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

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            <s xml:id="echoid-s205" xml:space="preserve">
              <pb o="321" file="0021" n="21" rhead="HYPERB. ELLIPS. ET CIRC."/>
            riam dividatur, jungantur K F, F H. </s>
            <s xml:id="echoid-s206" xml:space="preserve"> Demonſtrandum eſt, quòd magnitudinis compoſitæ ex portione A B C & </s>
            <s xml:id="echoid-s207" xml:space="preserve">trian-
              <lb/>
            gulo K F H, centrum gravitatis eſt punctum F.</s>
            <s xml:id="echoid-s208" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s209" xml:space="preserve">Si non eſt in F, ſit ſi fieri poteſt primùm ab ea parte pun-
              <lb/>
            cti F quæ eſt verſus A B C portionem, atque eſto pun-
              <lb/>
            ctum L; </s>
            <s xml:id="echoid-s210" xml:space="preserve">conſtat autem futurum in recta B D G, quum in
              <lb/>
            hac ſint utraque centra gravitatis portionis & </s>
            <s xml:id="echoid-s211" xml:space="preserve">trianguli K F H.
              <lb/>
            </s>
            <s xml:id="echoid-s212" xml:space="preserve">Jungantur A B, B C, & </s>
            <s xml:id="echoid-s213" xml:space="preserve">quam rationem habet G F ad F L,
              <lb/>
            eam habeat magnitudo compoſita ex triangulis A B C, K F H
              <lb/>
            ad ſpatium quoddam M; </s>
            <s xml:id="echoid-s214" xml:space="preserve">& </s>
            <s xml:id="echoid-s215" xml:space="preserve">circumſcribantur portioni & </s>
            <s xml:id="echoid-s216" xml:space="preserve">tri-
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            angulo K F H figuræ ordinatè, ex parallelogrammis quo-
              <lb/>
            rum omnium ſit eadem latitudo, ita ut duo ſimul exceſſus
              <lb/>
            quibus iſtæ figuræ ſuperant portionem A B C & </s>
            <s xml:id="echoid-s217" xml:space="preserve">triangu-
              <lb/>
            lum K F H, minores ſint ſpatio M . </s>
            <s xml:id="echoid-s218" xml:space="preserve">Igitur duorum
              <note symbol="1" position="right" xlink:label="note-0021-01" xlink:href="note-0021-01a" xml:space="preserve">Theor. 2. h.</note>
            triangulorum A B C, K F H ad dictos duos exceſſus ſive
              <lb/>
            reſidua major erit ratio quàm ad M, id eſt quàm G F ad
              <lb/>
            F L; </s>
            <s xml:id="echoid-s219" xml:space="preserve">ac proinde longè major ratio portionis A B C unà cum
              <lb/>
            K F H triangulo ad eadem reſidua quam G F ad F L. </s>
            <s xml:id="echoid-s220" xml:space="preserve">Sit
              <lb/>
            itaque N F ad F L, ſicut portio A B C ſimul cum trian-
              <lb/>
            gulo K F H ad duo reſidua, & </s>
            <s xml:id="echoid-s221" xml:space="preserve">cadet terminus N ultra tri-
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            anguli baſin K H. </s>
            <s xml:id="echoid-s222" xml:space="preserve">Jam per F ducatur O Ξ parallela baſi
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            A C vel K H; </s>
            <s xml:id="echoid-s223" xml:space="preserve">& </s>
            <s xml:id="echoid-s224" xml:space="preserve">duorum quorumcunque parallelogram-
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            morum, quæ in portione & </s>
            <s xml:id="echoid-s225" xml:space="preserve">in triangulo K F H æqualiter
              <lb/>
            à diametro diſtabunt, ut ſunt R Q, Σ T, ſint centra gra-
              <lb/>
            vitatis V & </s>
            <s xml:id="echoid-s226" xml:space="preserve">X; </s>
            <s xml:id="echoid-s227" xml:space="preserve">per quæ ducatur recta Z Λ Δ Ω, ſecans li-
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            neam Ο Ξ in Y; </s>
            <s xml:id="echoid-s228" xml:space="preserve">& </s>
            <s xml:id="echoid-s229" xml:space="preserve">ducatur R P baſi A C parallela, abſciſ-
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            ſæque ad verticem lineæ P B ſumatur æqualis, ex altero
              <lb/>
            diametri figuræ termino, E S.</s>
            <s xml:id="echoid-s230" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s231" xml:space="preserve">Quoniam igitur ad diametrum figuræ ordinatim ſunt ap-
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            plicatæ C D & </s>
            <s xml:id="echoid-s232" xml:space="preserve">R P, erit ut rectangulum B D E ad rectan-
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            gulum B P E, ita quadratum C D ad R P quadratum ;</s>
            <s xml:id="echoid-s233" xml:space="preserve">
              <note symbol="2" position="right" xlink:label="note-0021-02" xlink:href="note-0021-02a" xml:space="preserve">21. lib. 1.
                <lb/>
              Con.</note>
            verùm ut C D ad R P, hoc eſt, ut H G ad Ψ G, ita eſt H F
              <lb/>
            ad Σ F, & </s>
            <s xml:id="echoid-s234" xml:space="preserve">ita Z Y ad Λ Y igitur ut C D quadratum ad
              <lb/>
            quadratum R P, id eſt ut rectangulum B D E ad B P E,
              <lb/>
              <note symbol="*" position="foot" xlink:label="note-0021-03" xlink:href="note-0021-03a" xml:space="preserve">Notatu dignum quod K F, F H in hyperbole ſunt aſymptoti.</note>
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