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

Table of Notes

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            angulus C K A æqualis ang. </s>
            <s xml:id="echoid-s10701" xml:space="preserve">A Q K, ſed demonſtravimus
              <lb/>
            angulos A P K & </s>
            <s xml:id="echoid-s10702" xml:space="preserve">A Q K eſſe æquales, ergo anguli B K A,
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            C K A erunt inter ſe æquales Q. </s>
            <s xml:id="echoid-s10703" xml:space="preserve">E. </s>
            <s xml:id="echoid-s10704" xml:space="preserve">D.</s>
            <s xml:id="echoid-s10705" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10706" xml:space="preserve">Si punctum H cadat in circumferentiam circuli punctum
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            H erit punctum K, quod quæritur & </s>
            <s xml:id="echoid-s10707" xml:space="preserve">lineæ H P, K P, K O
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            in unicam H P coaleſcunt; </s>
            <s xml:id="echoid-s10708" xml:space="preserve">& </s>
            <s xml:id="echoid-s10709" xml:space="preserve">ſimiliter lineæ H Q, K Q,
              <lb/>
            K I in unam H Q, & </s>
            <s xml:id="echoid-s10710" xml:space="preserve">quæ ſuperius demonſtrata ſunt & </s>
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            hic locum habent, in quo caſu Hyperbolâ non indigemus.</s>
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        <div xml:id="echoid-div507" type="section" level="1" n="192">
          <head xml:id="echoid-head272" xml:space="preserve">III.</head>
          <head xml:id="echoid-head273" xml:space="preserve">ALITER.</head>
          <head xml:id="echoid-head274" style="it" xml:space="preserve">Dato Speculo Cavo aut Convexo, itemque Oculo &
            <lb/>
          Puncto Rei viſæ, invenire Punctum Reflexionis.</head>
          <p>
            <s xml:id="echoid-s10713" xml:space="preserve">ESto ſpeculum ex ſphæra quæ Centrum habeat A punctum;
              <lb/>
            </s>
            <s xml:id="echoid-s10714" xml:space="preserve">
              <note position="left" xlink:label="note-0504-01" xlink:href="note-0504-01a" xml:space="preserve">TAB. LVI.
                <lb/>
              fig. 2.</note>
            oculus vero ſit in B, & </s>
            <s xml:id="echoid-s10715" xml:space="preserve">punctum viſibile in C, Pla-
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            numque ductum per A, B, C, faciat in ſphæra Circulum
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            D d, in quo invenienda ſint Reflexionis Puncta. </s>
            <s xml:id="echoid-s10716" xml:space="preserve">Per tria
              <lb/>
            Puncta A, B, C, deſcribatur Circuli Circumferentia, cujus
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            ſit Centrum Z; </s>
            <s xml:id="echoid-s10717" xml:space="preserve">occurrat autem ei producta A E, Perpend.
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            </s>
            <s xml:id="echoid-s10718" xml:space="preserve">B C, in R; </s>
            <s xml:id="echoid-s10719" xml:space="preserve">& </s>
            <s xml:id="echoid-s10720" xml:space="preserve">ſit duabus R A, O A, tertia Proportionalis
              <lb/>
            N A; </s>
            <s xml:id="echoid-s10721" xml:space="preserve">eritque N M, Parallela B C, altera Aſymptoton. </s>
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              <lb/>
            Rurſus ſint Proportionales E A, {1/2} A O, A I, & </s>
            <s xml:id="echoid-s10723" xml:space="preserve">ſumma
              <lb/>
            I Y æquali I N, ducatur Y M Parallela A Z; </s>
            <s xml:id="echoid-s10724" xml:space="preserve">eaque erit
              <lb/>
            altera Aſymptotos. </s>
            <s xml:id="echoid-s10725" xml:space="preserve">Denique ſumptis I X, I S, quæ ſin-
              <lb/>
            gulæ poſſint dimidium quadratum A O, una cum quadrato
              <lb/>
            A I; </s>
            <s xml:id="echoid-s10726" xml:space="preserve">erunt Puncta X & </s>
            <s xml:id="echoid-s10727" xml:space="preserve">S in Hyperbola, aut ſectionibus
              <lb/>
            oppoſitis D d, ad inventas Aſymptotos deſcribendis, qua-
              <lb/>
            rum interſectiones cum Circumferentia D O, oſtendent
              <lb/>
            Puncta Reflexionis quæſita. </s>
            <s xml:id="echoid-s10728" xml:space="preserve">Conſtructio hæc, in omni
              <lb/>
            Caſu, quo Problema ſolidum eſt, locum habet, præter-
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            quam in uno, ubi non Hyperbola ſed Parabola deſcriben-
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            da eſt; </s>
            <s xml:id="echoid-s10729" xml:space="preserve">cum nimirum Circumferentia per Puncta A, B, C,
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            deſcripta, tangit Rectam A E.</s>
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