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

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              <pb o="368" file="0078" n="83" rhead="CHRISTIANI HUGENII"/>
            additis ad 6978128, fiunt 10471980. </s>
            <s xml:id="echoid-s1428" xml:space="preserve">Hæigitur omnino ex-
              <lb/>
            cedunt {1/60} circumferentiæ, & </s>
            <s xml:id="echoid-s1429" xml:space="preserve">ſexagecuplum ipſarum, hoc
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            eſt 628318800 majus erit circumferentiâ totâ. </s>
            <s xml:id="echoid-s1430" xml:space="preserve">Quod ſi verò
              <lb/>
            polygona adhibeamus laterum 10800, quorum inſcripti qui-
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            dem latus, calculo Ludolphi Colonienſis, Arithmetici nobi-
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            lis, inventum eſt partium 58177640912684919 non unâ am-
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            plius, ſubtenditurque duobus ſcrup. </s>
            <s xml:id="echoid-s1431" xml:space="preserve">primis; </s>
            <s xml:id="echoid-s1432" xml:space="preserve">circumſcripti
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            autem latus 58177643374063182 non unâ minus. </s>
            <s xml:id="echoid-s1433" xml:space="preserve">Prætereaque
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            latus polygoni ſubduplo laterum numero inſcripti, quod eſt
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            116355276902613523 non unâ minus. </s>
            <s xml:id="echoid-s1434" xml:space="preserve">Hinc peripheriæ lon-
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            gitudo invenitur major quam partium 6283185307179584;
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            <s xml:id="echoid-s1435" xml:space="preserve">minor autem quam 6283185307179589, qualium radius
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            1000000000000000. </s>
            <s xml:id="echoid-s1436" xml:space="preserve">Solitâ autem methodo ex additis inſcri-
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            pti circumſcriptique polygoni iſtius lateribus, invenietur
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            tantum majorem eſſe peripheriam partibus 62831852, & </s>
            <s xml:id="echoid-s1437" xml:space="preserve">mi-
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            norem 62831855. </s>
            <s xml:id="echoid-s1438" xml:space="preserve">Patet igitur notarum verarum amplius quam
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            duplum numerum eſſe à nobis inventum. </s>
            <s xml:id="echoid-s1439" xml:space="preserve">Hoc autem & </s>
            <s xml:id="echoid-s1440" xml:space="preserve">in
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            præcedentibus ita ſe habet, ſemperque evenire neceſſe eſt quot-
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            cunque laterum polygonis utamur. </s>
            <s xml:id="echoid-s1441" xml:space="preserve">At per ea, quæ poſtea
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            trademus, triplum numerum notarum facile obtineri appare-
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            bit.</s>
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            <emph style="sc">Problema</emph>
          II.
            <emph style="sc">Prop</emph>
          . XI.</head>
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            <s xml:id="echoid-s1443" xml:space="preserve">Rectam ſumere peripheriæ dati circuli æqualem.</s>
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            <s xml:id="echoid-s1445" xml:space="preserve">Oſtenſum eſt ſuperius, quod octo inſcripti dodecagoni la-
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            tera dempto circuli radio minora ſunt peripheriâ dimidiâ.
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            </s>
            <s xml:id="echoid-s1446" xml:space="preserve">In conſtructione autem ut plurimum defectus animadverti ne-
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            quit. </s>
            <s xml:id="echoid-s1447" xml:space="preserve">Nam ſi quatermilleſima diametri pars accedat longitu-
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            dini ſic inventæ, jam dimidiam peripheriam excedet. </s>
            <s xml:id="echoid-s1448" xml:space="preserve">Quod
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            ſic fiet manifeſtum. </s>
            <s xml:id="echoid-s1449" xml:space="preserve">Quarum partium radius eſt 10000, earum
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            latus dodecagoni inſcripti circulo eſt amplius quam 5176 {3/8}. </s>
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            Unde latera octo majora quam 41411. </s>
            <s xml:id="echoid-s1451" xml:space="preserve">& </s>
            <s xml:id="echoid-s1452" xml:space="preserve">dempto radio 10000,
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            erit reliqua major quam 31411. </s>
            <s xml:id="echoid-s1453" xml:space="preserve">cui ſi addantur partes 5,
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            hoc eſt, {1/4000} diametri, fient jam 31416; </s>
            <s xml:id="echoid-s1454" xml:space="preserve">quibus minorem eſſe
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            circumferentiam dimidiam liquet ex præcedentibus. </s>
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