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

Table of Notes

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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>
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            <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
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            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
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            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-
              <lb/>
            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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            <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,
              <lb/>
            & </s>
            <s xml:id="echoid-s3937" xml:space="preserve">æquationis reſolutionem ſecundum vulgatas Geome-
              <lb/>
            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-
              <lb/>
            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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