20 PASCAL AND FERMAT. 



publish, among wliicli was to be one on chances. His language 

 shews that he had a high opinion of the novelty and importance 

 of the matter he proposed to discuss ; he says, 



Novissima autem ac penitus intentatse materise tractatio, scilicet de 

 compositione alece in hid is ijysi subjeclis, qnod gallico nostro idiomate 

 dicitur (/aire les ^;ar^is cles jeux) : ubi ancej)s fortuna sequitate rationis 

 ita reprimitur ut utrique lusorum quod jure competit exacte semper 

 assignetur. Quod quidem eo fortius ratiocinando quserendnm, quo 

 minus tentando investigari possit : ambigiii enim sortis eventus fortiiitse 

 contingentise potius quam nattirali necessitati meritb tribuuntur. Ideo 

 res hactenus erravit incerta ; nunc autem qu?e experimento rebellis 

 fuerat, rationis dominium effugere non potuit : eam quippe tanta se- 

 curitate in artem per geometriam reduximus, ut certitudinis ejus 

 j^articeps facta, jam audacter prodeat ; et sic matheseos demonstrationes 

 cum alese incertitudine jungendo, et qu?e contraria videntur conciliando, 

 ab utraque nominationem suam accipiens stupendum hunc titulum jure 

 sibi arrogat : alece geometria. 



But the design was probably never accomplished. The letter 

 is dated 1651; Pascal died in 1662, at the early age of 39. 



26. Neglecting the trifling hints which may be found in pre- 

 ceding writers we may say that the Theory of Probability really 

 commenced with Pascal and Format ; and it would be difficult to 

 find two names which could confer higher honour on the subject. 



The fame of Pascal rests on an extensive basis, of which 

 mathematical and physical science form only a part ; and the 

 regret which we may feel at his renunciation of the studies in 

 which he gained his earliest renown may be diminished by reflect- 

 ing on his memorable Letters, or may be lost in deeper sorrow 

 wdien we contemplate the fragments which alone remain of the 

 great work on the evidences of religion that was to have engaged 

 the efforts of his maturest powers. 



The fame of Format is confined to a narrower range ; but it is 

 of a special kind which is without a parallel in the history of 

 science. Format enunciated various remarkable propositions in 

 the theory of numbers. Two of these are more important than 

 the rest; one of them after bafiling the powers of Euler and La- 

 grange finally yielded to Cauchy, and tlie other remains still un- 



