SECT. II.] DETERMINATION OF COEFFICIENTS. 141 



Similarly if we knew the value of c for the case of three 

 unknowns, we should multiply this value by the successive factors 



_r_ 9* ir 



7*-5 2&amp;gt; 9 2 -5 2 ir-5 2 &quot; 



We should calculate the value of d for the case of four unknowns 

 only, and multiply this value by 



9 2 II 2 13 2 



The calculation of the value of a is subject to the same rule, 

 for if its value be taken for the case of one unknown, and multi 

 plied successively by 



3 2 5 2 T 9 2 



3* -1 s &quot; 5^T 2 r^V 9^T 2 



the final value of this quantity will be found. 



175. The problem is therefore reduced to determining the 

 value of a in the case of one unknown, the value of b in the case 

 of two unknowns, that of c in the case of three unknowns, and so 

 on for the other unknowns. 



It is easy to conclude, by inspection only of the equations and 

 without any calculation, that the results of these successive elimi 

 nations must be 



176. It remains only to multiply the preceding quantities by 

 the series of products which ought to complete them, and which 

 we have given (Art. 174). We shall have consequently, for the 



