Cum in editione elegantissimorum ingenii Tui monumentorum, quam præ manibus nunc habes, Vir Clarissime, id inter coetera Te spectare sciam, ut varietate rerum, quarum tractationem instituisti, ostendas quam late se protendat divina Analytices scientia, facile intelligo etiam illa plurimum proposito Tuo inservire posse, quæ de Aleæ Ratiociniis conscripsimus; quanto enim minus rationis terminis comprehendi posse videbantur, quæ fortuita sunt atque incerta, tanto admirabilior ars censebitur, cui ista quoque subjacent. Quare cum subtilissimis Tuis inventis in lucem exeant, adeo Tibi non refragabor, ut etiam e re mea esse existimem ac potissimum ratione ipsa in manus hominum pervenire. Quippe cum in re levi ac frivola operam colacasse videri alioqui possem, non tamen prorsus utilitas expers ac nullius pretit censebitur, quod Tu veluti inter Tua adoptaveris, nec sine multo labore e vernacula linqua nostra in Latinam converteris. Quanquam, si quis penitius ea quæ tradimus examinare cæperit, non dubito quin continuo reperturus sit, rem non, ut videtur ludicram agi, sed pulchræ subtilissimæque contemplationis fundamenta explicari, Et Problemata quidem quæ in hoc genere proponuntur, nihilo minus profundæ indaginis visum iri confido, quam quæ Diophanti libris continentur, voluptatis autem aliquanto plus habitura, cum non, sicut illa, in nuda numerorum consideratione terminentur. Sciendum vero, quod jam pridem inter præstantissimos tota Gallia Geometras calculus his agitatus fuerit, ne quis indebitam mihi primæ inventionis gloriam hac in re tribuat. Cæterum illi, difficillimis quibusque quæstionibus se invicem exercere soliti, methodum suam quisque occultam retinuere, adeo ut a primis elementis universam hanc materiam evolvere mihi necesse fuerit. Quamobrem ignoro etiamnum an eodem mecum principio illi utantur; at in resolvendis Problematis pulchre nobis sæpenumero expertus sum. Horum Problematum nun nulla in fine operis addidisse me invenies, omissi tamen analysi, cum quod prolixam nimis operam poscebant, si perspicue omnia exequi voluissem, tum quod relinquendum dum aliquid videbatur exercitationi nostrorum, si qui erunt, Lectorum. Vale.

ALthough the Events of Games, which Fortune solely governs, are uncertain, yet it may be certainly determin'd, how much one is more ready to lose than gain. For Example, If one should wager, at the first Throw with one Dye, to throw Six, it's an [2] accident if he gains or not, but by how much it's more probable he will lose or gain, is really determin'd by the nature of the thing, and capable of a strict calculation. So likewise, if I should play with another on this condition, that the Victory should be to the Three first Games and I had gain'd one already, it is still uncertain who shall first gain the third; yet by demonstrative reasoning I can estimate both the Value of his Expectation and mine, and consequently (if we agree to leave the Game unperfect) determin how great a share of the Stakes belong to my and how much to my Play-fellow;[3] or if any were desirous to take my Place, at what rate I ought to sell it. Hence may arise innumerable Queries among two, three, or more Gamesters: and since the Calculation of these things is a little out of the common road, and can oft-times be applyd to good purpose; I shall briefly here shew how it is to be done, and afterwards explain those things that belong properly to Dice.

In both cases I shall make use of this Principle Ones Hazard or Expectation to gain any thing, is worth so much, as, if he had it, he could purchase the like Hazard or Expectation again in a just and equal Game.

[4] For Example, if one, without my knowledge, should hide in one Hand 7 Shillings and in his other 3, and put it to my Choice which Hand I would take, I say, this is as much worth to me as if he should give me 5 Shillings; because, if I have 5 Shillings I can purchase as good a Chance again, and that in a fair and just Game.