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

Table of figures

< >
[161] Fig. 42.* 19. Maii.
[162] Fig. 43.* 17. Dec.
[163] Fig. 44.* 18. Dec.
[164] Fig. 45.* 27. Dec.
[165] Fig. 46.* 11. Mart 1658.
[166] Fig. 47.* 16. Mart.
[167] Fig. 48.* 23. Mart.
[168] Fig. 49.* 3. Apr.
[169] Fig. 50.* 10. Nov.
[170] Fig. 51.* 16. Ian. 1659.
[171] Fig. 52.12. Febr. *
[172] Fig. 53.* 24. Febr.
[173] Fig. 54.25. Febr. *
[174] Fig. 55.14. Mart. *
[175] Fig. 56.16. Mart. *
[176] Fig. 57.* 21. Mart.
[177] Fig. 58.* 22. Mart.
[178] Fig. 59.26. Mart. *
[179] Pag. 574.TAB. XLIX.Fig. 2.
[180] Fig. 1.C K O B H N G M S * F D A L E
[181] Fig. 3.E C D A * B
[182] Fig. 4.P Q O N M L * C R
[183] Fig. 5.C * V S X T Y
[184] Fig. 6.
[185] Fig. 7.
[186] Pag. 580.TAB. L.Fig. 2.R ♈ L D I T A N ♋ H G E P F K C Q O B M S
[187] Fig. 3.
[188] Fig. 4.N Q F C P L E A M H O D f
[189] Fig. 1.B A
[Figure 190]
< >
page |< < (440) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div188" type="section" level="1" n="90">
          <p>
            <s xml:id="echoid-s3509" xml:space="preserve">
              <pb o="440" file="0158" n="167" rhead="VERA CIRCULI"/>
            eadem F major eſt. </s>
            <s xml:id="echoid-s3510" xml:space="preserve">eadem modo utramque ſeriem in infini-
              <lb/>
            tum continuando, ſemper demonſtratur terminum quemlibet
              <lb/>
            ſeriei A B, C D, minorem eſſe quam idem numero terminus
              <lb/>
            ſeriei. </s>
            <s xml:id="echoid-s3511" xml:space="preserve">A B, G H; </s>
            <s xml:id="echoid-s3512" xml:space="preserve">& </s>
            <s xml:id="echoid-s3513" xml:space="preserve">igitur terminatio ſeriei A B, C D, nem-
              <lb/>
            pe Z minor erit terminatione ſeriei A B, G H, nempe X;
              <lb/>
            </s>
            <s xml:id="echoid-s3514" xml:space="preserve">atque ex hujus 7, terminatio ſeriei A B, G H, ſeu X æqua-
              <lb/>
            lis eſt majori duarum mediarum arithmeticè continuè propor-
              <lb/>
            tionalium inter A & </s>
            <s xml:id="echoid-s3515" xml:space="preserve">B, & </s>
            <s xml:id="echoid-s3516" xml:space="preserve">ideo Z eadem minor eſt, quod
              <lb/>
            demonſtrandum erat.</s>
            <s xml:id="echoid-s3517" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div190" type="section" level="1" n="91">
          <head xml:id="echoid-head127" xml:space="preserve">PROP. XXII. THEOREMA.</head>
          <p>
            <s xml:id="echoid-s3518" xml:space="preserve">IIsdem poſitis quæ ſupra; </s>
            <s xml:id="echoid-s3519" xml:space="preserve">dico Z
              <lb/>
              <note position="right" xlink:label="note-0158-01" xlink:href="note-0158-01a" xml:space="preserve">
                <lb/>
              A B # A B
                <lb/>
              C D # G H
                <lb/>
              E F # M N
                <lb/>
              K L # O P
                <lb/>
              Z # X
                <lb/>
              </note>
            ſeu ſectorem circuli vel ellipſeos
              <lb/>
            minorem eſſe quam major duarum
              <lb/>
            mediarum geometricè continuè pro-
              <lb/>
            portionalium inter A & </s>
            <s xml:id="echoid-s3520" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3521" xml:space="preserve">inter A
              <lb/>
            & </s>
            <s xml:id="echoid-s3522" xml:space="preserve">B ſit media geometrica G, & </s>
            <s xml:id="echoid-s3523" xml:space="preserve">inter
