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

Table of handwritten notes

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        <div xml:id="echoid-div249" type="section" level="1" n="122">
          <p>
            <s xml:id="echoid-s4750" xml:space="preserve">
              <pb o="498" file="0220" n="231" rhead="CHRIST. HUGENII"/>
            id ex hoc ſequenti exemplo intelligetur rectè præcipi. </s>
            <s xml:id="echoid-s4751" xml:space="preserve">Sint
              <lb/>
            enim reperti termini priores, quos maximum aut mini-
              <lb/>
            mum deſignare oporteat, iſti {x
              <emph style="super">3</emph>
            /2a - x} - 2vx + xx + vv;
              <lb/>
            </s>
            <s xml:id="echoid-s4752" xml:space="preserve">ubi vv quantitatem cognitam ſignificet: </s>
            <s xml:id="echoid-s4753" xml:space="preserve">id igitur delendum
              <lb/>
            eſſe ut appareat, videamus quid futurum ſit ſi non delea-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s4754" xml:space="preserve">Nempe ut ad eundem denominatorem cum cæteris
              <lb/>
            omnibus reducatur, ducendum erit vv in 2a - x, fietque
              <lb/>
            inde {2avv - xvv/2a - x} in terminis prioribus. </s>
            <s xml:id="echoid-s4755" xml:space="preserve">Propter quos in
              <lb/>
            terminis poſterioribus, ſecundum ſuperius, explicata ſcribetur
              <lb/>
            {- evv/- e}, adeoque multiplicatione alternatim utrinque per
              <lb/>
            denominatores inſtituta, ducendum erit hinc 2a - x in
              <lb/>
            - evv; </s>
            <s xml:id="echoid-s4756" xml:space="preserve">inde - e in 2avv - xvv. </s>
            <s xml:id="echoid-s4757" xml:space="preserve">Ex quibus multiplica-
              <lb/>
            tionibus eoſdem utrinque terminos oriri neceſſe eſt, cum
              <lb/>
            utrobique eadem hæc tria in ſe mutuo ducantur 2a - x in
              <lb/>
            - e in vv, qui proinde termini ſe ſe mutuo ſublaturi eſſent,
              <lb/>
            eoque fruſtra ſcriberentur; </s>
            <s xml:id="echoid-s4758" xml:space="preserve">ac proinde liquet tuto deleri
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            poſſe ab initio quantitatem vv, idemque quod in hoc exem-
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            plo accidit, neceſſario quoque in quibuslibet aliis continge-
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            re, diligenter intuenti manifeſtum erit.</s>
            <s xml:id="echoid-s4759" xml:space="preserve"/>
          </p>
          <figure number="90">
            <image file="0220-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0220-01"/>
          </figure>
        </div>
        <div xml:id="echoid-div251" type="section" level="1" n="123">
          <head xml:id="echoid-head168" xml:space="preserve">III.</head>
          <head xml:id="echoid-head169" xml:space="preserve">REGULA</head>
          <head xml:id="echoid-head170" style="it" xml:space="preserve">Ad inveniendas Tangentes linearum curvarum.</head>
          <p>
            <s xml:id="echoid-s4760" xml:space="preserve">IDem Fermatius linearum curvarum Tangentes regula ſibi
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            peculiari inquirebat, quam Carteſius ſuſpicabatur non ſa-
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            tis ipſum intelligere quo fundamento niteretur, ut ex epiſto-
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            lis ejus hac de re ſcriptis apparet. </s>
            <s xml:id="echoid-s4761" xml:space="preserve">Sanè in Fermatii operi-
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            bus poſt mortem editis, ncc bene expoſitus eſt regulæ uſus,
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            nec demonſtrationem ullam adjectam habet. </s>
            <s xml:id="echoid-s4762" xml:space="preserve">Carteſium ve-
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            ro in his quas dixi literis, rationem ejus aliquatenus aſſecu-
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            tum invenio, nec tamen tam perſpicuè eam explicuiſſe </s>
          </p>
        </div>
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