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

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            <s xml:id="echoid-s262" xml:space="preserve">
              <pb o="323" file="0023" n="23" rhead="HYPERB. ELLIPS. ET CIRC."/>
            B D G, quoniam in ea ſunt centra gravitatis utriusque fi-
              <lb/>
            guræ circumſcriptæ ; </s>
            <s xml:id="echoid-s263" xml:space="preserve">igitur magnitudinis ex dictis
              <note symbol="8" position="right" xlink:label="note-0023-01" xlink:href="note-0023-01a" xml:space="preserve">Theor. 3. h.</note>
            compoſitæ centrum grav. </s>
            <s xml:id="echoid-s264" xml:space="preserve">eſt ipſum punctum F. </s>
            <s xml:id="echoid-s265" xml:space="preserve">Poſitum au-
              <lb/>
            tem fuit L punctum centrum gravitatis ejus magnitudinis quæ
              <lb/>
            ex portione A B C & </s>
            <s xml:id="echoid-s266" xml:space="preserve">K F H triangulo componitur; </s>
            <s xml:id="echoid-s267" xml:space="preserve">igi-
              <lb/>
            tur magnitudinis reliquæ, compoſitæ ex duobus reſiduis,
              <lb/>
            quæ in figuris circumſcriptis remanent, erit centr. </s>
            <s xml:id="echoid-s268" xml:space="preserve">grav. </s>
            <s xml:id="echoid-s269" xml:space="preserve">in
              <lb/>
            producta L F, ubi ea ſic terminatur, ut pars adjecta habeat
              <lb/>
            ad F L eandem rationem quam portio A B C ſimul cum
              <lb/>
            K F H triangulo ad dicta duo reſidua : </s>
            <s xml:id="echoid-s270" xml:space="preserve">is autem
              <note symbol="9" position="right" xlink:label="note-0023-02" xlink:href="note-0023-02a" xml:space="preserve">8
                <unsure/>
              . lib. 1.
                <lb/>
              Archine. d e
                <lb/>
              Æquipond</note>
            nus eſt N; </s>
            <s xml:id="echoid-s271" xml:space="preserve">itaque N punctum eſt centrum gravitatis duo-
              <lb/>
            rum reſiduorum. </s>
            <s xml:id="echoid-s272" xml:space="preserve">Quod fieri nequit; </s>
            <s xml:id="echoid-s273" xml:space="preserve">Nam ſi per N ducatur
              <lb/>
            recta baſi K H parallela, erunt ab una parte ſpatia omnia è
              <lb/>
            quibus utrumque reſiduum conſtat. </s>
            <s xml:id="echoid-s274" xml:space="preserve">Non eſt igitur L pun-
              <lb/>
            ctum centrum gravitatis magnitudinis ex portione A B C & </s>
            <s xml:id="echoid-s275" xml:space="preserve">
              <lb/>
            K F H triangulo compoſitæ. </s>
            <s xml:id="echoid-s276" xml:space="preserve">Sed neque erit ab altera parte
              <lb/>
            puncti F. </s>
            <s xml:id="echoid-s277" xml:space="preserve">Namque hoc ſi dicatur, planè ſimili demonſtratio-
              <lb/>
            ne eò devenietur ut duorum reſiduorum quæ demptâ portio-
              <lb/>
            ne A B C & </s>
            <s xml:id="echoid-s278" xml:space="preserve">K F H triangulo, in circumſcriptis figuris ſu-
              <lb/>
            pererunt, centrum gravitatis ſit ultra portionem A B C;
              <lb/>
            </s>
            <s xml:id="echoid-s279" xml:space="preserve">quod eſt æquè abſurdum. </s>
            <s xml:id="echoid-s280" xml:space="preserve">Reliquum eſt igitur ut ſit ipſum pun-
              <lb/>
            ctum F; </s>
            <s xml:id="echoid-s281" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s282" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div28" type="section" level="1" n="15">
          <head xml:id="echoid-head27" xml:space="preserve">
            <emph style="sc">Theorema</emph>
          VI.</head>
          <p style="it">
            <s xml:id="echoid-s283" xml:space="preserve">OMnis hyperboles portio ad triangulum inſcri-
              <lb/>
            ptum, eandem cum ipſa baſin habentem ean-
              <lb/>
            demque altitudinem, hanc habet rationem; </s>
            <s xml:id="echoid-s284" xml:space="preserve">quam
              <lb/>
            ſubſeſquialtera duarum, lateris tranſverſi & </s>
            <s xml:id="echoid-s285" xml:space="preserve">dia-
              <lb/>
            metri portionis, ad eam quæ ex centro ſectionis
              <lb/>
            ducitur ad portionis centrum gravitatis.</s>
            <s xml:id="echoid-s286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s287" xml:space="preserve">Eſto hyperboles portio, & </s>
            <s xml:id="echoid-s288" xml:space="preserve">inſcriptus ei, qualem diximus,
              <lb/>
              <note position="right" xlink:label="note-0023-03" xlink:href="note-0023-03a" xml:space="preserve">TAB. XXXIV.
                <lb/>
              Fig. 8.</note>
            triangulus A B C; </s>
            <s xml:id="echoid-s289" xml:space="preserve">diameter autem portionis ſit B D, & </s>
            <s xml:id="echoid-s290" xml:space="preserve">
              <lb/>
            latus tranſverſum ſive diameter ſectionis B E, in cujus me-
              <lb/>
            dio centrum ſectionis F. </s>
            <s xml:id="echoid-s291" xml:space="preserve">Et ponatur centrum gravitatis </s>
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