An introduction to the summation of differences of a function; an elementary exposition of the nature of the algebraic processes replaced by the abbreviations of the infinitesimal calculus, by B. F. Groat.

PREFACE
No student should enter upon the study of analytic geometry without an elementary knowledge of that part of the
theory of determinants which treats of elimiation and the solutilon of simultaneous equations. This will be the more readily
conceded when it is shown that such knowledge may be gained
in fewer than a dozen lessons. Seven introductory lessons in
theory of inversions and determinants would scarcely suffice
per se to make a lasting impression upon the student; but
if the elementary principles thus learned are immediately applied to the solution of problems in analytic geometry the
good gained from such a brief course should be very considerable. In whatever manner the student be introduced to a subject, it is, in most cases, only by constant recurrence and many
varied illustrations that the value of a process is finally realized.
It is thought by the writer that the treatment of inversions
as applied to determinants is new in some respects, and attention is invited to the numbered theorems and related matter
which form a chain of reasoning leading up to Laplace's development.

UNIVERSITY OF MINNESOTA
April, 1902.