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

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        <div xml:id="echoid-div210" type="section" level="1" n="102">
          <pb o="452" file="0172" n="182" rhead="VERA CIRCULI"/>
          <p>
            <s xml:id="echoid-s3811" xml:space="preserve">Poteſtigitur abſque periculo erroris ſumi ſequens numerus
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            pro hyperbolæ ſectore, cujus numeri multiplices uſque ad
              <lb/>
            decem, diviſionis facilitandæ gratia in compoſitione logorith-
              <lb/>
            morum, hic ſubjicimus; </s>
            <s xml:id="echoid-s3812" xml:space="preserve">in magnis namque diviſionibus præ-
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            ſtat uti repetita diviſoris multiplicium ſubſtractione quam or-
              <lb/>
            dinaria diviſione, ut conſtat expertis arithmeticis.</s>
            <s xml:id="echoid-s3813" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3814" xml:space="preserve">Manifeſtum eſt hoc
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              <note position="right" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">
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              1 # 23025850929940456240178700
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            problema eodem
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            ferè modo poſſe reſol-
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            vi, etiamſi aſymptota
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            A O, A K, non ſint
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            conſtiruta ad angulum
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            rectum: </s>
            <s xml:id="echoid-s3815" xml:space="preserve">nos autem ita
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            fuppoſuimus, ut faci-
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            lior & </s>
            <s xml:id="echoid-s3816" xml:space="preserve">paratior eſſet
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            problematis uſus in doctrina logorithmica, quam primò
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            invenit nobiliſſimus noſter Neperus, & </s>
            <s xml:id="echoid-s3817" xml:space="preserve">quam nos (ni fal-
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            lor) ad ſummum perfectionis faſtigium nunc elevamus.</s>
            <s xml:id="echoid-s3818" xml:space="preserve"/>
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        <div xml:id="echoid-div213" type="section" level="1" n="103">
          <head xml:id="echoid-head142" xml:space="preserve">PROP. XXXIII. PROBLEMA.</head>
          <head xml:id="echoid-head143" style="it" xml:space="preserve">Propoſiti cujuscunque numeri logorithmum invenire.</head>
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            <s xml:id="echoid-s3819" xml:space="preserve">Eiſdem poſitis quæ in antecedente, manifeſtum eſt, poſita
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              <note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">TAB. XLIV.
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              fig. 1.</note>
            I K unitate, M L eſſe decem: </s>
            <s xml:id="echoid-s3820" xml:space="preserve">poſita ergo I K unitate ſit
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            G H aſymptoto quoque A O parallela numerus propoſitus
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            cujus deſideratur logorithmus@ manifeſtum eſt ex data rectà
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            G H dari K F, & </s>
            <s xml:id="echoid-s3821" xml:space="preserve">ex præcedenti dari etiam ſpatium hyper-
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            bolicum G I K H, quod ſpatium hyperbolicum dico eſſe lo-
              <lb/>
            gorithmum numeri propoſiti G H, poſito ſpatio hyperbo-
              <lb/>
            lico L I K M logorithmo numeri denarii: </s>
            <s xml:id="echoid-s3822" xml:space="preserve">eſt enim (ex Gre-
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            gorio à S. </s>
            <s xml:id="echoid-s3823" xml:space="preserve">Vincentio) ſpatium G H K I in eadem ratione ad
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            ſpatium L M K I, in qua ratio G H ad I K eſt multiplicata
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            rationis L M ad I K; </s>
            <s xml:id="echoid-s3824" xml:space="preserve">ſed ratio G H ad I K eſt </s>
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