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

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        <div xml:id="echoid-div477" type="section" level="1" n="163">
          <p>
            <s xml:id="echoid-s10051" xml:space="preserve">
              <pb o="728" file="0472" n="494" rhead="DE RATIOCINIIS"/>
            ludo tanti æſtimandam eſſe cujuſque ſortem ſeu expectatio-
              <lb/>
            nem ad aliquid obtinendum, quantum ſi habeat, poſſit de-
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            nuo ad ſimilem ſortem ſive expectationem pervenire, æquâ
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            conditione certans. </s>
            <s xml:id="echoid-s10052" xml:space="preserve">Ut, exempli gratiâ ſi quis me inſcio
              <lb/>
            alterâ manu 3 ſolidos occultet, alterâ 7 ſolidos, mihique
              <lb/>
            optionem det ex utra manu ſolidos accipere malim; </s>
            <s xml:id="echoid-s10053" xml:space="preserve">hoc tan-
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            tundem mihi valere dico, ac ſi 5 ſolidi mihi dentur. </s>
            <s xml:id="echoid-s10054" xml:space="preserve">Quo-
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            niam quinque ſolidos habens, denuo eò pervenire poſſum,
              <lb/>
            ut æquam expectationem nanciſcar ad 3 vel 7 ſolidos obti-
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            nendos: </s>
            <s xml:id="echoid-s10055" xml:space="preserve">idque æquo luſu contendens.</s>
            <s xml:id="echoid-s10056" xml:space="preserve"/>
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        <div xml:id="echoid-div478" type="section" level="1" n="164">
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            <emph style="sc">Propositio</emph>
          I.</head>
          <head xml:id="echoid-head228" style="it" xml:space="preserve">Si a vel b expectem, quorum utrumvis æquè
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          facilè mihi obtingere poſſit, expectatio
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          mea dicenda eſt valere {a + b/2}.</head>
          <p>
            <s xml:id="echoid-s10057" xml:space="preserve">AD hanc regulam non ſolùm demonſtrandam, verùm et-
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            iam primitùs eruendam poſito x pro eo quod æquivalet
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            expectationi meæ, oportet me, quum x habeo, rurſus ad
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            ſimilem ſortem pervenire poſſe, æquâ conditione certantem.
              <lb/>
            </s>
            <s xml:id="echoid-s10058" xml:space="preserve">Ponatur itaque luſus eſſe talis, ut cum altero certem hâc con-
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            ditione, ut quiſque deponat x, ac ut victor victo traditurus
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            ſit a. </s>
            <s xml:id="echoid-s10059" xml:space="preserve">Hic autem luſus juſtus eſt, & </s>
            <s xml:id="echoid-s10060" xml:space="preserve">patet me hâc ratione
              <lb/>
            æquam habere ſortem ad obtinendum a, ſi luſum perdam ſci-
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            licet; </s>
            <s xml:id="echoid-s10061" xml:space="preserve">aut 2x— a, ſi vincam: </s>
            <s xml:id="echoid-s10062" xml:space="preserve">tum enim obtineo 2x, id nem-
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            pe quod depoſitum eſt, de quo alteri erogandum eſt a. </s>
            <s xml:id="echoid-s10063" xml:space="preserve">
              <lb/>
            Quod ſi autem 2x — a tantundem valeret atque b, æqua mi-
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            hi ſors obtingeret ad a quàm ad b. </s>
            <s xml:id="echoid-s10064" xml:space="preserve">Pono itaque 2x — a = b,
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            & </s>
            <s xml:id="echoid-s10065" xml:space="preserve">fit x = {a + b/2}, pro valore meæ expectationis. </s>
            <s xml:id="echoid-s10066" xml:space="preserve">Cujus de-
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            monſtratio facilis eſt. </s>
            <s xml:id="echoid-s10067" xml:space="preserve">Etenim habens {a + b/2} poſſum cum a-
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            lio certare, qui etiam {a + b/2} deponere volet, hâc </s>
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