Review of the Cambridge Course of Mathematics. 325 



c:lutled by formulas for calculating the interest of money 

 and annuities. These formulas are derived from progres- 

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

 bra 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 ^qw particu- 

 lars, however, concerning both the original and translation 

 merit notice. The demonstration of the binomial formuh'i, 

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

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

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

 theory of permutations and combinations on which it is 

 founded, ought to be more fully developed. In art. 42, 

 there is an error both in the original and translation. 

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

 as the multiplicand when the multiplier has the sign +, 

 and that it has in the contrary case the sign — , &c." It 

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

 But that appears otherwise, since — by — produces +. 

 And the construction allows neither multiplicand nor mul- 

 tiplier to be the legitimate antecedent of it, But we con- 

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

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

 be thus; recollecting that when a product has the same 

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

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

 page 1 14 the author appears to us to render a very plain 

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

 independently of either 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 the 

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

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



clause, " and retaining the accents, which belonged to the 

 coefficients ;" does not express the meaning of the original. 

 Several valuable explanatory notes are added by the trans- 

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

 parentheses which ought to indicate the multiplications 

 between the factors, are omitted. There is not a uniformi- 



* The above remark was suggested by a valuable scientific friend. 



Vol. v.. ..No. II. 42 



