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

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        <div xml:id="echoid-div491" type="section" level="1" n="177">
          <pb o="742" file="0486" n="508" rhead="DE RATIOCINIIS"/>
        </div>
        <div xml:id="echoid-div492" type="section" level="1" n="178">
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            <emph style="sc">Propositio</emph>
          XIV.</head>
          <p style="it">
            <s xml:id="echoid-s10376" xml:space="preserve">Si ego & </s>
            <s xml:id="echoid-s10377" xml:space="preserve">alius duabus teſſeris alternatim jaciamus,
              <lb/>
            hâc conditione, ut ego vincam ſimul atque ſe-
              <lb/>
            ptenarium jaciam, ille vero quam primùm ſena-
              <lb/>
            rium jaciat; </s>
            <s xml:id="echoid-s10378" xml:space="preserve">ita videlicet, ut ipſi primum ja-
              <lb/>
            ctum concedam: </s>
            <s xml:id="echoid-s10379" xml:space="preserve">invenire rationem meæ ad ipſius
              <lb/>
            ſortem.</s>
            <s xml:id="echoid-s10380" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10381" xml:space="preserve">POnatur, ſortem meam valere x, & </s>
            <s xml:id="echoid-s10382" xml:space="preserve">id quod depoſi-
              <lb/>
            tum eſt vocari a; </s>
            <s xml:id="echoid-s10383" xml:space="preserve">eritque ſors alterius = a—x. </s>
            <s xml:id="echoid-s10384" xml:space="preserve">Et
              <lb/>
            patet, quandocunque ipſius vices jaciendi revertuntur, ſor-
              <lb/>
            tem meam tum rurſus debere eſſe = x. </s>
            <s xml:id="echoid-s10385" xml:space="preserve">At quandocunque
              <lb/>
            meæ vices ſunt ut jaciam, ſors mea pluris æſtimanda eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s10386" xml:space="preserve">Ponatur itaque pro ejus valore y. </s>
            <s xml:id="echoid-s10387" xml:space="preserve">ſam quo niam ex 36 ja-
              <lb/>
            ctibus reperiuntur 5 in 2 teſſeris, qui colluſori meo ſena-
              <lb/>
            rium dare luſuſque victorem reddere poſſunt; </s>
            <s xml:id="echoid-s10388" xml:space="preserve">& </s>
            <s xml:id="echoid-s10389" xml:space="preserve">31 jactus,
              <lb/>
            quibus diverſum eveniat, id eſt, qui meas jaciendi vices pro-
              <lb/>
            movent: </s>
            <s xml:id="echoid-s10390" xml:space="preserve">habebo, priuſquam jacit, 5 caſus ad obtinen-
              <lb/>
            dum 0, & </s>
            <s xml:id="echoid-s10391" xml:space="preserve">31 caſus ad obtinendum y. </s>
            <s xml:id="echoid-s10392" xml:space="preserve">id quod per 3
              <emph style="super">tiam</emph>
            Pro-
              <lb/>
            poſitionem valet {31 y/36}. </s>
            <s xml:id="echoid-s10393" xml:space="preserve">Poſuimus autem caſum meum à
              <lb/>
            principio eſſe = x. </s>
            <s xml:id="echoid-s10394" xml:space="preserve">Quocirca erit {31 y/36} = x, adeo-
              <lb/>
            que y = {36 x/31}. </s>
            <s xml:id="echoid-s10395" xml:space="preserve">Deinde poſitum fuit, vicibus meis ve-
              <lb/>
            nientibus, ſortem meam valere y. </s>
            <s xml:id="echoid-s10396" xml:space="preserve">Ego verò jacturus,
              <lb/>
            habeo 6 caſus ad obtinendum a, quandoquidem 6 ja-
              <lb/>
            crus reperiuntur 7 puncrorum, qui me victorem red-
              <lb/>
            dunt; </s>
            <s xml:id="echoid-s10397" xml:space="preserve">habeoque 30 caſus, quibus vices colluſoris mei
              <lb/>
            revertuntur, id eſt, ut mihi obtineam x. </s>
            <s xml:id="echoid-s10398" xml:space="preserve">id quod per 3
              <emph style="super">tiam</emph>
            </s>
          </p>
        </div>
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