OF THE ELEMENTARY PRINCIPLES OF QUATERNIONS, ETC. 39 
As to the versor of the product, and abstraction made of the tensor, as to 
the product itself, in so far as composed of scalar and vector, it will not be 
unnecessary to show: that the proposed expression of c+y, as product of 
(a+a)(b+ 8), can be deduced as a consequence of the rule of multiplication 
of vector factors, adopted by definition, in the case of more than two factors, 
so that there will be only one rule of multiplication to be adopted by definition, 
and not two (not one for vectors and another for quaternions). 
In such a case namely, Let us suppose that the product of several factors 
has been obtained. It will be a quaternion, which we may represent by +8. 
Let us suppose that \ and p represent the not yet employed factors. Then in 
order to form the product \x|[ux(b+)| we have to make the product 
pb+pB , and afterwards effect the multiplication by }. Thus we will have : 
Xx [w(0+8)] = wb + x pB. 
But at page 199 it is shown (by vector multiplication) that the terms of each 
of the developments of the two products 
hx pB and ux B 
are each to each the same, only under another form, and therefore we may 
consider the effected product under the form 
(Az) x (6+ 8), 
where Ap is considered as a whole ; only of course for the sake of effecting the 
multiplication of b+ by \p the expression of Ay will be represented by the 
several terms which constitute it. 
But now we may suppose that 4, w, have been chosen so as to represent 
a+a by their product, and then the product (@+«)(6+ £8), when effected, will 
have been effected by the rule of the multiplication of vectors only. 






