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

Table of figures

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[61] Fig. 5.G L B H D O A E C K
[62] Fig. 7.K F A C D B E H G
[63] Pag. 404.TAB. XLII.Fig. 1.K F M A C D B L E N G
[64] Fig. 3.G R D B H F E N A X C M P Q K
[65] Fig. 2.K A F c S C L E B T G D R d
[66] Fig. 4.K e G P E m B D f R F S H M C A N L Q n
[67] Fig. 5.B C R E G A F M Q D O
[68] Fig. 6.B C H G E A M Q P K D
[69] Fig. 7.B C E G A M P Q K H D
[Figure 70]
[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]
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          <pb o="419" file="0137" n="146" rhead="ET HYPERBOLÆ QUADRATURA."/>
        </div>
        <div xml:id="echoid-div154" type="section" level="1" n="70">
          <head xml:id="echoid-head105" xml:space="preserve">SCHOLIUM.</head>
          <p>
            <s xml:id="echoid-s2879" xml:space="preserve">Duæ præcedentes propoſitiones eodem modo demon-
              <lb/>
            ſtrari poſſunt de duobus quibuſcunque polygonis
              <lb/>
            complicatis loco polygonorum complicatorum ABIP,
              <lb/>
            A B D L P; </s>
            <s xml:id="echoid-s2880" xml:space="preserve">polygonum enim à tangentibus comprehenſum
              <lb/>
            tot continet æqualia trapezia, quot continet polygonum à
              <lb/>
            ſubtendentibus comprehenſum æqualia triangula: </s>
            <s xml:id="echoid-s2881" xml:space="preserve">atque hinc
              <lb/>
            evidens eſt has polygonorum analogias ita ſe habere in infi-
              <lb/>
            nitum, ducendo nimirum rectas AN, AK, AG, AC, per
              <lb/>
            puncta R, T, S, V, & </s>
            <s xml:id="echoid-s2882" xml:space="preserve">adhuc alia & </s>
            <s xml:id="echoid-s2883" xml:space="preserve">alia polygona intra & </s>
            <s xml:id="echoid-s2884" xml:space="preserve">
              <lb/>
            extra ſemper ſcribendo: </s>
            <s xml:id="echoid-s2885" xml:space="preserve">notandum nos appellare hanc poly-
              <lb/>
            gonorum inſcriptionem & </s>
            <s xml:id="echoid-s2886" xml:space="preserve">circumſcriptionem, inſcriptionem
              <lb/>
            & </s>
            <s xml:id="echoid-s2887" xml:space="preserve">circumſcriptionem ſubduplam, ex prædictis patet (ſi po-
              <lb/>
            natur triangulum A B P =
              <emph style="super">a</emph>
            , & </s>
            <s xml:id="echoid-s2888" xml:space="preserve">trapezium A B F P =
              <emph style="super">b</emph>
            ) tra-
              <lb/>
            pezium A B I P eſſe vqab & </s>
            <s xml:id="echoid-s2889" xml:space="preserve">polygonum A B D L P {2ab/a + vqab}:
              <lb/>
            </s>
            <s xml:id="echoid-s2890" xml:space="preserve">eodem modo poſito trapezio A B I P =
              <emph style="super">c</emph>
            , & </s>
            <s xml:id="echoid-s2891" xml:space="preserve">polygono
              <lb/>
            A B D L P =
              <emph style="super">d</emph>
            , erit polygonum A B E I O P = vqcd & </s>
            <s xml:id="echoid-s2892" xml:space="preserve">po-
              <lb/>
            lygonum A B C G K N P = {2cd/c + vqcd,}, ita ut evidens ſit hanc
              <lb/>
            polygonorum ſeriem eſſe convergentem; </s>
            <s xml:id="echoid-s2893" xml:space="preserve">atque in infinitum
              <lb/>
            illam continuando, manifeſtum eſt tandem exhiberi quanti-
              <lb/>
            tatem ſectori circulari, elliptico vel hyperbolico A B E I O P
              <lb/>
            æqualem; </s>
            <s xml:id="echoid-s2894" xml:space="preserve">differentia enim polygonorum complicatorum in
              <lb/>
            ſeriei continuatione ſemper diminuitur, ita ut omni exhibita
              <lb/>
            quantitate fieri poſſit minor, ut in ſequentis theorematis
              <lb/>
            Scholio demonſtrabimus: </s>
            <s xml:id="echoid-s2895" xml:space="preserve">ſi igitur prædicta polygonorum ſe-
              <lb/>
            ries terminari poſſet, hoc eſt, ſi inveniretur ultimum illud
              <lb/>
            polygonum inſcriptum (ſi ita loqui liceat) æquale ultimo
              <lb/>
            illi polygono circumſcripto, daretur infallibiliter circuli & </s>
            <s xml:id="echoid-s2896" xml:space="preserve">
              <lb/>
            hyperbolæ quadratura: </s>
            <s xml:id="echoid-s2897" xml:space="preserve">ſed quoniam difficile eſt, & </s>
            <s xml:id="echoid-s2898" xml:space="preserve">in geo-
              <lb/>
            metria omnino fortaſſe inauditum tales ſeries terminare; </s>
            <s xml:id="echoid-s2899" xml:space="preserve">præ-
              <lb/>
            mittendæ ſunt quædam propoſitiones è quibus inveniri poſ-
              <lb/>
            ſint hujuſmodi aliquot ſerierum terminationes, & </s>
            <s xml:id="echoid-s2900" xml:space="preserve">tandem </s>
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