Number and its algebra : syllabus of lectures on the theory of number and its algebra introductory to a collegiate course in algebra

Arthur Lefevre

Description

UC-NRLF i It TTl$B 531 '^THOU 'I THAT TEACHES"? ^ »ANOTHER Mi/ THOUNOT™,.,JEACHEST THYSELF 7''I , 3 1 s^. ( 1 *Js?fj/t'* i I IHtAI 'in :i'. PI:!)AGO(j I' \ iXl" I a) *dotation a line to the numberpresentedally laterally or a colon : or a combination of bothsymbols (— ), (/ ), todivision. The first is begenerally(-f-) represents preferred. 50. With number division amounts to repeatedprimary but it defined as the inverse ofissubtraction, only safely §multiplication. (Vide 45.) of if a num-51. Under the developed concept number, ber is to be combined with a series of others which operate and there is freein multiplication division,successively commutation and association in the in theusing operators —in :manner thedisplayed following = = =c b a h c a -i- cX -^ -i- X X b;(1) (a f^) (a c) / / -~ = a = c h-i- c he -^ ;(2) {a h) / aj = = -~ =ac bd a d b e ac h(ft -V- X -^h) {c d) j / j(3) j -^ etc.d, ; ^ = =^ -^ -^ ad a c-^b-d ad b{fi(4) b) (c d) jbc I / -f- etc.c, ; " "* is to numberThe minus endwise tliesign presented .symbols. —PRIMARY KUMBER. NUMERICAL OPERATIONS. 53 as be from the laws ofeasily proved multiplicationmay the definition of to be true forand division, primary the have at all.number, if opei'ations any meaning itBut as in the case of subtraction is vain to43),(§ with division under theattempt generalizations primary of for division is inconcept number, possible only par- ticular cases.

Sujets

• Álgebra
• Mathematics
• Philosophy

Informations

• Publié par: les_archives_du_savoir
• Nombre de lectures: 19
• Langue: English
• Poids de l'ouvrage: 10 Mo

Extrait

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•li tjr—u"\and its AlgebraNumber
OF ON THE THEORYSYLLABUS LECTURES
OF NUMBER AND ITS ALGEBRA
INTRODUCTORY TO A
COURSE IN ALGEBRACOLLEGIATE
BY
ARTHUR C.E.LEFEVRE,
Instructor in Pure University of TexasMathematics,
university)
U.S.A.BOSTON,
D. C. HEATH & PUBLISHERSCO.,
1896Copyright, 1896,
By Akthue Lefevre.
C. J. Peteks & SON, Typoqbaphees, Boston.
S. J. PaEKHTI.I, & PBINTEB8.Co.,DEDICATED
OF MATHEMATICSTHE TEACHERS
IX THE
C0M:\I0X SCHOOLS.
(trNIVERSITT^(.svs^f•0NI
G^UFORN.
CONTENTS.
CHAPTER PAGE
'
. 5Introduction '. .
I. Pbimaky Number 19
II. Counting 21
,
III. Fundamental Theory 24Some
25IV. Notation
'. 31Y. Algebra
VI. Calculation 37
—Primary Number. Numerical Operations . . 42VII.
58YIII. Devices of Computation
61IX. First Extension of the Number-Concept. . .
— —Eatio. Fractions. Surds.
X. Significance of and Special Opera-Operations,
tional Devices Appropriate to the First
Extension of the Number-Concept .... 65
—XI. Final Extension of the Number-Concept.
Principle of Continuity 73
op-xii. signlificance and efficacy of numerical
—concept.erations under the ultimate
— Com-Infinity. Neomonic,Zero, Negative,
85plex Number
125XIII. Measurement
XIV. 134Mathematics
146XV. Some Theorems and ProblemsJ