An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

THE

DIFFERENTIAL CALCULUS.
CHAPTER I.
PRELIMINARY REMARKS. VARIABLES AND CONSTANTS. FUNCTIONS,
CONTINUOUS AND DISCONTINUOUS. ILLUSORY FUNCTIONS.
EXAMPLES.
1. AT the commencement of a treatise upon any science, The nature
of the Difthe reader naturally expects to find some brief statement of ferential
the nature and object of that science; but in the present Calctub
instance it is impossible to make such a statement, unless explained
at first.
the meaning of certain terms, necessary to be used, be previously explained: for the Differential Calculus, from the very
first, involves notions which must be new to one who is acquainted with no more than the common elements of Algebra
and Analytic Geometry; and in the following pages we must
suppose the reader to have advanced only so far in the study
of mathematics.
We shall therefore make a few preliminary remarks, and
explain certain fundamental notions, before we state what the
Differential Calculus is.
2. Any quantity capable of variation is called a Vari- Variables
and Con..
able. stants.
Any quantity which cannot vary, or, if it can, is supposed not to vary, is called a Constant.
Thus in the general equation to a right lipe, namely,
y = mx + c, if we suppose the line never to change its position,
1