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

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          <p>
            <s xml:id="echoid-s2464" xml:space="preserve">Sit datus rhombus A B cujus producantur latera A F, A E;
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            </s>
            <s xml:id="echoid-s2465" xml:space="preserve">
              <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">TAB. XLII.
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              Fig. 2.</note>
            data autem ſit recta K cui æqualem ponere oporteat C D,
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            per angulum B tranſeuntem. </s>
            <s xml:id="echoid-s2466" xml:space="preserve">Ducatur diameter A B, eique
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            ad angulos rectos linea S B R, quæ quidem æqualis erit
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            duplæ diametro F E. </s>
            <s xml:id="echoid-s2467" xml:space="preserve">Igitur K non minor debet eſſe quam
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            S R. </s>
            <s xml:id="echoid-s2468" xml:space="preserve">Si vero æqualis, factum eſt quod proponebatur. </s>
            <s xml:id="echoid-s2469" xml:space="preserve">Sed
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            ponatur K major data eſſe quam S R. </s>
            <s xml:id="echoid-s2470" xml:space="preserve">Erit jam in ſchemate
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            hoc prout propoſitum eſt conſtructio eadem, quæ in Pro-
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            blemate præcedenti. </s>
            <s xml:id="echoid-s2471" xml:space="preserve">Demonſtratio autem nonnihil diverſa.
              <lb/>
            </s>
            <s xml:id="echoid-s2472" xml:space="preserve">Etenim hoc primò aliter oſtenditur quod circumferentia ſu-
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            per B G deſcripta ſecat productam A F. </s>
            <s xml:id="echoid-s2473" xml:space="preserve">Sit A L ad E B
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            perpendicularis & </s>
            <s xml:id="echoid-s2474" xml:space="preserve">ducatur S T ut ſit angulus B S T æqua-
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            lis angulo E A F vel B F S. </s>
            <s xml:id="echoid-s2475" xml:space="preserve">Eſt itaque triangulus B S T
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            triangulo B F S ſimilis; </s>
            <s xml:id="echoid-s2476" xml:space="preserve">(nam & </s>
            <s xml:id="echoid-s2477" xml:space="preserve">angulos ad B æquales ha-
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            bent:) </s>
            <s xml:id="echoid-s2478" xml:space="preserve">ac proinde æquicruris etiam triangulus B S T. </s>
            <s xml:id="echoid-s2479" xml:space="preserve">Ap-
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            paret igitur lineam A S æquari ipſi L B cum dimidia B T. </s>
            <s xml:id="echoid-s2480" xml:space="preserve">
              <lb/>
            Quare dupla A S æquabitur duplæ L B & </s>
            <s xml:id="echoid-s2481" xml:space="preserve">toti B T. </s>
            <s xml:id="echoid-s2482" xml:space="preserve">Sed
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            dupla A S eſt quadrupla A F vel E B. </s>
            <s xml:id="echoid-s2483" xml:space="preserve">Ergo quadrupla E B
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            æqualis duplæ L B & </s>
            <s xml:id="echoid-s2484" xml:space="preserve">B T. </s>
            <s xml:id="echoid-s2485" xml:space="preserve">Sumptâque communî altitudi-
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            ne B T, erit rectangulum ſub quadrupla E B & </s>
            <s xml:id="echoid-s2486" xml:space="preserve">B T con-
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            tentum, æquale duplo rectangulo L B T & </s>
            <s xml:id="echoid-s2487" xml:space="preserve">quadrato B T. </s>
            <s xml:id="echoid-s2488" xml:space="preserve">
              <lb/>
            Et addito utrimque quadrato B L, erit rectangulum E B T
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            quater cum quadrato L B æquale rectangulo L B T bis cum
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            quadratis B T, B L, hoc eſt quadrato L T. </s>
            <s xml:id="echoid-s2489" xml:space="preserve">Quia vero
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            propter triangulos ſimiles eſt T B ad B S ut B S ad B F
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            ſive B E, æquale erit rectang. </s>
            <s xml:id="echoid-s2490" xml:space="preserve">E B T quadrato B S; </s>
            <s xml:id="echoid-s2491" xml:space="preserve">& </s>
            <s xml:id="echoid-s2492" xml:space="preserve">
              <lb/>
            quater ſumptum quadrato R S. </s>
            <s xml:id="echoid-s2493" xml:space="preserve">Itaque quadr. </s>
            <s xml:id="echoid-s2494" xml:space="preserve">S R cum qua-
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            drato L B æquale quadrato L T. </s>
            <s xml:id="echoid-s2495" xml:space="preserve">Quadratum vero K (quod
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            majus eſt quam R S quadr.) </s>
            <s xml:id="echoid-s2496" xml:space="preserve">unà cum eodem quadrato L B
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            æquale eſt quadrato L G, uti ex conſtructione manifeſtum
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            eſt, quia ſcilicet quadr. </s>
            <s xml:id="echoid-s2497" xml:space="preserve">A G æquale poſitum fuit quadratis
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            ex K & </s>
            <s xml:id="echoid-s2498" xml:space="preserve">A B. </s>
            <s xml:id="echoid-s2499" xml:space="preserve">Itaque majus eſt quadr. </s>
            <s xml:id="echoid-s2500" xml:space="preserve">L G quam L T, & </s>
            <s xml:id="echoid-s2501" xml:space="preserve">
              <lb/>
            L G major quam L T, & </s>
            <s xml:id="echoid-s2502" xml:space="preserve">B G quam B T. </s>
            <s xml:id="echoid-s2503" xml:space="preserve">Quamobrem
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            circumferentia ſuper B G deſcripta capax anguli E A F ſe-
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            cabit rectam A S; </s>
            <s xml:id="echoid-s2504" xml:space="preserve">nam ſimilis circumferentia, ſi ſuper B T
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            deſcribatur, ea continget ipſam in S puncto, quoniam </s>
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