. Review of the Camhridge Course of Mathematics. 325 



dnded by formulas for calculating the interest of mone/ 

 Qnd annuitie>. These formulas are derived from progres- 

 sions and logarithms, and form a useful application of arlge- 

 hra to the practical pursuits of life. 



Our opinion of M. Lacroix's work, will be sufficiently 

 collected from the preceding observations. The transla- 

 tion is performed with ability and fidelity, A few particu- 

 lars, however, concernifig both the original and translatiofi 

 merit ftotice. The demon-^tration of the binomial formula, 

 we think, ought to be more elementary, as an understand- 

 ing of it is at present too difficult for manj such students, as 

 are to be found in the American colleges. At least, the 

 theory of permutations and cofnf)inations on which it is 

 founded, ouj^ht to be more fully developed. In art* 42, 

 there is an error both in the original and trar^-lation. 

 *' Recollecting," it is said, that a product has the same sign 

 ^3 the naultipjicand when the multiplier has the sign +, 

 ^lld that it has in the cotitrary case the sign — , &c." It 

 has : what has ? the construction says the product has. 

 But that appears othtTwise, since — by — produces +• 

 And the construction allows neither multiplicand nor nml- 

 tiplier to be the legitimate aniecedent of ?7. But we con- 

 clude for the sake of truth, that the latter ought to be un- 

 derstood by the pronoun //; and that the reading ought to 

 ^e thus; recollecting that when a product has the same, 

 sign as the multiplicand, the multiplier has the sign + ; - 

 and that in the contrary case, it has the sign — &c.* In 

 p^gc 114 the author appears to us to render a very plain 

 thing, almost obscure. The letter x, in this case, is taken 

 independently of cither of the signs + or — ; being used 

 independently^ of any relations expressed by those signs. It 

 is an independent symbol of the value of the unknown 

 quantity sought, whether this quantity is affected with (he 

 sign + or — . There are instances of incorrect transla- 

 tion at pp. 18, 23, 54 At p 37 near the top, the last 



clajise, '' and retainin<r the accents^ which belonged to the 

 •coefficient!! ;" does not express the njeanmg of the origmnl. 

 Several valuable explanatorj notes are added bj- the trans- 

 lator. In that given at p. 95, doubtless hy inadvertence, the 

 areritheses which ouj^ht to indicate the multiplications 

 etween the factors, are omitted. There U not a uniformi- 



h 



* T2ie above remark wassu^^esteJ by a valuahls scieatitic friend. 



Vol. V....No. IJ. 42 



