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

Table of figures

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[Figure 191]
[192] Pag. 626.TAB. LI.Fig. 1.F E D V S 30 20 10 C L G R H K P A M Z I O X B
[193] Fig. 2.L K O R E H N I S D G B C
[194] Fig. 3.A 16 15 14 13 12 11 10 9 B 8 7 6 5 4 3 2 1
[195] Fig. 4
[196] Fig. 5.
[197] Fig. 6.
[198] Fig. 1.
[199] Fig. 2.
[200] Fig. 3.
[201] Fig. 4.
[202] Fig. 5.
[203] Fig. 6.
[204] Fig. 7.
[205] Fig. 8.
[206] Fig. 9.
[207] Fig. 10.
[208] Fig. 11.
[209] Fig. 12.
[210] Fig. 13.
[Figure 211]
[Figure 212]
[Figure 213]
[Figure 214]
[Figure 215]
[Figure 216]
[217] Pg. 700TAB. LIII.4 3 2 1 Annu Sat. lus
[218] 4 3 2 1 Jup.
[219] Luna Tellus
[220] Pag. 704.TAB. LIV.Fig. 1.Satu@@i. Jovis. Martis. Telluris. veneris. M@rc. ♎ Sol. ♈ VS
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            G H, nempe X; </s>
            <s xml:id="echoid-s3624" xml:space="preserve">atque ex hujus 7 terminatio ſeriei A B,
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            G H, nempe X, æqualis eſt minori duarum mediarum arith-
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            meticè continuè proportionalium inter A & </s>
            <s xml:id="echoid-s3625" xml:space="preserve">B, & </s>
            <s xml:id="echoid-s3626" xml:space="preserve">ideo Z ea-
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            dem minor eſt, quod demonſtrare oportuit.</s>
            <s xml:id="echoid-s3627" xml:space="preserve"/>
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        <div xml:id="echoid-div197" type="section" level="1" n="95">
          <head xml:id="echoid-head131" xml:space="preserve">PROP. XXV. THEOREMA.</head>
          <p>
            <s xml:id="echoid-s3628" xml:space="preserve">Iisdem poſitis; </s>
            <s xml:id="echoid-s3629" xml:space="preserve">dico Z ſeu ſectorem
              <lb/>
              <note position="right" xlink:label="note-0161-01" xlink:href="note-0161-01a" xml:space="preserve">
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              A B # A B
                <lb/>
              C D # G H
                <lb/>
              E F # M N
                <lb/>
              K L # O P
                <lb/>
              Z # X
                <lb/>
              </note>
            hyperbolæ minorem eſſe quam mi-
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            nor duarum mediarum geometricè con-
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            tinuè proportionalium inter A & </s>
            <s xml:id="echoid-s3630" xml:space="preserve">B.
              <lb/>
            </s>
            <s xml:id="echoid-s3631" xml:space="preserve">Inter A & </s>
            <s xml:id="echoid-s3632" xml:space="preserve">B ſit media geometrica G,
              <lb/>
            & </s>
            <s xml:id="echoid-s3633" xml:space="preserve">inter G & </s>
            <s xml:id="echoid-s3634" xml:space="preserve">B media geometrica H; </s>
            <s xml:id="echoid-s3635" xml:space="preserve">
              <lb/>
            Item inter G & </s>
            <s xml:id="echoid-s3636" xml:space="preserve">H media geometrica M, & </s>
            <s xml:id="echoid-s3637" xml:space="preserve">inter M & </s>
            <s xml:id="echoid-s3638" xml:space="preserve">H media
              <lb/>
            geometriea N; </s>
            <s xml:id="echoid-s3639" xml:space="preserve">continueturque hæc ſeries convergens AB, GH,
              <lb/>
            MN, OP, &</s>
            <s xml:id="echoid-s3640" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3641" xml:space="preserve">in infinitum ut fiat ejus terminatio X. </s>
            <s xml:id="echoid-s3642" xml:space="preserve">ſatis patet
              <lb/>
            ex prædictis C & </s>
            <s xml:id="echoid-s3643" xml:space="preserve">G eſſe inter ſe æquales, & </s>
            <s xml:id="echoid-s3644" xml:space="preserve">H majorem eſſe
              <lb/>
            quam D; </s>
            <s xml:id="echoid-s3645" xml:space="preserve">atque ob hanc rationem M media geometrica inter G
              <lb/>
            & </s>
            <s xml:id="echoid-s3646" xml:space="preserve">H major eſt quam E media geometrica inter C & </s>
            <s xml:id="echoid-s3647" xml:space="preserve">D. </s>
            <s xml:id="echoid-s3648" xml:space="preserve">Deinde
              <lb/>
            N media geometrica inter M & </s>
            <s xml:id="echoid-s3649" xml:space="preserve">H major eſt media harmonica
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            inter eaſdem; </s>
            <s xml:id="echoid-s3650" xml:space="preserve">& </s>
            <s xml:id="echoid-s3651" xml:space="preserve">quoniam M major eſt quam E & </s>
            <s xml:id="echoid-s3652" xml:space="preserve">H quam D, erit
              <lb/>
            media harmonica inter M & </s>
            <s xml:id="echoid-s3653" xml:space="preserve">H major quam F media harmo-
              <lb/>
            nica inter E & </s>
            <s xml:id="echoid-s3654" xml:space="preserve">D; </s>
            <s xml:id="echoid-s3655" xml:space="preserve">proinde N media geometrica inter M & </s>
            <s xml:id="echoid-s3656" xml:space="preserve">H
              <lb/>
            major eritquam F. </s>
            <s xml:id="echoid-s3657" xml:space="preserve">eadem methodo utramque ſeriem in in-
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            finitum continuando, ſemper demonſtratur terminum quem-
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            libet ſeriei A B, C D, minorem eſſe quam idem numero ter-
              <lb/>
            minus ſeriei A B, G H; </s>
            <s xml:id="echoid-s3658" xml:space="preserve">& </s>
            <s xml:id="echoid-s3659" xml:space="preserve">igitur terminatio ſeriei A B, C D,
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            nempe Z minor erit quam terminatio ſeriei A B, G H, nem-
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            pe X; </s>
            <s xml:id="echoid-s3660" xml:space="preserve">atque ex hujus 9 terminatio ſeriei A B, G H, ſeu X, æqua-
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            lis eſt minori duarum mediarum geometricè continuè propor-
              <lb/>
            tionalium inter A & </s>
            <s xml:id="echoid-s3661" xml:space="preserve">B; </s>
            <s xml:id="echoid-s3662" xml:space="preserve">& </s>
            <s xml:id="echoid-s3663" xml:space="preserve">ideo Z eadem minor eſt, quod
              <lb/>
            demonſtrare oportuit.</s>
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            <s xml:id="echoid-s3665" xml:space="preserve">Ex dictis manifeſtum eſt hanc approximationem exactio-
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            rem eſſe illa, in antecedenti propoſitione, demonſtrata, et-
              <lb/>
            iamſi hæc ſit paulò laborioſior. </s>
            <s xml:id="echoid-s3666" xml:space="preserve">ſed non diſſimulandum
              <lb/>
            eſt duas poſſe eſſe ſeries æquales terminationes habentes, </s>
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