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

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        <div xml:id="echoid-div480" type="section" level="1" n="166">
          <p>
            <s xml:id="echoid-s10108" xml:space="preserve">
              <pb o="731" file="0475" n="497" rhead="IN LUDO ALEÆ."/>
            æquale eſſet ipſi a, haberem p expectationes ad a, (quando-
              <lb/>
            quidem jam p — 1 expectationes ad id habebam) & </s>
            <s xml:id="echoid-s10109" xml:space="preserve">q expe-
              <lb/>
            ctationes ad b, & </s>
            <s xml:id="echoid-s10110" xml:space="preserve">ſic ad priorem meam exſpectationem rur-
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            ſus perveniſſem. </s>
            <s xml:id="echoid-s10111" xml:space="preserve">Quocirca porrò px + qx - bq - ap + a = a,
              <lb/>
            & </s>
            <s xml:id="echoid-s10112" xml:space="preserve">fit x = {ap + bq/p + q}, pro valore expectationis meæ, omnino ut
              <lb/>
            in initio poſitum fuit.</s>
            <s xml:id="echoid-s10113" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10114" xml:space="preserve">In numeris. </s>
            <s xml:id="echoid-s10115" xml:space="preserve">Si 3 mihi expectationes forent ad 13, & </s>
            <s xml:id="echoid-s10116" xml:space="preserve">2
              <lb/>
            expectationes ad 8, haberem per hanc regulam tantundem
              <lb/>
            ac 11. </s>
            <s xml:id="echoid-s10117" xml:space="preserve">Et facile eſt oſtendere, me, ſi 11 habeam, rurſus ad
              <lb/>
            eandem expectationem pervenire poſſe. </s>
            <s xml:id="echoid-s10118" xml:space="preserve">Ludens enim con-
              <lb/>
            tra 4 alios, & </s>
            <s xml:id="echoid-s10119" xml:space="preserve">quiſque noſtrum quinque deponens II, cum
              <lb/>
            duobus ex illis ſigillatim pactum inibo, ut horum qui vincat
              <lb/>
            mihi ſit daturus 8, aut ego ipſi idem 8, ſi vincam. </s>
            <s xml:id="echoid-s10120" xml:space="preserve">Simili-
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            ter cum duobus reliquis, ut eorum quiſque, qui ludum vin-
              <lb/>
            cit, mihi ſit daturus 13, aut ego ipſi tantundem, ſi ego vin-
              <lb/>
            cam. </s>
            <s xml:id="echoid-s10121" xml:space="preserve">Qui quidem luſus juſtus eſt. </s>
            <s xml:id="echoid-s10122" xml:space="preserve">Et patet me hoc modo
              <lb/>
            duas habere expectationes ad 8, nimirum ſi alteruter eorum,
              <lb/>
            qui mihi 8 promiſerunt, vincat, & </s>
            <s xml:id="echoid-s10123" xml:space="preserve">3 expectationes ad 13,
              <lb/>
            nimirum ſi alteruter reliquorum duorum, qui mihi 13 trade-
              <lb/>
            re debent, vincat, aut ſi ipſe ludum vincam: </s>
            <s xml:id="echoid-s10124" xml:space="preserve">ego enim lu-
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            dum vincens obtineo depoſitum, id eſt, 55, de quo unicui-
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            que duorum tradere debeo 13, & </s>
            <s xml:id="echoid-s10125" xml:space="preserve">unicuique reliquorum duo-
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            rum 8, ita ut & </s>
            <s xml:id="echoid-s10126" xml:space="preserve">mihi relinquatur 13.</s>
            <s xml:id="echoid-s10127" xml:space="preserve"/>
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        <div xml:id="echoid-div481" type="section" level="1" n="167">
          <head xml:id="echoid-head233" xml:space="preserve">
            <emph style="sc">Propositio</emph>
          IV.</head>
          <head xml:id="echoid-head234" style="it" xml:space="preserve">Ut igitur ad primò propoſitam quæſtionem veniamus,
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          nimirum, de facienda diſtributione inter diverſos
            <lb/>
          colluſores, quando eorum ſortes inæquales ſunt,
            <lb/>
          opus eſt ut a facilioribus incipiamus.</head>
          <p>
            <s xml:id="echoid-s10128" xml:space="preserve">SUmpto itaque me cum aliquo certare, hoc pacto: </s>
            <s xml:id="echoid-s10129" xml:space="preserve">ut qui
              <lb/>
            priùs ter vicerit, quod depoſitum eſt, lucretur, & </s>
            <s xml:id="echoid-s10130" xml:space="preserve">me jam
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            bis viciſſe, alterum verò ſemel. </s>
            <s xml:id="echoid-s10131" xml:space="preserve">Scire cupio, ſi luſum </s>
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