              <lb/>
            G & </s>
            <s xml:id="echoid-s3524" xml:space="preserve">B ſit media geometrica H; </s>
            <s xml:id="echoid-s3525" xml:space="preserve">Item
              <lb/>
            inter G & </s>
            <s xml:id="echoid-s3526" xml:space="preserve">H media Geometrica M, & </s>
            <s xml:id="echoid-s3527" xml:space="preserve">inter M & </s>
            <s xml:id="echoid-s3528" xml:space="preserve">H media Geo-
              <lb/>
            metrica N; </s>
            <s xml:id="echoid-s3529" xml:space="preserve">continuetúrque hæc ſeries convergens A B, G H,
              <lb/>
            M N, O P, &</s>
            <s xml:id="echoid-s3530" xml:space="preserve">c, in infinitum, ut fiat ejus terminatio X. </s>
            <s xml:id="echoid-s3531" xml:space="preserve">ſatis
              <lb/>
            patet ex prædictis C & </s>
            <s xml:id="echoid-s3532" xml:space="preserve">G eſſe inter ſe æquales, item H majorem
              <lb/>
            eſſe quam D; </s>
            <s xml:id="echoid-s3533" xml:space="preserve">atque ob hanc rationem M media Geometrica in-
              <lb/>
            ter G & </s>
            <s xml:id="echoid-s3534" xml:space="preserve">H major eſt quam E media geometrica inter G & </s>
            <s xml:id="echoid-s3535" xml:space="preserve">D.
              <lb/>
            </s>
            <s xml:id="echoid-s3536" xml:space="preserve">deinde N media Geometrica inter M & </s>
            <s xml:id="echoid-s3537" xml:space="preserve">H major eſt media har-
              <lb/>
            monica inter easdem; </s>
            <s xml:id="echoid-s3538" xml:space="preserve">& </s>
            <s xml:id="echoid-s3539" xml:space="preserve">quoniam M major eſt quam E & </s>
            <s xml:id="echoid-s3540" xml:space="preserve">H
              <lb/>
            major quam D, erit media harmonica inter M & </s>
            <s xml:id="echoid-s3541" xml:space="preserve">H major quam
              <lb/>
            F media harmonica inter E & </s>
            <s xml:id="echoid-s3542" xml:space="preserve">D; </s>
            <s xml:id="echoid-s3543" xml:space="preserve">& </s>
            <s xml:id="echoid-s3544" xml:space="preserve">ideo N media Geometrica
              <lb/>
            inter M & </s>
            <s xml:id="echoid-s3545" xml:space="preserve">H major erit quam F. </s>
            <s xml:id="echoid-s3546" xml:space="preserve">eadem methodo utramque
              <lb/>
            ſeriem in infinitum continuando ſemper demonſtratur termi-
              <lb/>
            num quemlibet ſeriei A B, C D, minorem eſſe quam idem
              <lb/>
            numero terminus ſeriei A B, G H; </s>
            <s xml:id="echoid-s3547" xml:space="preserve">& </s>
            <s xml:id="echoid-s3548" xml:space="preserve">igitur terminatio ſeriei
              <lb/>
            A B, C D, nempe Z minor erit terminatione ſeriei A B,
              <lb/>
            G H, nempè X; </s>
            <s xml:id="echoid-s3549" xml:space="preserve">atque ex hujus 9 terminatio ſeriei A B,
              <lb/>
            G H, ſeu X, æqualis eſt majori duarum mediarum Geometri-
              <lb/>
            cè continuè proportionalium inter A & </s>
            <s xml:id="echoid-s3550" xml:space="preserve">B; </s>
            <s xml:id="echoid-s3551" xml:space="preserve">& </s>
            <s xml:id="echoid-s3552" xml:space="preserve">ideo Z eadem
              <lb/>
            minor eſt, quod demonſtrare oportuit.</s>
            <s xml:id="echoid-s3553" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>