459 
1887.] Dr T. Muir on the Theory of Determinants. 
Our second list of Bezoub’s contributions thus is: — 
(1) An unexplained artificial process for finding the numerators 
and denominators of fractions "which express the values of the 
unknowns in a set of linear equations, or for finding the resultant 
of the elimination of n quantities from n 4- 1 linear equations, — a 
process especially useful when the coefficients have particular 
values. (n. 3 + hi. 4 + iv. 2.) 
(2) An improved mode of finding Laplace’s expansions, especially 
(but not exclusively) useful when the coefficients have particular 
values. (xiv. 3.) 
(3) A proof of Vandermonde’s theorem regarding the effect of 
the equality of two indices belonging to the same set. (xii. 3.) 
(4) A series of identities regarding vanishing aggregates of 
products. (xxiii.) 
HINDENBURG, C. F. (1784). 
[/ Specimen analyticum de lineis curvis secundi ordinis , in delucida- 
tionem Analyseos Finitorum Kaestneriance. Auctore Clvristiano 
Friderico Riidigero. Cum praefatione Caroli Friderici 
FLindenburgii, professor is Lipsiensis. (xlviii + 74 pp.) pp. xiv- 
xlviii. Lipsiceff 
One of the problems dealt with by Biidiger being the finding 
of the equation of the conic passing through five given points 
(“ coeffcientium determinate Traiectoriae secundi ordinis per data 
quinque puncta ”), Hindenburg, in his preface, takes occasion to 
show how the generalised problem for \n{in + 3) points has been 
treated, pointing out that it is, of course, immediately dependent 
on the solution of a set of simultaneous linear equations. He directs 
attention to the labours of Cramer and B4zout, specially lauding 
the method of the latter, given in the treatise of 1779. Then he 
repeat both of them so as to have a set of four, and then proceed by the 
methode pour abreger to find the equation de condition , we obtain 
\ab'\.\cd'\ - \ac'\.\bd'\ + \ad'\.\bc’\+ \fict\.\ad'\ - \bd'\.\ac'\ + \cd'\.\ab'\ = 0, 
i.e. < i[\ab , \.\cd'\ - \ac'\.\bd'\ + \ad'\.\bc'\} = 0. 
This is the identity at foot of p. 457, and all the others are readily seen to be 
obtainable in the same way. 
* My best thanks are due the Committee of Management of University Col- 
lege, London, for the loan of a copy of Hindenburg’s tract from the Graves 
Library. 
