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

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PREFACE.

"If the assumption be not true, definite values cannot be obtained for A, B, C, &c."
These defective steps of reasoning and others which
might be mentioned, are objectionable, not because they
lead to erroneous conclusions, but because they ought
not to be found in a subject like the present, in which
every thing should be comformable to the strictest rules
of logical deduction. M. Cauchy has done much towards the improvement and perfection of the Differential Calculus, and his writings on this, like those on
the more abstruse branches of mathematics, are most
valuable. In one or two places the methods I have
employed in the following pages are apparently similar
to those of M. Cauchy, but in reality they are essentially different: so far as I am aware I am indebted
to him only for article 48.
CAMBRIDGE,
October, 1842.
ERRATA.
The reader is requested to make the following correction which is of
some importance.
3rd line from foot of page 75 instead of (2) read (0).