Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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        <div xml:id="echoid-div36" type="section" level="1" n="17">
          <pb o="328" file="0032" n="34" rhead="THEOR. DE QUADRAT. HYPERB. &c."/>
          <p>
            <s xml:id="echoid-s408" xml:space="preserve">Eſto jam denique ſector D A B C ſemicirculo major, & </s>
            <s xml:id="echoid-s409" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0032-01" xlink:href="note-0032-01a" xml:space="preserve">TAB. XXXVI.
                <lb/>
              Fig. 5.</note>
            ponantur ea quæ priùs, & </s>
            <s xml:id="echoid-s410" xml:space="preserve">perficiatur circulus B A F C,
              <lb/>
            & </s>
            <s xml:id="echoid-s411" xml:space="preserve">totius diameter ſit B D F, in qua erit quoque centrum
              <lb/>
            grav. </s>
            <s xml:id="echoid-s412" xml:space="preserve">ſectoris reliqui D A F C , quot ſit G.</s>
            <s xml:id="echoid-s413" xml:space="preserve"/>
          </p>
          <note symbol="1" position="left" xml:space="preserve">8. lib. 1.
            <lb/>
          Arch. de
            <lb/>
          Æquip.</note>
          <p>
            <s xml:id="echoid-s414" xml:space="preserve">Quia igitur circuli totius centrum gravitatis eſt D, & </s>
            <s xml:id="echoid-s415" xml:space="preserve">duorum
              <lb/>
            ſectorum centra grav. </s>
            <s xml:id="echoid-s416" xml:space="preserve">E & </s>
            <s xml:id="echoid-s417" xml:space="preserve">G, erit ſicut ſector D A B C, ad ſecto-
              <lb/>
            rem D A F C, id eſt, ſicut arcus A B C ad arcum A F C, ita
              <lb/>
            G D ad D E : </s>
            <s xml:id="echoid-s418" xml:space="preserve">verum ut arcus A F C ad {2/3} A C, ita eſt D
              <note symbol="2" position="left" xlink:label="note-0032-03" xlink:href="note-0032-03a" xml:space="preserve">8. lib. 1.
                <lb/>
              Arch. de
                <lb/>
              Æquip.</note>
            ad D G, ſicuti modò oſtenſum eſt; </s>
            <s xml:id="echoid-s419" xml:space="preserve">ergo ex æquali in pro-
              <lb/>
            portione perturbata, ſicut arcus A B C ad {2/3} A C, ita erit
              <lb/>
            D F vel B D ad D E . </s>
            <s xml:id="echoid-s420" xml:space="preserve">Conſtat itaque quod in
              <note symbol="3" position="left" xlink:label="note-0032-04" xlink:href="note-0032-04a" xml:space="preserve">23. lib. 5.
                <lb/>
              Elem.</note>
            lo & </s>
            <s xml:id="echoid-s421" xml:space="preserve">quolibet circuli ſectore &</s>
            <s xml:id="echoid-s422" xml:space="preserve">c. </s>
            <s xml:id="echoid-s423" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s424" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div41" type="section" level="1" n="18">
          <head xml:id="echoid-head30" xml:space="preserve">ἘΞἘΤΑΣΙΣ
            <lb/>
          CYCLOMETRIÆ
            <lb/>
          CLARISSIMI VIRI,
            <lb/>
          GREGORII à S. VINCENTIO, S. J.</head>
          <head xml:id="echoid-head31" xml:space="preserve">Editæ Anno D. cIↄ Iↄc
            <emph style="sc">XLVII</emph>
          .</head>
          <p>
            <s xml:id="echoid-s425" xml:space="preserve">ANte quinquennium circiter Vir eruditiſſimus & </s>
            <s xml:id="echoid-s426" xml:space="preserve">
              <lb/>
            Geometriâ celeberrimus, Gregorius à S. </s>
            <s xml:id="echoid-s427" xml:space="preserve">Vin-
              <lb/>
            centio, quatuor modos propoſuit quadrandi Cir-
              <lb/>
            culum, unum vero eorum etiam Quadraturæ Hy-
              <lb/>
            perboles applicavit: </s>
            <s xml:id="echoid-s428" xml:space="preserve">quem cæteris potiorem ab
              <lb/>
            ipſo exiſtimari ex multis indiciis colligere licet. </s>
            <s xml:id="echoid-s429" xml:space="preserve">Unum eſt
              <lb/>
            hoc ipſum quod duas diverſarum figurarum quadraturas per
              <lb/>
            eundem hunc demonſtravit; </s>
            <s xml:id="echoid-s430" xml:space="preserve">alterum quod evidentior multò
              <lb/>
            ſit hic modus quam reliqui tres, ideoque minus errori obno-
              <lb/>
            xius videri debuerit; </s>
            <s xml:id="echoid-s431" xml:space="preserve">nonnullum etiam quod primo eum lo-
              <lb/>
            co produxit; </s>
            <s xml:id="echoid-s432" xml:space="preserve">Et denique hoc maximum eſt, quod in iis quæ
              <lb/>
            @d lectorem in principio totius operis præfatur, ubi ſuæ </s>
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