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\ REESE LIBRARY
OF THI-:
UNIVERSITY OF CALIFORNIA.
\ essioiis No. (:;i^^O f. CLns No.
•li—tjr—u"\
Number and its Algebra
SYLLABUS OF LECTURES ON THE THEORY
OF NUMBER AND ITS ALGEBRA
INTRODUCTORY TO A
COLLEGIATE COURSE IN ALGEBRA
BY
ARTHUR LEFEVRE, .
Instructor in Pure Mathematics, University of Texas
university)
BOSTON, .
D. C. HEATH & CO., PUBLISHERS
1896
Copyright, 1896,
By Akthue Lefevre.
C. J. Peteks & SON, Typoqbaphees, Boston.
S. J. , & Co., PBINTEB8.
DEDICATED
THE TEACHERS OF MATHEMATICS
IX THE
C0M:\I0X SCHOOLS.
(trNIVERSITT^
(.svs^f
•0NI
G^UFORN.
CONTENTS.
CHAPTER PAGE
'
Introduction '. . . 5
I. Pbimaky Number 19
21
II. Counting ,
III. Some Fundamental Theory 24
IV. Notation 25
Y. Algebra '. 31
VI. Calculation 37
VII. Primary Number. — Numerical Operations . . 42
YIII. Devices putation 58
IX. First Extension of the Number-Concept. . . 61
Eatio. — Fractions. — Surds.
X. Significance of Operations, and Special Opera-
tional Devices Appropriate to the First
Extension of the Number-Concept .... 65
XI. Final Extension of the Number-Concept. —
Principle of Continuity 73
xii. signlificance and efficacy of numerical op-
erations under the ultimate concept. —
Zero, Infinity. — Negative, Neomonic, Com-
plex Number 85
XIII. Measurement 125
XIV. Mathematics 134
XV. Some Theorems and Problems 146
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