml:space="preserve"> Etiam
              <lb/>
            per 4,2 El.
              <lb/>
            […] Addatur utrovisque
              <lb/>
            […] Ergo
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Also by Elements II.4
              <lb/>
              <lb/>
            Hence the ]</s>
          </p>
          <head xml:space="preserve"> Hinc tale Consectarium potest
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          Here a Consequence of this kind may be ]</head>
          <p xml:lang="lat">
            <s xml:space="preserve"> Datis tribus continue proportionalibus: invenire lineam cuius
              <lb/>
            quadratum sit tertia pars adgregati quadratorum e tribus
              <lb/>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Given three continued proportionals, find a line whose square is a third of the sum of the squares of all three proportionals.</s>
          </p>
        </div>
      </text>
    </echo>
Impressum