Page 14 - Foundations Of Differential Calculus

Translator’s Introduction

In 1748 Euler published Introductio in Analysin Infinitorum, which has
been translated as Introduction to Analysis of the Infinite, in two books.
This can be thought of as Euler’s “precalculus.” In 1755 he published In-
stitutiones Calculi Differentialis. This came in two parts. The first part is
the theory of differential calculus, while the second part is concerned with
applications of differential calculus. The first part consists of the first nine
chapters, with chapters ten through twenty-seven dedicated to the second
part. Here, I have translated the first part, that is, the first nine chapters,
from Latin into English. The remaining chapters must remain as a future
project.
The translation is based on Volume X of the first series of the Opera Om-
nia, edited by Gerhard Kowalewski. I have incorporated in my translation
the corrections noted by Kowalewski.
Euler’s notation is remarkably modern. However, I have modernized his
notation is a few cases. For instance, he rather consistently wrote xx, which
2
I have changed to x . For his l x, I have written ln x; for tang x, cosc x,I
2
2
have written tan x, csc x; and for cos x , I have written cos x. I have also
modernized his notation for partial derivatives. For his “transcendental
quantities depending on a circle,” I have substituted “trigonometric quan-
tities.”
I would like to thank Kanitra Fletcher, Assistant Editor, and Frank Ganz,
T X Evaluations Manager, at Springer-Verlag New York, Inc., for their gen-
E
erous help. Finally, I would like to thank my wife, Claire, and my children
Paul, Drew, and Anne for their patience while I was working on this trans-