PREFACE 
v 
egun by developing the 
Cantor and Dedekind, 
. To obtain sufficient 
the more simple prop- 
owever, has been made 
enerality. The author 
espect. Some theorems 
le others are enunciated 
lese latter will be taken 
lentioned here. In the 
tion has been adopted, 
ions is stated and then 
book less attractive to 
> usefulness as a book of 
bor of running through 
: up sundry conditions 
5 without any explicit 
>n. 
rect forms of reasoning 
the calculus have been 
bhe volume. It is the 
;es the student’s critical 
it the flaws in a piece of 
5 training he considered 
sen introduced, but only 
their employment suffi- 
3 enunciation of certain 
It may be well to note 
in the sense of any one 
lie. The words “ each,” 
id in an indiscriminate 
3 difficulty the beginner 
Mathematischen Wissenschaften. The author feels it his pleasant 
duty, however, to acknowledge his large indebtedness to the writ 
ings of Jordan, Stolz, and Vallée-Poussin. He hopes, however, 
that it will be found that he has not used them servilely, but in an 
individual and independent manner. 
Finally, he wishes to express his hearty thanks to his friend 
Professor M. B. Porter, and to his former pupil Dr. E. L. Dodd, 
for the unflagging interest they have shown during the composi 
tion of this volume and for their many and valuable suggestions. 
JAMES PIERPONT. 
New Haven, Conn., August, 1905. 
Note 
A list of some of the mathematical terms and symbols employed in this 
work will be found at the end of the volume. 
the various results here 
: has been rendered un- 
of the Encyclopadie der