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

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          <p>
            <s xml:id="echoid-s143" xml:space="preserve">
              <pb o="319" file="0019" n="19" rhead="HYPERB. ELLIPS. ET CIRC."/>
            A D ad D F; </s>
            <s xml:id="echoid-s144" xml:space="preserve">multoque major quam A D ad D H, vel
              <lb/>
            quàm L K ad K E. </s>
            <s xml:id="echoid-s145" xml:space="preserve">Sit itaque M K ad K E ſicut portio
              <lb/>
            A B C ad exceſſum quo ipſa ſuperatur à figura ordinatè cir-
              <lb/>
            cumſcripta. </s>
            <s xml:id="echoid-s146" xml:space="preserve">Itaque cum K ſit centrum grav. </s>
            <s xml:id="echoid-s147" xml:space="preserve">figuræ portio-
              <lb/>
            ni circumſcriptæ, & </s>
            <s xml:id="echoid-s148" xml:space="preserve">E centrum grav. </s>
            <s xml:id="echoid-s149" xml:space="preserve">ipſius portionis; </s>
            <s xml:id="echoid-s150" xml:space="preserve">erit
              <lb/>
            M centrum gravitatis omnium ſpatiorum quæ eundem exceſ-
              <lb/>
            ſum conſtituunt . </s>
            <s xml:id="echoid-s151" xml:space="preserve">Quod eſſe non poteſt; </s>
            <s xml:id="echoid-s152" xml:space="preserve">Nam ſi per
              <note symbol="1" position="right" xlink:label="note-0019-01" xlink:href="note-0019-01a" xml:space="preserve">8. lib. 1.
                <lb/>
              Arch. de
                <lb/>
              Æquipond.</note>
            linea ducatur diametro B D parallela, erunt ab una parte
              <lb/>
            omnia quæ diximus ſpatia. </s>
            <s xml:id="echoid-s153" xml:space="preserve">Manifeſtum eſt igitur, portio-
              <lb/>
            nis A B C centrum grav. </s>
            <s xml:id="echoid-s154" xml:space="preserve">eſſe in B D portionis diametro.</s>
            <s xml:id="echoid-s155" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s156" xml:space="preserve">Eſto nunc A B C portio ellipſis vel circuli, dimidiâ fi-
              <lb/>
              <note position="right" xlink:label="note-0019-02" xlink:href="note-0019-02a" xml:space="preserve">TAB. XXXIV.
                <lb/>
              Fig. 5.</note>
            gurá major. </s>
            <s xml:id="echoid-s157" xml:space="preserve">Abſolvatur figura, & </s>
            <s xml:id="echoid-s158" xml:space="preserve">producatur B D uſque
              <lb/>
            dum ſectioni occurrat in E; </s>
            <s xml:id="echoid-s159" xml:space="preserve">erit igitur portionis A E C dia-
              <lb/>
            meter E D, & </s>
            <s xml:id="echoid-s160" xml:space="preserve">B D E diameter totius figuræ. </s>
            <s xml:id="echoid-s161" xml:space="preserve">Et quoniam
              <lb/>
            in B D E diametro eſt figuræ totius centrum gravitatis, (hoc
              <lb/>
            enim ex prædemonſtratis conſtabit, ſi in duo æqualia tota
              <lb/>
            figura dividatur diametro quæ ipſi A C ſit parallela,) & </s>
            <s xml:id="echoid-s162" xml:space="preserve">in
              <lb/>
            eadem centr. </s>
            <s xml:id="echoid-s163" xml:space="preserve">gravitatis A E C portionis minoris, ſicut mo-
              <lb/>
            dò oſtenſum fuit; </s>
            <s xml:id="echoid-s164" xml:space="preserve">erit quoque centr. </s>
            <s xml:id="echoid-s165" xml:space="preserve">gravitatis portionis re-
              <lb/>
            liquæ A B C in B D E ; </s>
            <s xml:id="echoid-s166" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s167" xml:space="preserve"/>
          </p>
          <note symbol="2" position="right" xml:space="preserve">8. lib. 1.
            <lb/>
          Archim. dc
            <lb/>
          Æqu@pond.</note>
        </div>
        <div xml:id="echoid-div21" type="section" level="1" n="13">
          <head xml:id="echoid-head25" xml:space="preserve">
            <emph style="sc">Lemma</emph>
          .</head>
          <p>
            <s xml:id="echoid-s168" xml:space="preserve">Eſto linea E B, cui ad utrumque terminum adjiciantur æ-
              <lb/>
              <note position="right" xlink:label="note-0019-04" xlink:href="note-0019-04a" xml:space="preserve">TAB. XXXIV.
                <lb/>
              Fig. 6.</note>
            quales duæ E S, B P, & </s>
            <s xml:id="echoid-s169" xml:space="preserve">inſuper alia P D. </s>
            <s xml:id="echoid-s170" xml:space="preserve">Dico id quo
              <lb/>
            rectangulum E D B excedit E P B, æquari rectangulo S D P.
              <lb/>
            </s>
            <s xml:id="echoid-s171" xml:space="preserve">Eſt enim rectangulum E D B æquale iſtis duobus, rectangulo
              <lb/>
            E D P & </s>
            <s xml:id="echoid-s172" xml:space="preserve">rectangulo ſub E D, P B: </s>
            <s xml:id="echoid-s173" xml:space="preserve">quorum ultimum ſuperat
              <lb/>
            rectangulum E P B rectangulo D P B. </s>
            <s xml:id="echoid-s174" xml:space="preserve">Igitur exceſſus rectan-
              <lb/>
            guli E D B ſupra rectangulum E P B æqualis eſt duobus iſtis,
              <lb/>
            rectangulo E D P, & </s>
            <s xml:id="echoid-s175" xml:space="preserve">D P B. </s>
            <s xml:id="echoid-s176" xml:space="preserve">Sed rectangulum E D P addito
              <lb/>
            rectangulo D P B, id eſt rectangulo ſub E S, D P, æquale
              <lb/>
            fit rectangulo S D P. </s>
            <s xml:id="echoid-s177" xml:space="preserve">Manifeſtum eſt igitur, exceſſum re-
              <lb/>
            ctanguli E D B ſupra E P B, æquari rectangulo S D P.</s>
            <s xml:id="echoid-s178" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s179" xml:space="preserve">Eſto rurſus linea E B, cui ad utrumque terminum
              <note position="right" xlink:label="note-0019-05" xlink:href="note-0019-05a" xml:space="preserve">TAB. XXXIV.
                <lb/>
              Fig. 7.</note>
              <note symbol="*" position="foot" xlink:label="note-0019-06" xlink:href="note-0019-06a" xml:space="preserve">Idem hoc aliter demonſtratum reperi apud Pappum, lib. 7. Prop. 24.</note>
              <note symbol="†" position="foot" xlink:label="note-0019-07" xlink:href="note-0019-07a" xml:space="preserve">Vide eundem, lib. 7. Prop. 57.</note>
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