Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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DE RATIOCINIIS
"/>
ludo tanti æſtimandam eſſe cujuſque ſortem ſeu expectatio-
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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. </
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<
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xml:space
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">Ut, exempli gratiâ ſi quis me inſcio
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alterâ manu 3 ſolidos occultet, alterâ 7 ſolidos, mihique
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optionem det ex utra manu ſolidos accipere malim; </
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<
s
xml:id
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xml:space
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preserve
">hoc tan-
<
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tundem mihi valere dico, ac ſi 5 ſolidi mihi dentur. </
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>
<
s
xml:id
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xml:space
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">Quo-
<
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niam quinque ſolidos habens, denuo eò pervenire poſſum,
<
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ut æquam expectationem nanciſcar ad 3 vel 7 ſolidos obti-
<
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/>
nendos: </
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<
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xml:id
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xml:space
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">idque æquo luſu contendens.</
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</
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<
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emph
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I.</
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style
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xml:space
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">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
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<
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<
s
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xml:space
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">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.
<
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</
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>
<
s
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xml:space
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">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. </
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<
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xml:space
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">Hic autem luſus juſtus eſt, & </
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<
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xml:space
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">patet me hâc ratione
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æquam habere ſortem ad obtinendum a, ſi luſum perdam ſci-
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licet; </
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>
<
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xml:space
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">aut 2x— a, ſi vincam: </
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>
<
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xml:space
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">tum enim obtineo 2x, id nem-
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pe quod depoſitum eſt, de quo alteri erogandum eſt a. </
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<
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Quod ſi autem 2x — a tantundem valeret atque b, æqua mi-
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hi ſors obtingeret ad a quàm ad b. </
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<
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xml:space
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">Pono itaque 2x — a = b,
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& </
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<
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">fit x = {a + b/2}, pro valore meæ expectationis. </
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xml:space
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">Cujus de-
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monſtratio facilis eſt. </
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<
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xml:space
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">Etenim habens {a + b/2} poſſum cum a-
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lio certare, qui etiam {a + b/2} deponere volet, hâc </
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