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

Table of Notes

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          <pb o="459" file="0179" n="189" rhead="ET HYTERBOLÆ QUADRATURA."/>
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        <div xml:id="echoid-div216" type="section" level="1" n="105">
          <head xml:id="echoid-head145" xml:space="preserve">PROP. XXXIV. PROBLEMA.</head>
          <head xml:id="echoid-head146" style="it" xml:space="preserve">Ex dato logorithmo invenire ejus
            <lb/>
          numerum.</head>
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            <s xml:id="echoid-s3901" xml:space="preserve">Ex demonſtratis manifeſtum eſt hoc problema idem eſſe
              <lb/>
              <note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">TAB. XLIV.
                <lb/>
              fig. 1.</note>
            ac ſi quis proponeret; </s>
            <s xml:id="echoid-s3902" xml:space="preserve">ex dato ſpatio hyperbolico, & </s>
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              <lb/>
            una recta uni aſymptotorum parallela illud comprehenden-
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            te, alteram invenire idem ſpatium comprehendentem, & </s>
            <s xml:id="echoid-s3904" xml:space="preserve">
              <lb/>
            eidem aſymptoto parallelam. </s>
            <s xml:id="echoid-s3905" xml:space="preserve">Conſideretur ex quot notis
              <lb/>
            arithmeticis conſtet logorithmus denarii arbitrarius; </s>
            <s xml:id="echoid-s3906" xml:space="preserve">& </s>
            <s xml:id="echoid-s3907" xml:space="preserve">ſuma-
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            tur logorithmi vel ſpatii dati talis pars aliquota nempe ſpa-
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            tium L I K M, ut pentagoni ſpatio L I K M regulariter cir-
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            cumſcripti, & </s>
            <s xml:id="echoid-s3908" xml:space="preserve">hexagoni eidem regulariter inſcripti toties
              <lb/>
            multiplicia, quoties ſpatium datum multiplex eſt ſpatii
              <lb/>
            L I K M, concordent in tot notis arithmeticis, quot conti-
              <lb/>
            net radix quadrata logorithmi arbitrarii; </s>
            <s xml:id="echoid-s3909" xml:space="preserve">hoc enim facile fie-
              <lb/>
            ri poteſt ex inſpectione tabellæ 32 hujus: </s>
            <s xml:id="echoid-s3910" xml:space="preserve">datur ergo ſpatii
              <lb/>
            L I K M menſura & </s>
            <s xml:id="echoid-s3911" xml:space="preserve">recta I K unitas ex ſuppoſitione. </s>
            <s xml:id="echoid-s3912" xml:space="preserve">Sit
              <lb/>
            L M, z; </s>
            <s xml:id="echoid-s3913" xml:space="preserve">ſicut in hujus 32 datur pentagonum ſpatio L I K M
              <lb/>
            regulariter circumſcriptum & </s>
            <s xml:id="echoid-s3914" xml:space="preserve">hexagonum eidem regulariter
              <lb/>
            inſcriptum, inter quæ ſpatium datum L I K M eſt ſecunda
              <lb/>
            duarum mediarum arithmeticè continuè proportionalium;
              <lb/>
            </s>
            <s xml:id="echoid-s3915" xml:space="preserve">& </s>
            <s xml:id="echoid-s3916" xml:space="preserve">ideo duplum haxagoni una cum pentagono æquatur triplo
              <lb/>
            ſpatii, cujus æquationis reſolutio manifeſtat ignotam z ſeu
              <lb/>
            numerum L M, cujus toties multiplicatus, quoties ſpatium
              <lb/>
            L I K M eſt ſubmultiplex ſpatii vel logorithmi dati, eſt nu-
              <lb/>
            merus quæſitus, quem invenire oportuit.</s>
            <s xml:id="echoid-s3917" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3918" xml:space="preserve">Hoc problema idem eſt cum hujus 8, ſed aliter genera-
              <lb/>
            lius & </s>
            <s xml:id="echoid-s3919" xml:space="preserve">methodo plerumque minus operoſa hic reſolu-
              <lb/>
            tum.</s>
            <s xml:id="echoid-s3920" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div218" type="section" level="1" n="106">
          <head xml:id="echoid-head147" style="it" xml:space="preserve">Tom. II. Mmm</head>
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