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

Table of figures

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[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]
[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.
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          <pb o="460" file="0180" n="190" rhead="VERA CIRCULI"/>
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        <div xml:id="echoid-div219" type="section" level="1" n="107">
          <head xml:id="echoid-head148" xml:space="preserve">PROP. XXXV. PROBLEMA.</head>
          <head xml:id="echoid-head149" style="it" xml:space="preserve">Rectâ per datum punctum in diametro ductâ,
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          ſemicirculum in ratione data dividere.</head>
          <p>
            <s xml:id="echoid-s3921" xml:space="preserve">Sit ſemicirculus A D G, cujus diameter A G, centrum E,
              <lb/>
              <note position="left" xlink:label="note-0180-01" xlink:href="note-0180-01a" xml:space="preserve">TAB. XLIV.
                <lb/>
              fig. 2.</note>
            punctum in diametro datum B. </s>
            <s xml:id="echoid-s3922" xml:space="preserve">ſupponatur factum quod
              <lb/>
            jubetur; </s>
            <s xml:id="echoid-s3923" xml:space="preserve">ſitque recta B D ſemicirculum dividens in ratione
              <lb/>
            data: </s>
            <s xml:id="echoid-s3924" xml:space="preserve">quoniam datur ſemicirculi menſura & </s>
            <s xml:id="echoid-s3925" xml:space="preserve">ratio in qua
              <lb/>
            dividitur, igitur datur ejus portio nempe D B G. </s>
            <s xml:id="echoid-s3926" xml:space="preserve">Sit recta
              <lb/>
            B D, z: </s>
            <s xml:id="echoid-s3927" xml:space="preserve">ex datis rectis B D, B E, E D, innoteſcunt tri-
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            angula D E B, D E F, D E G: </s>
            <s xml:id="echoid-s3928" xml:space="preserve">deinde ſit ut D E F una cum
              <lb/>
            D E G ad D E G ità duplum D E G ad trapezium circum-
              <lb/>
            ſcriptum D E G H: </s>
            <s xml:id="echoid-s3929" xml:space="preserve">& </s>
            <s xml:id="echoid-s3930" xml:space="preserve">poſitis primis terminis convergenti-
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            bus D E G, D E G H continuetur ſeries convergens poly-
              <lb/>
            gonorum complicatorum, ſecundum circuli proprietates ſæ-
              <lb/>
            pius repetitas, donec conveniens fuerit approximationem ad-
              <lb/>
            hibere ita ut exhibeatur ſector D E G, qui una cum trian-
              <lb/>
            gulo D B E æquatur portioni D B G cognitæ, cujus æquatio-
              <lb/>
            nis reſolutio manifeſtat ignotam quantitatem z ſeu rectam
              <lb/>
            B D: </s>
            <s xml:id="echoid-s3931" xml:space="preserve">reliqua patent.</s>
            <s xml:id="echoid-s3932" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3933" xml:space="preserve">Idem problema eodem omnino modo reſolvitur in ellipſe,
              <lb/>
            hyperbola vel earum ſectore dato.</s>
            <s xml:id="echoid-s3934" xml:space="preserve"/>
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        <div xml:id="echoid-div221" type="section" level="1" n="108">
          <head xml:id="echoid-head150" xml:space="preserve">SCHOLIUM.</head>
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            <s xml:id="echoid-s3935" xml:space="preserve">Si quis prædictorum problematum mechanicam deſideret
              <lb/>
            praxim; </s>
            <s xml:id="echoid-s3936" xml:space="preserve">non difficile erit calculum, approximationem,
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            & </s>
            <s xml:id="echoid-s3937" xml:space="preserve">æquationis reſolutionem ſecundum vulgatas Geome-
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            triæ practicæ regulas quodammodo imitari, multa talia
              <lb/>
            problemata poſſem hic reſolvere ope analyſios & </s>
            <s xml:id="echoid-s3938" xml:space="preserve">noſtræ ſe-
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            ricrum convergentium doctrinæ, quæ antea impoſſibilia æſti-
              <lb/>
            mabantur: </s>
            <s xml:id="echoid-s3939" xml:space="preserve">ſed dicet fortè aliquis has reſolutiones non eſſe geo-
              <lb/>
            metricas; </s>
            <s xml:id="echoid-s3940" xml:space="preserve">reſpondeo, ſi per geometricum intelligatur </s>
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