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

Table of Notes

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            <s xml:id="echoid-s321" xml:space="preserve">
              <pb o="325" file="0027" n="28" rhead="HYPERB. ELLIPS. ET CIRC."/>
            tione A B C punctum L. </s>
            <s xml:id="echoid-s322" xml:space="preserve">Dico igitur portionem ad inſcri-
              <lb/>
            ptum ſibi triangulum A B C eam habere rationem quam duæ
              <lb/>
            tertiæ E D ad F L. </s>
            <s xml:id="echoid-s323" xml:space="preserve">Conſtituatur enim ut ſupra triangulus
              <lb/>
            K F H, cujus nimirum baſis K H ſit baſi A C æqualis & </s>
            <s xml:id="echoid-s324" xml:space="preserve">
              <lb/>
            parallela, & </s>
            <s xml:id="echoid-s325" xml:space="preserve">F G quæ à vertice ad mediam baſin pertingit
              <lb/>
            poſſit rectangulum B D E: </s>
            <s xml:id="echoid-s326" xml:space="preserve">& </s>
            <s xml:id="echoid-s327" xml:space="preserve">centrum gravitatis trianguli
              <lb/>
            K F H ſit M punctum, ſumptâ ſcilicet F M æquali duabus
              <lb/>
              <note symbol="1" position="right" xlink:label="note-0027-01" xlink:href="note-0027-01a" xml:space="preserve">14. lib. 1.
                <lb/>
              Arch. de
                <lb/>
              Æquip.</note>
            tertiis lineæ F G .</s>
            <s xml:id="echoid-s328" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s329" xml:space="preserve">Triangulus igitur K F H eſt ad triangulum A B C, ut
              <lb/>
            F G ad B D; </s>
            <s xml:id="echoid-s330" xml:space="preserve">ut autem F G ad B D, ſic eſt E D ad F G,
              <lb/>
            quia quadratum F G æquale eſt B D E rectangulo; </s>
            <s xml:id="echoid-s331" xml:space="preserve">& </s>
            <s xml:id="echoid-s332" xml:space="preserve">ut
              <lb/>
            E D ad F G, ſic ſunt duæ tertiæ E D ad duas tertias F G,
              <lb/>
            id eſt, ad F M. </s>
            <s xml:id="echoid-s333" xml:space="preserve">Ergo triangulus K F H ad triangulum A B C,
              <lb/>
            ſicut duæ tertiæ E D ad F M. </s>
            <s xml:id="echoid-s334" xml:space="preserve">Portio autem A B C eſt ad
              <lb/>
            triangulum K F H, ut F M ad F L , quoniam
              <note symbol="2" position="right" xlink:label="note-0027-02" xlink:href="note-0027-02a" xml:space="preserve">7. lib. 1.
                <lb/>
              Archim. de
                <lb/>
              Æquipond.</note>
            brium eorum eſt in F , & </s>
            <s xml:id="echoid-s335" xml:space="preserve">centra gravitatis ſingulorum
              <note symbol="3" position="right" xlink:label="note-0027-03" xlink:href="note-0027-03a" xml:space="preserve">Theor. 5. h.</note>
            cta L & </s>
            <s xml:id="echoid-s336" xml:space="preserve">M; </s>
            <s xml:id="echoid-s337" xml:space="preserve">Ergo ex æquali in proportione perturbata,
              <lb/>
            erit portio A B C ad A B C triangulum, ſicut duæ tertiæ
              <lb/>
            E D ad F L .</s>
            <s xml:id="echoid-s338" xml:space="preserve"/>
          </p>
          <note symbol="4" position="right" xml:space="preserve">23. lib. 5.
            <lb/>
          Elem.</note>
          <p>
            <s xml:id="echoid-s339" xml:space="preserve">Sit nunc portio A B C dimidiâ figurâ major. </s>
            <s xml:id="echoid-s340" xml:space="preserve">Dico eam
              <lb/>
              <note position="right" xlink:label="note-0027-05" xlink:href="note-0027-05a" xml:space="preserve">TAB. XXXVI.
                <lb/>
              Fig. 1. 2.</note>
            rurſus ad inſcriptum triangulum eam habere rationem, quam
              <lb/>
            duæ tertiæ E D ad F L.</s>
            <s xml:id="echoid-s341" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s342" xml:space="preserve">Ponatur enim portionis reliquæ A E C centrum gravitatis
              <lb/>
            H punctum, & </s>
            <s xml:id="echoid-s343" xml:space="preserve">jungantur A E, E C. </s>
            <s xml:id="echoid-s344" xml:space="preserve">Igitur per ea quæ jam
              <lb/>
            oſtendimus, erit portio A E C ad A E C triangulum, ut
              <lb/>
            duæ tertiæ B D ad F H; </s>
            <s xml:id="echoid-s345" xml:space="preserve">verùm ut triangulus A E C ad
              <lb/>
            triangulum A B C, ſic eſt E D ad B D, ſive duæ tertiæ
              <lb/>
            E D ad duas tertias B D; </s>
            <s xml:id="echoid-s346" xml:space="preserve">ex æquali igitur in proportione
              <lb/>
            perturbata, erit ſicut portio A E C ad triangulum A B C,
              <lb/>
            ita duæ tertiæ E D ad F H . </s>
            <s xml:id="echoid-s347" xml:space="preserve">Sed ut portio A B C
              <note symbol="5" position="right" xlink:label="note-0027-06" xlink:href="note-0027-06a" xml:space="preserve">23. lib. 5.
                <lb/>
              Elem.</note>
            A E C portionem, ita eſt F H ad F L , quoniam
              <note symbol="6" position="right" xlink:label="note-0027-07" xlink:href="note-0027-07a" xml:space="preserve">8. lib. 1.
                <lb/>
              Arch. de
                <lb/>
              Æquipond.</note>
            figuræ centrum gravitatis eſt F, centraque dictarum portio-
              <lb/>
            num L & </s>
            <s xml:id="echoid-s348" xml:space="preserve">H; </s>
            <s xml:id="echoid-s349" xml:space="preserve">Ergo iterum ex æquali in proportione per-
              <lb/>
            turbata, erit portio A B C ad A B C triangulum, ut duæ
              <lb/>
            tertiæ E D ad F L. </s>
            <s xml:id="echoid-s350" xml:space="preserve">Omnis igitur Ellipſis vel circuli portio
              <lb/>
            &</s>
            <s xml:id="echoid-s351" xml:space="preserve">c. </s>
            <s xml:id="echoid-s352" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s353" xml:space="preserve"/>
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