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

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        <div xml:id="echoid-div66" type="section" level="1" n="30">
          <p>
            <s xml:id="echoid-s1317" xml:space="preserve">
              <pb o="364" file="0072" n="76" rhead="CHRISTIANI HUGENII"/>
            nus triente minoris. </s>
            <s xml:id="echoid-s1318" xml:space="preserve">Quare ſi à ſexdecim inſcripti dodecago-
              <lb/>
            ni lateribus duo latera inſcripti hexagoni, hoc eſt, diameter
              <lb/>
            circuli deducatur, reliqua circuli circumferentiâ minor erit,
              <lb/>
            aut ſi ab octo dodecagoni lateribus radius deducatur, reliqua
              <lb/>
            minor erit circumferentiæ ſemiſſe. </s>
            <s xml:id="echoid-s1319" xml:space="preserve">Hoc autem ad conſtructio-
              <lb/>
            nem mechanicam utile eſt, quoniam exigua eſt differentia,
              <lb/>
            ſicut poſtea oſtendetur.</s>
            <s xml:id="echoid-s1320" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1321" xml:space="preserve">Manifeſtum etiam, in omni arcu qui ſemicircumferen-
              <lb/>
            tiâ minor ſit, ſi ad ſubtenſam addatur triens exceſſus quo
              <lb/>
            ſubtenſa ſinum ſuperat, compoſitam arcu minorem eſſe.</s>
            <s xml:id="echoid-s1322" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div68" type="section" level="1" n="31">
          <head xml:id="echoid-head52" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . VIII.
            <emph style="sc">Prop</emph>
          . VIII.</head>
          <p style="it">
            <s xml:id="echoid-s1323" xml:space="preserve">CIrculo dato, ſi ad diametriterminum contingens
              <lb/>
            ducatur, ducatur autem & </s>
            <s xml:id="echoid-s1324" xml:space="preserve">ab oppoſito diametri
              <lb/>
            termino quæ circumferentiam ſecet occurratque tan-
              <lb/>
            genti ductæ: </s>
            <s xml:id="echoid-s1325" xml:space="preserve">erunt interceptæ tangentis duæ tertiæ
              <lb/>
            cum triente ejus quæ ab interſectionis puncto dia-
              <lb/>
            metro ad angulos rectos incidet, ſimul arcu abſciſ-
              <lb/>
            ſo adjacente majores.</s>
            <s xml:id="echoid-s1326" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1327" xml:space="preserve">Eſto circulus centro A, diametro B C; </s>
            <s xml:id="echoid-s1328" xml:space="preserve">& </s>
            <s xml:id="echoid-s1329" xml:space="preserve">ducatur ex C
              <lb/>
              <note position="left" xlink:label="note-0072-01" xlink:href="note-0072-01a" xml:space="preserve">TAB. XXXVIII.
                <lb/>
              Fig. 8.</note>
            recta quæ circulum contingat C D: </s>
            <s xml:id="echoid-s1330" xml:space="preserve">huic autem occurrat
              <lb/>
            ducta ab altero diametri termino recta B D, quæ circumfe-
              <lb/>
            rentiam ſecet in E: </s>
            <s xml:id="echoid-s1331" xml:space="preserve">ſitque E F diametro B C ad angulos re-
              <lb/>
            ctos. </s>
            <s xml:id="echoid-s1332" xml:space="preserve">Dico tangentis interceptæ C D duas tertias ſimul cum
              <lb/>
            triente ipſius E F, arcu E C majores eſſe. </s>
            <s xml:id="echoid-s1333" xml:space="preserve">Jungantur enim
              <lb/>
            A E, E C; </s>
            <s xml:id="echoid-s1334" xml:space="preserve">& </s>
            <s xml:id="echoid-s1335" xml:space="preserve">ducatur tangens circulum in E puncto, quæ
              <lb/>
            tangenti C D occurrat in G. </s>
            <s xml:id="echoid-s1336" xml:space="preserve">Erit igitur G E ipſi G C æqua-
              <lb/>
            lis, itemque D G; </s>
            <s xml:id="echoid-s1337" xml:space="preserve">nam ſi centro G circumferentia deſcriba-
              <lb/>
            tur quæ tranſeat per puncta C, E, eadem tranſibit quoque
              <lb/>
            per D punctum, quoniam angulus C E D rectus eſt. </s>
            <s xml:id="echoid-s1338" xml:space="preserve">Oſten-
              <lb/>
            ſum autem fuit ſuprà, duas tertias quadrilateri A E G C una
              <lb/>
            cum triente trianguli A E C ſimul majores eſſe ſectore A E C .</s>
            <s xml:id="echoid-s1339" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">per 6. huj.</note>
            Eſtque quadrilaterum A E G C æquale triangulo baſin </s>
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