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

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            <s xml:id="echoid-s10398" xml:space="preserve">
              <pb o="743" file="0487" n="509" rhead="IN LUDO ALEÆ."/>
            Propoſitionem valet {6 a + 30 x/36}. </s>
            <s xml:id="echoid-s10399" xml:space="preserve">Hoc autem cum ſit
              <lb/>
            = y, erit, invento, ut ante, {36 x/31} = y, {30 x + 6 a/36}
              <lb/>
            = {36 x/31}. </s>
            <s xml:id="echoid-s10400" xml:space="preserve">Unde invenitur x = {31 a/61}, valor meæ ſor-
              <lb/>
            tis. </s>
            <s xml:id="echoid-s10401" xml:space="preserve">Et per conſequens colluſoris mei erit {30 a/61}; </s>
            <s xml:id="echoid-s10402" xml:space="preserve">ita ut
              <lb/>
            ratio ſortis meæ ad illius ſortem ſit, ut 31 ad 30.</s>
            <s xml:id="echoid-s10403" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div493" type="section" level="1" n="179">
          <head xml:id="echoid-head253" style="it" xml:space="preserve">Coronidis loco ſubjungantur ſequentia Problemata.</head>
          <head xml:id="echoid-head254" xml:space="preserve">
            <emph style="sc">Problema</emph>
          I.</head>
          <p>
            <s xml:id="echoid-s10404" xml:space="preserve">A & </s>
            <s xml:id="echoid-s10405" xml:space="preserve">B unà ludunt duabus teſſeris, hâc conditione,
              <lb/>
            ut A vincat, ſi ſenarium jaciat, at B ſi ſeptenarium ja-
              <lb/>
            ciat. </s>
            <s xml:id="echoid-s10406" xml:space="preserve">A primò unum jactum inſtituet; </s>
            <s xml:id="echoid-s10407" xml:space="preserve">deinde B duos
              <lb/>
            jactus conſequenter; </s>
            <s xml:id="echoid-s10408" xml:space="preserve">tum rurſus A duos jactus, atque
              <lb/>
            ſic deinceps, donec hic vel ille victor evadat. </s>
            <s xml:id="echoid-s10409" xml:space="preserve">Quæri-
              <lb/>
            tur ratio ſortis ipſius A ad ſortem ipſius B? </s>
            <s xml:id="echoid-s10410" xml:space="preserve">Reſp. </s>
            <s xml:id="echoid-s10411" xml:space="preserve">ut
              <lb/>
            10355 ad 12276.</s>
            <s xml:id="echoid-s10412" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div494" type="section" level="1" n="180">
          <head xml:id="echoid-head255" xml:space="preserve">
            <emph style="sc">Problema</emph>
          II.</head>
          <p>
            <s xml:id="echoid-s10413" xml:space="preserve">Tres colluſores A, B & </s>
            <s xml:id="echoid-s10414" xml:space="preserve">C aſſumentes 12 calculos,
              <lb/>
            quorum 4 albi & </s>
            <s xml:id="echoid-s10415" xml:space="preserve">8 nigri exiſtunt, ludunt hâc condi-
              <lb/>
            tione: </s>
            <s xml:id="echoid-s10416" xml:space="preserve">ut, qui primus ipſorum velatis oculis album cal-
              <lb/>
            culum elegerit, vincat; </s>
            <s xml:id="echoid-s10417" xml:space="preserve">& </s>
            <s xml:id="echoid-s10418" xml:space="preserve">ut prima electio ſit penes A,
              <lb/>
            ſecunda penes B, & </s>
            <s xml:id="echoid-s10419" xml:space="preserve">tertia penes C, & </s>
            <s xml:id="echoid-s10420" xml:space="preserve">tum ſequens rur-
              <lb/>
            ſus penes A, atque ſic deinceps alternatim. </s>
            <s xml:id="echoid-s10421" xml:space="preserve">Quæritur,
              <lb/>
            quænam futura ſit ratio illorum ſortium?</s>
            <s xml:id="echoid-s10422" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div495" type="section" level="1" n="181">
          <head xml:id="echoid-head256" xml:space="preserve">
            <emph style="sc">Problema</emph>
          III.</head>
          <p>
            <s xml:id="echoid-s10423" xml:space="preserve">A certat cum B quòd ipſe ex 40 chartis luſoriis, id
              <lb/>
            eſt, 10 cujuſque ſpeciei, 4 chartas extracturus ſit; </s>
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