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

Table of figures

< >
[Figure 1]
[Figure 2]
[Figure 3]
[4] Pag. 324.TAB. XXXIV.Fig. 1.O B E P L S Q M R N A K H G D F C
[5] Fig. 3.B Q P S O N R M E H K G A F D L C
[6] Fig. 2.B E A G M C D H R F K L
[7] Fig. 4.B M L K E A D F H C
[8] Fig. 5.B B A D C A D C E E
[9] Fig. 8.K G H M E F B L A D C
[10] Fig. 6.S E B P D
[11] Fig. 7.E S D P B
[12] Pag. 326.TAB. XXXV.Fig. 1.N H T Z Ψ G K X S Σ Α E Ξ Y F O L B Δ R P V C Q Ω D M
[13] Fig. 5.B L A C D F M G K E H
[14] Fig. 4.B L A C D F M G K H E
[15] Fig. 2.B Δ P R V C Q Ω D A L F O Y Ξ Α Σ X S G K Ψ Z T H E N M
[16] Fig. 3.B Δ P R V A D Ω Q C L F O Y Ξ Α Σ X S G K E Ψ Z T H E N M
[17] Pag. 328.Fig. 2.B L F A D C H E
[18] Fig. 1.B L F A D C H E
[19] Fig. 3.B E A D C
[20] Fig. 4.Q B H A F C E G R D K
[21] Fig. 5.B E D A C G F
[Figure 22]
[23] Pag. 340.TAB. XXXVII.Fig. 1.C G H F E DH A X Q Y T N V B G
[24] Fig. 3.γ A F D X B P N V E Q C
[25] Fig. 2.K C Δ R Θ Z O Γ D I
[26] Fig. 4.A B D C Π Φ N E S P F
[27] Fig. 2.M E Ψ Λ Φ S Ξ Π Ρ Σ Ω F L
[28] Fig. 5.K B Δ E Z A C R O D Θ Γ I
[Figure 29]
[Figure 30]
< >
page |< < (368) 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-s1427" xml:space="preserve">
              <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
              <lb/>
            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-
              <lb/>
            dem latus, calculo Ludolphi Colonienſis, Arithmetici nobi-
              <lb/>
            lis, inventum eſt partium 58177640912684919 non unâ am-
              <lb/>
            plius, ſubtenditurque duobus ſcrup. </s>
            <s xml:id="echoid-s1431" xml:space="preserve">primis; </s>
            <s xml:id="echoid-s1432" xml:space="preserve">circumſcripti
              <lb/>
            autem latus 58177643374063182 non unâ minus. </s>
            <s xml:id="echoid-s1433" xml:space="preserve">Prætereaque
              <lb/>
            latus polygoni ſubduplo laterum numero inſcripti, quod eſt
              <lb/>
            116355276902613523 non unâ minus. </s>
            <s xml:id="echoid-s1434" xml:space="preserve">Hinc peripheriæ lon-
              <lb/>
            gitudo invenitur major quam partium 6283185307179584;
              <lb/>
            </s>
            <s xml:id="echoid-s1435" xml:space="preserve">minor autem quam 6283185307179589, qualium radius
              <lb/>
            1000000000000000. </s>
            <s xml:id="echoid-s1436" xml:space="preserve">Solitâ autem methodo ex additis inſcri-
              <lb/>
            pti circumſcriptique polygoni iſtius lateribus, invenietur
              <lb/>
            tantum majorem eſſe peripheriam partibus 62831852, & </s>
            <s xml:id="echoid-s1437" xml:space="preserve">mi-
              <lb/>
            norem 62831855. </s>
            <s xml:id="echoid-s1438" xml:space="preserve">Patet igitur notarum verarum amplius quam
              <lb/>
            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
              <lb/>
            præcedentibus ita ſe habet, ſemperque evenire neceſſe eſt quot-
              <lb/>
            cunque laterum polygonis utamur. </s>
            <s xml:id="echoid-s1441" xml:space="preserve">At per ea, quæ poſtea
              <lb/>
            trademus, triplum numerum notarum facile obtineri appare-
              <lb/>
            bit.</s>
            <s xml:id="echoid-s1442" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div75" type="section" level="1" n="34">
          <head xml:id="echoid-head56" xml:space="preserve">
            <emph style="sc">Problema</emph>
          II.
            <emph style="sc">Prop</emph>
          . XI.</head>
          <p style="it">
            <s xml:id="echoid-s1443" xml:space="preserve">Rectam ſumere peripheriæ dati circuli æqualem.</s>
            <s xml:id="echoid-s1444" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1445" xml:space="preserve">Oſtenſum eſt ſuperius, quod octo inſcripti dodecagoni la-
              <lb/>
            tera dempto circuli radio minora ſunt peripheriâ dimidiâ.
              <lb/>
            </s>
            <s xml:id="echoid-s1446" xml:space="preserve">In conſtructione autem ut plurimum defectus animadverti ne-
              <lb/>
            quit. </s>
            <s xml:id="echoid-s1447" xml:space="preserve">Nam ſi quatermilleſima diametri pars accedat longitu-
              <lb/>
            dini ſic inventæ, jam dimidiam peripheriam excedet. </s>
            <s xml:id="echoid-s1448" xml:space="preserve">Quod
              <lb/>
            ſic fiet manifeſtum. </s>
            <s xml:id="echoid-s1449" xml:space="preserve">Quarum partium radius eſt 10000, earum
              <lb/>
            latus dodecagoni inſcripti circulo eſt amplius quam 5176 {3/8}. </s>
            <s xml:id="echoid-s1450" xml:space="preserve">
              <lb/>
            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,
              <lb/>
            erit reliqua major quam 31411. </s>
            <s xml:id="echoid-s1453" xml:space="preserve">cui ſi addantur partes 5,
              <lb/>
            hoc eſt, {1/4000} diametri, fient jam 31416; </s>
            <s xml:id="echoid-s1454" xml:space="preserve">quibus minorem eſſe
              <lb/>
            circumferentiam dimidiam liquet ex præcedentibus. </s>
            <s xml:id="echoid-s1455" xml:space="preserve">Latus </s>
          </p>
        </div>
      </text>
    </echo>