MONTMORT. 127 



matiere qiii renfcrme toute la Physique generale. Vous verres avec 

 admiration que ce grand hiomme a porte dans ces matieres obscures 

 cette nettete d'idces, cette sublimite de genie et d'invention qui bril- 

 lent avec tant d'eclat dans ses Traites de Metaphysique. 



Posterity has not adopted the high opinion which Montmort 

 here expresses respecting the physical speculations of his friend 

 and master ; Malebranche is now remembered and honoured for 

 his metaphysical works alone, Avhich have gained the following 

 testimony from one of the gi'eatest critics : 



As a thinker, he is perhaps the most profound that France has 

 ever produced, and as a writer on i)liilosopliical subjects, there is not 

 another European author who can be placed before him. 



Sir William Hamilton's Lectures on Metaphysics, Vol. i. page 262 ; 

 see also his edition of Reid's Works, page 266. 



218. The next letter is from Montmort to Nicolas Bernoulli ; 

 it occupies pages 3-52 — 360. We may notice that Montmort here 

 claims to be the first person who called attention to the theorem 

 which is now given in elementary treatises on Algebra under the 

 following enunciation : To find the number of terms in the expan- 

 sion of any multinomial, the exponent being a positive integer. 

 See Montmort's page 355. 



219. Montmort gives in this letter some examples of the recti- 

 fication of curves ; see his pages 35G, 357, 359, 360. In particular 

 he notices" one which he had himself discussed in the earty days 

 of the Integral Calculus, when, as he says, the subject was well 

 known only by five or six mathematicians. This example is the 

 rectification of the curve called after the name of its inventor De 

 Beaune ; see John Bernoulli's works. Vol. I. pages 62, 63. AMiat 

 Montmort gives in this letter is not intelligible by itself, but it can 

 be understood by the aid of the original memoii*, which is in the 

 Journal des Scavans, Vol. xxxi. 



These remarks by Montmort on the rectification of curves are 

 of no great interest except to a student of the history of the Inte- 

 gral Calculus, and they are not free from errors or misprints. 



