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

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        <div xml:id="echoid-div11" type="section" level="1" n="10">
          <pb o="317" file="0017" n="17" rhead="HYPERB. ELLIPS. ET CIRC."/>
          <p>
            <s xml:id="echoid-s82" xml:space="preserve">Data ſit portio A B C & </s>
            <s xml:id="echoid-s83" xml:space="preserve">triangulus D E F, baſibus A C,
              <lb/>
              <note position="right" xlink:label="note-0017-01" xlink:href="note-0017-01a" xml:space="preserve">TAB. XXXIV
                <lb/>
              Fig, 2.</note>
            D F æqualibus; </s>
            <s xml:id="echoid-s84" xml:space="preserve">& </s>
            <s xml:id="echoid-s85" xml:space="preserve">portionis diameter ſit B G, in trian-
              <lb/>
            gulo verò ducta à vertice in mediam baſin linea E H. </s>
            <s xml:id="echoid-s86" xml:space="preserve">Sint
              <lb/>
            autem utræque B G, E H vel ad baſes rectæ vel æqualiter
              <lb/>
            inclinatæ; </s>
            <s xml:id="echoid-s87" xml:space="preserve">& </s>
            <s xml:id="echoid-s88" xml:space="preserve">quam rationem habet B G ad E H, in eandem
              <lb/>
            dividatur ſpatium datum, ſintque partes K & </s>
            <s xml:id="echoid-s89" xml:space="preserve">L. </s>
            <s xml:id="echoid-s90" xml:space="preserve">Circumſcri-
              <lb/>
            batur jam ſicut antea portioni A B C figura ordinatè, quæ
              <lb/>
            portionem ſuperet exceſſu minore quàm ſit ſpatium K. </s>
            <s xml:id="echoid-s91" xml:space="preserve">Et
              <lb/>
            triangulo D E F circumſcribatur figura quæ totidem paral-
              <lb/>
            lelogrammis conſtet, quot ſunt in figura portioni A B C cir-
              <lb/>
            cumſcripta.</s>
            <s xml:id="echoid-s92" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s93" xml:space="preserve">Quoniam igitur baſes portionis & </s>
            <s xml:id="echoid-s94" xml:space="preserve">trianguli æquales ſunt,
              <lb/>
            apparet quidem omnium parallelogrammorum eandem fore
              <lb/>
            latitudinem. </s>
            <s xml:id="echoid-s95" xml:space="preserve">Hinc quum parallelogrammum B M ſit ad E R
              <lb/>
            ut B G ad E H, id eſt ut K ad L, ſitque B M minus quam
              <lb/>
            K , erit quoque E R minus quam L . </s>
            <s xml:id="echoid-s96" xml:space="preserve">Verùm omnia
              <note symbol="1" position="right" xlink:label="note-0017-02" xlink:href="note-0017-02a" xml:space="preserve">Ex conſit
                <unsure/>
              .</note>
              <note symbol="2" position="right" xlink:label="note-0017-03" xlink:href="note-0017-03a" xml:space="preserve">14. 5.
                <lb/>
              Elem.</note>
            gula quibus conſtat exceſſus figuræ circumſcriptæ ſupra trian-
              <lb/>
            gulum D E F, æqualia ſunt parallelogrammo E R, ergo
              <lb/>
            minor eſt idem exceſſus ſpatio L. </s>
            <s xml:id="echoid-s97" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s98" xml:space="preserve">exceſſus quo figu-
              <lb/>
            ra circumſcripta portionem A B C ſuperat, minor eſt ſpa-
              <lb/>
            tio K. </s>
            <s xml:id="echoid-s99" xml:space="preserve">Ergo utergue ſimul exceſſus minor erit ſpatio K L
              <lb/>
            dato. </s>
            <s xml:id="echoid-s100" xml:space="preserve">Et conſtat fieri poſſe quod proponebatur.</s>
            <s xml:id="echoid-s101" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div14" type="section" level="1" n="11">
          <head xml:id="echoid-head23" xml:space="preserve">
            <emph style="sc">Theorema</emph>
          III.</head>
          <p style="it">
            <s xml:id="echoid-s102" xml:space="preserve">SI portioni hyperboles, vel ellipſis vel circuli por-
              <lb/>
            tioni, dimidiâ ellipſi dimidiove circulo non majori,
              <lb/>
            circumſcribatur figur a or dinatè; </s>
            <s xml:id="echoid-s103" xml:space="preserve">ejus figuræ centrum
              <lb/>
            gravitatis erit in portionis diametro.</s>
            <s xml:id="echoid-s104" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s105" xml:space="preserve">Sit portio quælibet iſtarum A B C, diameter ejus B D;
              <lb/>
            </s>
            <s xml:id="echoid-s106" xml:space="preserve">
              <note position="right" xlink:label="note-0017-04" xlink:href="note-0017-04a" xml:space="preserve">TAB. XXXVI.
                <lb/>
              Fig. 3.</note>
            & </s>
            <s xml:id="echoid-s107" xml:space="preserve">circumſcribatur ei ut ſupra figura ordinatè. </s>
            <s xml:id="echoid-s108" xml:space="preserve">Oſtenden-
              <lb/>
            dum eſt ejus figuræ centrum gravitatis fore in B D diametro.
              <lb/>
            </s>
            <s xml:id="echoid-s109" xml:space="preserve">Ducantur lineæ H K, N R, P S, conjungentes ſuprema
              <lb/>
            latera parallelogrammorum quæ à diametro portionis æqua-
              <lb/>
            liter utrinque diſtant.</s>
            <s xml:id="echoid-s110" xml:space="preserve"/>
          </p>
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