Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of handwritten notes

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        <div xml:id="echoid-div191" type="section" level="1" n="69">
          <pb o="106" file="0156" n="169" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s2378" xml:space="preserve">Quæcunque vero problemata ad alterum è duobus hiſce
              <lb/>
              <note position="left" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">
                <emph style="sc">De linea-</emph>
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                <emph style="sc">RUM CUR-</emph>
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                <emph style="sc">VARUM</emph>
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                <emph style="sc">EVOLUTIO-</emph>
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                <emph style="sc">NE</emph>
              .</note>
            reducuntur, quamlibet veræ proximam ſolutionem per nu-
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            meros accipiunt, logarithmorum admirabili invento. </s>
            <s xml:id="echoid-s2379" xml:space="preserve">Cum
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            per hos hyperbolæ quadratura, ut olim invenimus, numeris
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            quam proxime explicetur. </s>
            <s xml:id="echoid-s2380" xml:space="preserve">Eſt autem regula hujusmodi.</s>
            <s xml:id="echoid-s2381" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2382" xml:space="preserve">Sit D A B portio hyperbolæ, cujus aſymptoti C S, C V,
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              <note position="left" xlink:label="note-0156-02" xlink:href="note-0156-02a" xml:space="preserve">TAB. XV.
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              Fig. 1.</note>
            ductis D E, B V parallelis aſymptoto S C.</s>
            <s xml:id="echoid-s2383" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2384" xml:space="preserve">Accipiatur differentia logarithmorum qui conveniunt nu-
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            meris, eandem inter ſe rationem habentibus quam rectæ D E,
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            B V; </s>
            <s xml:id="echoid-s2385" xml:space="preserve">ejusque differentiæ quæratur logarithmus. </s>
            <s xml:id="echoid-s2386" xml:space="preserve">Cui adda-
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            tur logarithmus hic (qui ſemper eſt idem) 0,36221,56887.
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            </s>
            <s xml:id="echoid-s2387" xml:space="preserve">Summa erit logarithmus numeri qui ſpatium D E V B A D
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            deſignabit, tribus rectis & </s>
            <s xml:id="echoid-s2388" xml:space="preserve">curva D A B comprehenſi, in
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            partibus qualium parallelogrammum D E eſt 100000,00000. </s>
            <s xml:id="echoid-s2389" xml:space="preserve">
              <lb/>
            Unde porro facile quoque habebitur area portionis D A B.</s>
            <s xml:id="echoid-s2390" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2391" xml:space="preserve">Sit ex. </s>
            <s xml:id="echoid-s2392" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s2393" xml:space="preserve">proportio D E ad B V ea quæ 36 ad 5.</s>
            <s xml:id="echoid-s2394" xml:space="preserve"/>
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          Ab # 1,55630,25008, logar
            <emph style="super">o</emph>
          . 36.
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          auferatur # 0,69897,00043.logar
            <emph style="super">us</emph>
          . 5.
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          Erit # 0,85733,24965.differ.logar
            <emph style="super">orum</emph>
          .
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          Et # 9,93314, 92856.logar
            <emph style="super">us</emph>
          .differentiæ.
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          Cui addatur # 0,36221,56887.logar
            <emph style="super">us</emph>
          .ſemper addendus.
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          Fit # 10,29536,49743. logar
            <emph style="super">us</emph>
          . ſpatii D E V B A D.
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          </note>
          <p>
            <s xml:id="echoid-s2395" xml:space="preserve">Habebit hujus logarithmi numerus 11 characteres, quum
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            characteriſtica ſit 10. </s>
            <s xml:id="echoid-s2396" xml:space="preserve">Quæratur itaque primo numerus pro-
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            xime minor, conveniens invento logarithmo, qui numerus
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            eſt 19740. </s>
            <s xml:id="echoid-s2397" xml:space="preserve">Deinde ex differentia logarithmi ejusdem, & </s>
            <s xml:id="echoid-s2398" xml:space="preserve">pro-
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            xime eum in tabula ſequentis, reliqui characteres eliciantur
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            81026, ſcribèndi poſt priores, ut fiat 197408, 10260, addi-
              <lb/>
            to ad ſinem zero, ut efficiatur numerus characterum 11. </s>
            <s xml:id="echoid-s2399" xml:space="preserve">Eſt
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            ergo area ſpatii D E V B A D proxime partium 197408,
              <lb/>
            10260, qualium partium parallelogrammum D C eſt 100000,
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            00000.</s>
            <s xml:id="echoid-s2400" xml:space="preserve"/>
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