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

Table of contents

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[71.] PROP. VI. THEOREMATA.
[72.] SCHOLIUM.
[73.] PROP. VII. PROBLEMA. Oportet prædictæ ſeriei terminationem invenire.
[74.] PROP. VIII. PROBLEMA.
[75.] PROP. IX. PROBLEMA.
[76.] PROP. X. PROBLEMA.
[77.] CONSECTARIUM.
[78.] PROP. XI. THEOREMA.
[79.] SCHOLIUM.
[80.] PROP. XII. THEOREMA.
[81.] PROP. XIII. THEOREMA.
[82.] PROP. XIV. THEOREMA.
[83.] PROP. XV. THEOREMA.
[84.] PROP. XVI. THEOREMA.
[85.] PROP. XVII. THEOREMA.
[86.] PROP. XVIII. THEOREMA.
[87.] PROP. XIX. THEOREMA.
[88.] CONSECTARIUM.
[89.] PROP. XX. THEOREMA.
[90.] PROP. XXI. THEOREMA.
[91.] PROP. XXII. THEOREMA.
[92.] SCHOLIUM.
[93.] PROP. XXIII. THEOREMA.
[94.] PROP. XXIV. THEOREMA.
[95.] PROP. XXV. THEOREMA.
[96.] PROP. XXVI. THEOREMA.
[97.] PROP. XXVII. THEOREMA.
[98.] PROP. XXVIII. THEOREMA.
[99.] PROP. XXIX. PROBLEMA. Dato circulo æquale invenire quadratum.
[100.] PROP. XXX. PROBLEMA. Ex dato ſinu invenire arcum.
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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
              <lb/>
            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-
              <lb/>
            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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                <lb/>
              1 # 23025850929940456240178700
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              2 # 46051701859880912480357400
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              3 # 69077552789821368720536100
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              4 # 92103403719761824960714800
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              5 # 115129254649702281200893500
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              6 # 138155105579642737441072200
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              7 # 161180956509583193681250900
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              9 # 207232658369464106161608300
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              </note>
            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
              <lb/>
            conſtiruta ad angulum
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            rectum: </s>
            <s xml:id="echoid-s3815" xml:space="preserve">nos autem ita
              <lb/>
            fuppoſuimus, ut faci-
              <lb/>
            lior & </s>
            <s xml:id="echoid-s3816" xml:space="preserve">paratior eſſet
              <lb/>
            problematis uſus in doctrina logorithmica, quam primò
              <lb/>
            invenit nobiliſſimus noſter Neperus, & </s>
            <s xml:id="echoid-s3817" xml:space="preserve">quam nos (ni fal-
              <lb/>
            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
              <lb/>
              <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
              <lb/>
            G H aſymptoto quoque A O parallela numerus propoſitus
              <lb/>
            cujus deſideratur logorithmus@ manifeſtum eſt ex data rectà
              <lb/>
            G H dari K F, & </s>
            <s xml:id="echoid-s3821" xml:space="preserve">ex præcedenti dari etiam ſpatium hyper-
              <lb/>
            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-
              <lb/>
            gorio à S. </s>
            <s xml:id="echoid-s3823" xml:space="preserve">Vincentio) ſpatium G H K I in eadem ratione ad
              <lb/>
            ſpatium L M K I, in qua ratio G H ad I K eſt multiplicata
              <lb/>
            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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