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

Table of figures

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[71] Pag. 450.TAB.XLIII.Fig. 4.B A F R P C D E G H I K S L M N O
[72] Fig. 1.F G I K D L E S T O C N H M V R B Q P A
[73] Fig. 2.F G I K D L E S T O C N V R B Q P A
[74] Fig. 5.A C B D E
[75] Fig. 3.A F G I K D L S T E O C N H M V R B Q P
[Figure 76]
[Figure 77]
[Figure 78]
[Figure 79]
[Figure 80]
[Figure 81]
[Figure 82]
[83] TAB. XLIV.Fig. 2.D H A B E F G
[84] Fig. 1.E G N L O I Q P D K M H F A
[85] Fig. 3.B E F A D G C
[86] I. CasusFig. 4.Y Q R C A B M L I K V C O S X
[87] II. CasusFig. 5.R C Y Q A B I L M K V O X S C
[88] III. CasusFig. 6.Q C D Y K L I N M S V B X C A G O
[89] Fig. 7.IV. CasusQ D C A B S L N X M I V Y K C G O
[Figure 90]
[91] Pag. 506.TAB. XLV.Fig. 1.C F D B
[92] Fig. 2.C B A E F
[93] Fig. 3.B b F f H c
[94] Fig. 4.C D B A E F G H
[95] Fig. 5.C b d D B E F G f g e
[96] Fig. 6.B G A C D
[Figure 97]
[Figure 98]
[Figure 99]
[Figure 100]
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              <pb o="443" file="0161" n="170" rhead="ET HYPERBOLÆ QUADRATURA."/>
            G H, nempe X; </s>
            <s xml:id="echoid-s3624" xml:space="preserve">atque ex hujus 7 terminatio ſeriei A B,
              <lb/>
            G H, nempe X, æqualis eſt minori duarum mediarum arith-
              <lb/>
            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">
                <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>
            hyperbolæ minorem eſſe quam mi-
              <lb/>
            nor duarum mediarum geometricè con-
              <lb/>
            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
              <lb/>
            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-
              <lb/>
            finitum continuando, ſemper demonſtratur terminum quem-
              <lb/>
            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,
              <lb/>
            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>
            <s xml:id="echoid-s3664" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3665" xml:space="preserve">Ex dictis manifeſtum eſt hanc approximationem exactio-
              <lb/>
            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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