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

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        <div xml:id="echoid-div85" type="section" level="1" n="40">
          <pb o="376" file="0086" n="91" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s1664" xml:space="preserve">Ex his manifeſtus eſt Orontii Finei error, qui circumfe-
              <lb/>
            rentiæ quadrantem æqualem minori duarum proportione me-
              <lb/>
            diarum inter inſcripti & </s>
            <s xml:id="echoid-s1665" xml:space="preserve">circumſcripti quadrati latera prodi-
              <lb/>
            dit, circulum vero æqualem quadrato quod fieret à majori.</s>
            <s xml:id="echoid-s1666" xml:space="preserve"/>
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        <div xml:id="echoid-div88" type="section" level="1" n="41">
          <head xml:id="echoid-head64" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . XII.
            <emph style="sc">Prop</emph>
          . XV.</head>
          <p style="it">
            <s xml:id="echoid-s1667" xml:space="preserve">
              <emph style="bf">S</emph>
            I inter productam circuli diametrum & </s>
            <s xml:id="echoid-s1668" xml:space="preserve">circum-
              <lb/>
            ferentiam recta aptetur radio æqualis, & </s>
            <s xml:id="echoid-s1669" xml:space="preserve">pro-
              <lb/>
            ducta circulum ſecet, occurr atque tangenti circulum
              <lb/>
            ad alterum diametri terminum: </s>
            <s xml:id="echoid-s1670" xml:space="preserve">Intercipiet eapar-
              <lb/>
            tem tangentis arcu adjacente abſciſſo majorem.</s>
            <s xml:id="echoid-s1671" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1672" xml:space="preserve">Eſto deſcriptus circulus centro C, cujus diameter A B.
              <lb/>
            </s>
            <s xml:id="echoid-s1673" xml:space="preserve">
              <note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">TAB. XXXIX.
                <lb/>
              Fig. 7.</note>
            Hæc autem producatur verſus A, interque ipſam & </s>
            <s xml:id="echoid-s1674" xml:space="preserve">cir-
              <lb/>
            cumferentiam ponatur E D recta radio A C æqualis. </s>
            <s xml:id="echoid-s1675" xml:space="preserve">Quæ
              <lb/>
            producta ſecet circumferentiam in F, occurratque tangenti
              <lb/>
            in G, ei nimirum quæ circulum contingit ad diametri ter-
              <lb/>
            minum B. </s>
            <s xml:id="echoid-s1676" xml:space="preserve">Dico tangentem B G majorem eſſe arcu B F.
              <lb/>
            </s>
            <s xml:id="echoid-s1677" xml:space="preserve">Ducatur enim per centrum recta H L parallela E G, quæ
              <lb/>
            circumferentiæ occurrat in punctis H, M: </s>
            <s xml:id="echoid-s1678" xml:space="preserve">tangenti vero B G
              <lb/>
            in L Et jungatur D H, quæ diametrum ſecet in K. </s>
            <s xml:id="echoid-s1679" xml:space="preserve">Simi-
              <lb/>
            les itaque ſunt trianguli E D K, C H K, quoniam angu-
              <lb/>
            los ad K æquales habent, & </s>
            <s xml:id="echoid-s1680" xml:space="preserve">angulum E æqualem angulo
              <lb/>
            C. </s>
            <s xml:id="echoid-s1681" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1682" xml:space="preserve">latus E D æquale eſt lateri H C, ſuntque hæc
              <lb/>
            latera æqualibus angulis ſubtenſa. </s>
            <s xml:id="echoid-s1683" xml:space="preserve">Ergo æquale etiam latus
              <lb/>
            D K lateri K H. </s>
            <s xml:id="echoid-s1684" xml:space="preserve">Itaque C A ſecat bifariam ipſam D H,
              <lb/>
            itemque arcum D A H. </s>
            <s xml:id="echoid-s1685" xml:space="preserve">Arcus igitur D H ſive huic æqua-
              <lb/>
            lis F M duplus eſt ad arcum A H. </s>
            <s xml:id="echoid-s1686" xml:space="preserve">Ipſi autem A H æqua-
              <lb/>
            lis eſt arcus M B. </s>
            <s xml:id="echoid-s1687" xml:space="preserve">Igitur arcus F B triplus erit ad arcum
              <lb/>
            A H. </s>
            <s xml:id="echoid-s1688" xml:space="preserve">Porro quoniam H K ſinus eſt arcus H A, ejuſdem-
              <lb/>
            que tangenti æquatur L B, erunt duæ tertiæ H K & </s>
            <s xml:id="echoid-s1689" xml:space="preserve">triens
              <lb/>
            L B ſimul majores arcu A H . </s>
            <s xml:id="echoid-s1690" xml:space="preserve">Quare ſumptis omnium
              <note symbol="*" position="left" xlink:label="note-0086-02" xlink:href="note-0086-02a" xml:space="preserve">per 9. huj.</note>
            plis erit dupla H K, hoc eſt, H D ſive G L una cum L B
              <lb/>
            major arcu A H triplo, hoceſt, arcu F B. </s>
            <s xml:id="echoid-s1691" xml:space="preserve">Apparet igitur
              <lb/>
            totam G B arcu F B majorem eſſe.</s>
            <s xml:id="echoid-s1692" xml:space="preserve"/>
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