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

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          <p>
            <s xml:id="echoid-s179" xml:space="preserve">
              <pb o="320" file="0020" n="20" rhead="THEOR. DE QUADRAT."/>
            rantur duæ æquales E S, B P, & </s>
            <s xml:id="echoid-s180" xml:space="preserve">inſuper alia P D. </s>
            <s xml:id="echoid-s181" xml:space="preserve">Dico
              <lb/>
            iterum, id quo rectangulum E D B excedit E P B, æquari
              <lb/>
            rectangulo S D P. </s>
            <s xml:id="echoid-s182" xml:space="preserve">Rectangulum enim E D B æquale eſt iſtis
              <lb/>
            duobus, rectangulo E D P, & </s>
            <s xml:id="echoid-s183" xml:space="preserve">rectangulo ſub E D, P B;
              <lb/>
            </s>
            <s xml:id="echoid-s184" xml:space="preserve">horum autem E D P rurſus æquale eſt duobus, rectangulo ni-
              <lb/>
            mirum S D P, & </s>
            <s xml:id="echoid-s185" xml:space="preserve">ei quod continetur ſub E S, D P, ſive
              <lb/>
            rectangulo D P B. </s>
            <s xml:id="echoid-s186" xml:space="preserve">Igitur rectangulum E D B iſtis tribus æ-
              <lb/>
            quale eſt rectangulis, S D P, D P B, & </s>
            <s xml:id="echoid-s187" xml:space="preserve">rectangulo ſub
              <lb/>
            E D, P B; </s>
            <s xml:id="echoid-s188" xml:space="preserve">horum vero duo poſtrema æquantur rectangu-
              <lb/>
            lo E P B; </s>
            <s xml:id="echoid-s189" xml:space="preserve">ergo rectangulum E D B æquale eſt duobus, re-
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            ctangulo nimirum S D P & </s>
            <s xml:id="echoid-s190" xml:space="preserve">E P B, unde apparet exceſ-
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            ſum rectanguli E D B ſupra rectangulum E P B æquari re-
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            ctangulo S D P.</s>
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            <emph style="sc">Theorema</emph>
          V.</head>
          <p style="it">
            <s xml:id="echoid-s192" xml:space="preserve">DAtâ portione hyperboles, vel ellipſis vel cir-
              <lb/>
            culi portione, dimidiâ figurâ non majore; </s>
            <s xml:id="echoid-s193" xml:space="preserve">ſi ad
              <lb/>
            diametrum conſtituatur triangulus hujuſmodi, qui
              <lb/>
            verticem habeat in centro figuræ, & </s>
            <s xml:id="echoid-s194" xml:space="preserve">baſin portio-
              <lb/>
            nis baſi æqualem & </s>
            <s xml:id="echoid-s195" xml:space="preserve">parallelam; </s>
            <s xml:id="echoid-s196" xml:space="preserve">eam verò quæ de-
              <lb/>
            inceps à vertice ad mediam baſin pertingit tantam,
              <lb/>
            ut poſſit ipſa rectangulum comprehenſum lineis, quæ
              <lb/>
            inter portionis baſin & </s>
            <s xml:id="echoid-s197" xml:space="preserve">terminos diametri figuræ in-
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            terjiciuntur. </s>
            <s xml:id="echoid-s198" xml:space="preserve">Erit magnitudinis, quæ ex portione & </s>
            <s xml:id="echoid-s199" xml:space="preserve">
              <lb/>
            præſcripto triangulo componitur, centrum gravita-
              <lb/>
            tis punctum idem quod eſt trianguli vertex, cen-
              <lb/>
            trum nimirum figuræ.</s>
            <s xml:id="echoid-s200" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s201" xml:space="preserve">Data ſit portio hyberboles, vel ellipſis vel circuli portio
              <lb/>
              <note position="left" xlink:label="note-0020-01" xlink:href="note-0020-01a" xml:space="preserve">TAB. XXXV.
                <lb/>
              Fig. 1. 2. 3.</note>
            dimidiâ figurâ non major, A B C. </s>
            <s xml:id="echoid-s202" xml:space="preserve">Diameter ejus ſit B D,
              <lb/>
            & </s>
            <s xml:id="echoid-s203" xml:space="preserve">figuræ diameter B E, in cujus medio centrum figuræ F.
              <lb/>
            </s>
            <s xml:id="echoid-s204" xml:space="preserve">Et ſumatur F G quæ poſſit rectangulum B D E, ductâque
              <lb/>
            K G H æquali & </s>
            <s xml:id="echoid-s205" xml:space="preserve">parallelâ baſi A C, quæque ad G </s>
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