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

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            <s xml:id="echoid-s1394" xml:space="preserve">
              <pb o="367" file="0077" n="82" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            62116 {1/2} & </s>
            <s xml:id="echoid-s1395" xml:space="preserve">705 {1/2}, hoc eſt, partibus 62822. </s>
            <s xml:id="echoid-s1396" xml:space="preserve">Atque hiſce pro-
              <lb/>
            inde omnino major erit circuli peripheria . </s>
            <s xml:id="echoid-s1397" xml:space="preserve">Eſt autem
              <note symbol="*" position="right" xlink:label="note-0077-01" xlink:href="note-0077-01a" xml:space="preserve">per 7. huj.</note>
            jor ratio 62822 ad 20000, longitudinem diametri, quam 3{10/71}
              <lb/>
            ad 1. </s>
            <s xml:id="echoid-s1398" xml:space="preserve">Ergo omnino etiam peripheriæ ad diametrum ratio ma-
              <lb/>
            jor erit.</s>
            <s xml:id="echoid-s1399" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1400" xml:space="preserve">Rurſus quoniam latus dodecagoni inſcripti minus eſt par-
              <lb/>
            tibus 5176 {2/5}. </s>
            <s xml:id="echoid-s1401" xml:space="preserve">Erunt octo latera, hoc eſt, {2/3} perimetri minora
              <lb/>
            quam 41411 {1/5}. </s>
            <s xml:id="echoid-s1402" xml:space="preserve">Item quia latus dodecagoni circumſcripti mi-
              <lb/>
            nus eſt quam 5359, erunt quatuor latera, hoc eſt, triens
              <lb/>
            perimetri minor quam 21436. </s>
            <s xml:id="echoid-s1403" xml:space="preserve">Quamobrem {2/3} perimetri dode-
              <lb/>
            cagoni inſcripti cum triente perimetri circumſcripti minores
              <lb/>
            erunt quam 62847 {1/5}. </s>
            <s xml:id="echoid-s1404" xml:space="preserve">Sed iſtis ſimul minor etiam eſt circuli
              <lb/>
            circumferentia . </s>
            <s xml:id="echoid-s1405" xml:space="preserve">Ergo hæc ad diametrum omnino minorem
              <note symbol="*" position="right" xlink:label="note-0077-02" xlink:href="note-0077-02a" xml:space="preserve">per 9. huj.</note>
            bebit rationem, quam 62847 {1/5} ad 20000; </s>
            <s xml:id="echoid-s1406" xml:space="preserve">& </s>
            <s xml:id="echoid-s1407" xml:space="preserve">multo minorem
              <lb/>
            proinde, quam 62857 {1/7} ad 20000, hoc eſt, quam triplam ſeſ-
              <lb/>
            quiſeptimam. </s>
            <s xml:id="echoid-s1408" xml:space="preserve">Demonſtrati itaque ſunt termini Rationis pe-
              <lb/>
            ripheriæ ad diametrum, quos Archimedes ſtatuit. </s>
            <s xml:id="echoid-s1409" xml:space="preserve">Eoſdem
              <lb/>
            verò poſtmodum ſolius inſcripti trigoni æquilateri latere in-
              <lb/>
            dagato comprobabimus. </s>
            <s xml:id="echoid-s1410" xml:space="preserve">Porrò ut propinquior inveniatur ra-
              <lb/>
            tio plurium laterum polygona conſideranda ſunt. </s>
            <s xml:id="echoid-s1411" xml:space="preserve">Intelliga-
              <lb/>
            tur igitur circumſcriptum circulo polygonum aliudque inſcri-
              <lb/>
            ptum laterum 60. </s>
            <s xml:id="echoid-s1412" xml:space="preserve">Et præter hæc ſubduplo numero laterum
              <lb/>
            inſcriptum, nempe trigintangulum.</s>
            <s xml:id="echoid-s1413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1414" xml:space="preserve">Et invenitur quidem latus inſcripti ſexagintanguli majus
              <lb/>
            partibus 10467191, qualium radius 100000000 & </s>
            <s xml:id="echoid-s1415" xml:space="preserve">latus tri-
              <lb/>
            gintanguli minus quam 20905693: </s>
            <s xml:id="echoid-s1416" xml:space="preserve">cujus dimidium 10452846 {1/2}
              <lb/>
            eſt ſinus arcus æquantis {1/60} circumferentiæ. </s>
            <s xml:id="echoid-s1417" xml:space="preserve">Subtenſa autem
              <lb/>
            erat 10467191. </s>
            <s xml:id="echoid-s1418" xml:space="preserve">Ergo differentia 14344 {1/2} minor verâ: </s>
            <s xml:id="echoid-s1419" xml:space="preserve">& </s>
            <s xml:id="echoid-s1420" xml:space="preserve">triens
              <lb/>
            differentiæ 4781 {1/2}, qui additus ad ſubtenſam 10467191 facit
              <lb/>
            10471972 {1/2}. </s>
            <s xml:id="echoid-s1421" xml:space="preserve">Quibus itaque major eſt arcus {1/60} circumferentiæ.
              <lb/>
            </s>
            <s xml:id="echoid-s1422" xml:space="preserve">Ductis autem 10471972 {1/2} ſexagies fiunt 628318250. </s>
            <s xml:id="echoid-s1423" xml:space="preserve">Hiſce
              <lb/>
            igitur partibus omnino major eſt circumferentia tota.</s>
            <s xml:id="echoid-s1424" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1425" xml:space="preserve">Rurſus quoniam latus inſcripti 60 anguli minus eſt quam
              <lb/>
            10467192, erunt duæ tertiæ ipſius minores quam 6978128.
              <lb/>
            </s>
            <s xml:id="echoid-s1426" xml:space="preserve">Circumſcripti autem 60 anguli latus cum ſit minus quam
              <lb/>
            10481556, erit triens ipſius minor quam 3493852. </s>
            <s xml:id="echoid-s1427" xml:space="preserve"/>
          </p>
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