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Mathematics. — Ou: “The Formation of the Resultant’. By 
Mr. K. Bes. (Communicated by Prof. J. CARDINAAL.) 
The method of elimination by means of the Brzour function as 
shown by me in my treatise “Théorie Générale de l’Elimination” 
(Verhand. der Kon. Akademie van Wetensch. te Amsterdam 1° Sectie, 
DI. VI, N°. 7) offers a means to form the resultant that is to be 
obtained, if between zn — 1 homogeneous equations of arbitrary degrees 
with n variables » — 2 of those variables are eliminated. 
I intend shortly to treat this subject in extenso; but looking 
forward to the time necessary for this work I thought it my duty 
at present to acquaint your assembly with the obtained result. For 
this the special case is taken of two homogeneous equations of the 
degrees / and m with three variables, viz.: 
p (a, y, 2) = a, el + agalh—ly + ag alle Hagal? + as al—2y 2 + 
fag th? 2 ore Sy? Ln ee aura) 2! = 0, 
; 2 
1). 
wle, yy 2) = b, am + bg am ly + dbgam—Vz + by am—2 y? + dbs am—2 ys + ) 
fg a ie a yt ere Tja 6” = 0 
2 
| 
It is known that in this case the resultant is of the degree /m. 
If we form an homogeneous function / of the degree /m as follows: 
OP NON iad os he teas 
where ® and ¥ are respectively homogeneous functions of the 
degrees Jm—J and lm— m with provisionally undetermined coeffi- 
cients s the equation 
Nk EE EN ae ena NN 
will represent the resultant, if we can determine the coefficients s 
in such a manner that all the terms containing one of the three 
variables disappear from the equation. 
The function £ can be developed in two ways, as was shown 
in the above-named treatise on the theory of elimination: 
Ist, according to the successive arguments of an homogeneous 
function ; 
24. according to the undeterinined coefficients sj, s2, 83, etc. 
