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

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          <pb o="738" file="0482" n="504" rhead="DE RATIOCINIIS"/>
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        <div xml:id="echoid-div488" type="section" level="1" n="174">
          <head xml:id="echoid-head245" xml:space="preserve">
            <emph style="sc">Propositio</emph>
          X.</head>
          <head xml:id="echoid-head246" style="it" xml:space="preserve">Invenire, quot vicibus ſuſcipere quis poſſit, ut
            <lb/>
          unâ teſſerâ 6 puncta jaciat.</head>
          <p>
            <s xml:id="echoid-s10274" xml:space="preserve">Si quis primâ vice ſenarium jacere contendat, apparet
              <lb/>
            unum eſſe caſum, quo vincat, habeatque id, quod pi-
              <lb/>
            gnoris loco depoſitum eſt; </s>
            <s xml:id="echoid-s10275" xml:space="preserve">quinque verò eſſe caſus, quibus
              <lb/>
            perdat, & </s>
            <s xml:id="echoid-s10276" xml:space="preserve">nihil habeat. </s>
            <s xml:id="echoid-s10277" xml:space="preserve">Sunt enim 5 jactus contra ipſum,
              <lb/>
            & </s>
            <s xml:id="echoid-s10278" xml:space="preserve">tantùm unus pro ipſo. </s>
            <s xml:id="echoid-s10279" xml:space="preserve">Quod autem depoſitum eſt voce-
              <lb/>
            tur a. </s>
            <s xml:id="echoid-s10280" xml:space="preserve">Eſt itaque ipſi unica expectatio ad obtinendum a, ſed
              <lb/>
            quinque ad obtinendum o; </s>
            <s xml:id="echoid-s10281" xml:space="preserve">id quod per 2
              <emph style="super">dam</emph>
            Propoſitionem
              <lb/>
            tantundem valet ac {1/6}a. </s>
            <s xml:id="echoid-s10282" xml:space="preserve">Et manet pro eo qui ipſi hunc ca-
              <lb/>
            ſum offert {5/6}a. </s>
            <s xml:id="echoid-s10283" xml:space="preserve">Ita ut tantummodo 1 contra 5 deponere poſ-
              <lb/>
            ſit, qui primâ vice ſuſcipere velit.</s>
            <s xml:id="echoid-s10284" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10285" xml:space="preserve">Qui duabus vicibus ſemel ſenarium jacere certet, ſors ejus
              <lb/>
            hoc pacto computatur. </s>
            <s xml:id="echoid-s10286" xml:space="preserve">Si primâ vice 6 jaciat, obtinet a.
              <lb/>
            </s>
            <s xml:id="echoid-s10287" xml:space="preserve">Si diverſum eveniat, unus ipſi reſtat jactus, qui ex præce-
              <lb/>
            denti tantum valet, quantum {1/6}a. </s>
            <s xml:id="echoid-s10288" xml:space="preserve">Atqui ut primâ vice 6 ja-
              <lb/>
            ciat, unus tantùm caſus eſt, & </s>
            <s xml:id="echoid-s10289" xml:space="preserve">quinque caſus, quibus diver-
              <lb/>
            ſum eveniat. </s>
            <s xml:id="echoid-s10290" xml:space="preserve">Itaque ab initio unus caſus eſt, qui det ipſi a; </s>
            <s xml:id="echoid-s10291" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s10292" xml:space="preserve">quinque quident {1/6}a, id quod per 2
              <emph style="super">dam</emph>
            Propoſitionem va-
              <lb/>
            let {11/36}a. </s>
            <s xml:id="echoid-s10293" xml:space="preserve">Unde contracertanti luſori cedit reliquum {25/36}a; </s>
            <s xml:id="echoid-s10294" xml:space="preserve">ad-
              <lb/>
            eo ut ſors utriuſque ſive æſtimatio expectationis eam ſervet
              <lb/>
            rationem, quam 11 ad 25; </s>
            <s xml:id="echoid-s10295" xml:space="preserve">id eſt minus quàm 1 ad 2.</s>
            <s xml:id="echoid-s10296" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10297" xml:space="preserve">Hinc eodem modo calculo ſubducitur, quòd ſors ejus, qui
              <lb/>
            tribus vicibus ſemel ſenarium jacere ſuſcipit, ſit futura {91/216}a;
              <lb/>
            </s>
            <s xml:id="echoid-s10298" xml:space="preserve">ita ut 91 contra 125 deponere poſſit; </s>
            <s xml:id="echoid-s10299" xml:space="preserve">id eſt, paulò minus
              <lb/>
            quàm 3 ad 4.</s>
            <s xml:id="echoid-s10300" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10301" xml:space="preserve">Qui quatuor vicibus idem ſuſcipit, ſors ejus eſt {671/1296}a; </s>
            <s xml:id="echoid-s10302" xml:space="preserve">ita
              <lb/>
            ut 671 contra 625 deponere poſſit; </s>
            <s xml:id="echoid-s10303" xml:space="preserve">id eſt, plùs quam 1
              <lb/>
            ad 1.</s>
            <s xml:id="echoid-s10304" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10305" xml:space="preserve">Qui quinque vicibus idem ſuſcipit, ſors ejus eſt {4651/7776}a, & </s>
            <s xml:id="echoid-s10306" xml:space="preserve">
              <lb/>
            poteſt 4651 contra 3125 deponere; </s>
            <s xml:id="echoid-s10307" xml:space="preserve">id eſt, paulò minus quàm
              <lb/>
            3 ad 2.</s>
            <s xml:id="echoid-s10308" xml:space="preserve"/>
          </p>
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