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

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        <div xml:id="echoid-div201" type="section" level="1" n="97">
          <p>
            <s xml:id="echoid-s3713" xml:space="preserve">
              <pb o="446" file="0164" n="173" rhead="VERA CIRCULI"/>
            metricum inter parallelogramma P D M L, F D M K, quod de-
              <lb/>
            monſtrare oportuit.</s>
            <s xml:id="echoid-s3714" xml:space="preserve"/>
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        <div xml:id="echoid-div203" type="section" level="1" n="98">
          <head xml:id="echoid-head134" xml:space="preserve">PROP. XXVIII. THEOREMA.</head>
          <p>
            <s xml:id="echoid-s3715" xml:space="preserve">Iisdem poſitis ducantur rectæ F E, L E, hyperbolam tan-
              <lb/>
              <note position="left" xlink:label="note-0164-01" xlink:href="note-0164-01a" xml:space="preserve">TAB. XLIII.
                <lb/>
              fig. 4.</note>
            gentes in punctis F, L, ut compleatur trapezium A F E L,
              <lb/>
            quod dico eſſe medium harmonicum inter parallelogramma
              <lb/>
            P D M L, F D M K. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">triangulum A F L, trapezium A F G L,
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            & </s>
            <s xml:id="echoid-s3717" xml:space="preserve">medium harmonicum inter parallelogramma P D M L,
              <lb/>
            F D M K, ſunt continuè proportionalia, quoniam triangu-
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            lum A F L eſt medium arithmeticum & </s>
            <s xml:id="echoid-s3718" xml:space="preserve">trapezium A F G L
              <lb/>
            medium geometricum inter eadem parallelogramma, ut pa-
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            tet ex hujus 13; </s>
            <s xml:id="echoid-s3719" xml:space="preserve">ſed triangulum A F L, trapezium A F G L,
              <lb/>
            & </s>
            <s xml:id="echoid-s3720" xml:space="preserve">trapezium A F E L ſunt continuè proportionalia ex hujus
              <lb/>
            1; </s>
            <s xml:id="echoid-s3721" xml:space="preserve">& </s>
            <s xml:id="echoid-s3722" xml:space="preserve">proinde trapezium A F E L eſt medium harmonicum
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            inter parallelogramma P D M L, F D M K, quod demon-
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            ftrare oportuit.</s>
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        <div xml:id="echoid-div205" type="section" level="1" n="99">
          <head xml:id="echoid-head135" xml:space="preserve">PROP. XXIX. PROBLEMA.
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          Dato circulo æquale invenire quadratum.</head>
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            <s xml:id="echoid-s3724" xml:space="preserve">Sit quadratum circulo circumſcriptum 4000000000000000;
              <lb/>
            </s>
            <s xml:id="echoid-s3725" xml:space="preserve">erit ergo eidem inſcriptum 2000000000000000, inter quæ
              <lb/>
            quadrata ſit medium geometricum 2828427124746190
              <lb/>
            octagonum nempe intra circulum: </s>
            <s xml:id="echoid-s3726" xml:space="preserve">deinde inter octago-
              <lb/>
            num intra circulum & </s>
            <s xml:id="echoid-s3727" xml:space="preserve">quadratum extra ſit medium har-
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            monicum, quod levi labore invenitur dividendoduplum
              <lb/>
            quadrati octagoni intra circulum ſeu duplum rectanguli à
              <lb/>
            quadratis intra & </s>
            <s xml:id="echoid-s3728" xml:space="preserve">extra circulum per ſummam quadrati & </s>
            <s xml:id="echoid-s3729" xml:space="preserve">
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            octagoni intra; </s>
            <s xml:id="echoid-s3730" xml:space="preserve">eritque inventum medium harmonicum, octa-
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            gonum circumſcriptum, nempe 3313708498984760. </s>
            <s xml:id="echoid-s3731" xml:space="preserve">conti-
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            nuetur hæc ſeries convergens polygonorum complicatorum
              <lb/>
            donec prima medietas notarum ſit eadem in utroque </s>
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