58 A Discourse on the Theory of Fluxions. 
which each term is a multiple, composed of an invariable 
factor, and one that is variable consisting of one or more 
terms, with, or without invariable coefficients. Here the in- 
variable factors may be of any assignable magnitudes, pro- 
vided they differ from each other; but the variable factors 
must be the same, or of equal value. When the invariable 
factor is not expressed, it is considered as being unity. It 
will be found on examination, that a fluxion is equal to a mul- 
tiple, composed of its corresponding fluent, and the quantity 
From the use which is made of the factor x- in this 
quantity, it is obvious, that it may be of any finite magni- 
tude, great or small, that can be assigned. To make use of 
this equation in explaining the relation under consideration, 
let Bx" and az” be two functions of the variable quantity x. 
Their corresponding fluxions nBa"~'z and nax"~1z" m y 
be considered as two terms, selected from a series of fluxions, 
constructed in conformity with the foregoing definition ; 
which selection may always be so made, that one of the 
terms shall be the fluxional expression, that occurs in the 
selves. 
Theorem, II. Any two terms, in a series of fluents, will 
have their corresponding fluxions in the same ratio with 
those fluents, 
ence, nBa”™”' 2° : Bz": inaz*™ 2" + ax". 
Let the antecedent be represented by A, the consequent 
by C, and the ratio by r. Then by the definition of a ratio 
c=". Any two of these being given the other may be ob- 
