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

Page concordance

< >
Scan Original
81
82 367
83 368
84 369
85 370
86 371
87 372
88 373
89 374
90 375
91 376
92
93
94
95 377
96 378
97 379
98 380
99 381
100 382
101 383
102 384
103 385
104 386
105
106 386
107
108 387
109
110 389
< >
page |< < (367) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div72" type="section" level="1" n="33">
          <p>
            <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>
        </div>
      </text>
    </echo>
Impressum