so " (" c)will denote the reverse of the reverse of + c,that
is," (" c)is equivalentto + c.
But, as we have impliedin Art. 41, trie beginnermust
be content to defer until a later period the completeenaxptilao-n
of the meaning of operationsperformed on neg
and thus we obtain a"cfw_b " c)=a " b + c.
Similarly a " cfw_b+ c " d)=a " b-c + d.
50. Consider the example
a-cfw_b-^c-~d)= a-b-c + d;
that is,if b + c-d be subtracted from a the result is
a-b~c+d. Here we see that,in the expressionto
Zb " h=2o; and 5c + 3c = 8c. Thus the proposed expression
may be put in the simplerform
3a + 2" + 8c.
Again; consider the expressiona " 3" " 46. This ia
equal to a " 7". For if Ave have first to subtmct 3" from
a number a, and then to subtract 46 from the
shall consider " 6 + a to mean the same thingas a " 6.
36. Thus the numerical value of an expressionremains
the same, whatever may be the order of the terms which
compose it. This,as we have seen, follows partlyfrom our
notions of addition and subtraction
a-\-'b " c)d denotes that the result expressed by
a-vh " c is to be multipliedby d^ or that the whole of
a + " " c is to be multipliedby d\ but if we omit the
brackets we have a + b " cd, and this denotes that c only
is to be multipUed by d and the result
the sixth degi-ee. A numencal coefficient is not counted ;
thus i)d'b* and a^b'^ are of the same dimensions, namely
seven dimensions. Thus the word ditnensicms refers to
the number of algebraicalmultiplicationsinvolved in the
tcnn; that is,tlie degree of
of a; ax ax ah called the third power of a; ax ax ax a
is called tha fourth power of a; and so on. And a itselfis
sometimes called thc^/v^ power of a.
6 FACTOR. COEFFICIENT. POIVER. TERMS,
16. A power is more brieflydenoted thus: instead of
used in the notation for decimal fractionsit, is advisable
to placethe pomt in the latter case higher up; thus
4*5 may be keptto denote 4 + "
. But in fact the pointis
not used instead of the signx except in cases where there
can be no ambiguity. For exam
2 THE PRINCIPAL SIGNS.
sented by a. If a represent9 and h represent3,then a-\-h
represents 12. The sign+ is called the plttssign,and
tj + 6 is read thus "
a plus b."
5. The sign- placedbefore a number denotes that the
number is to be subtracted. Thus a"b
XVII. Multiplication of Fractions
XVIII. Division of Fractions
XIX. Simple Equations .^ 94
XX. Simple Equations, continued
XXI. Problems ii"
XXII. Problems, continued m
XXIII. Simultaneous Equations of the first degree
In accordance with the recommendation of teachers, the
examples for exercise are very numerous. Some of these
have been selected from the College and University enaxatimio-n
papers, and some from the works of Saunderson and
Simpson ; many however are orig
ALGEBRA FOR BEGINNERS.
ALGEBRA FOR BEGINNERS.
WITH NUMEEOUS EXAMPLES.
If TODHUKTEB M.A., F. K. S.
D. H.SMITH " CO., BOOKSELLERS " STATIONERS,
Entered according to Act of the Parliament of Canada, In the
thousand eight hundred and sev
COLENSO'S ELEMENTS of ALGEBRA, adaptedfor the use of
Teachers and ^TCHBHTSin the UNIVERSITY; being the Larsre-Paper Edition of the
Parts I.imdII. as above" the Complete Work 8vo. i2". 6"i.-KBT, l2mo. 7s. Pd.
I"LANE TRIGONOMETRY, Pabt I. comprisin
167. (i)^= 17j (ii)^= g_J,= 2, "z_^(jii5i)^= "a
168. "40, "28, or "28,"52, accordingas A had more or less at
169. "v/cfw_"^+^J6x2()^"312^2^89 = 19.834.
_3 3 PI _vj xix^-Y)
170. ^-3 - 4.x ^j^+Sf, 171. a
" 6 *",T?Tr
172. l-^".l-2a%. 173. j^l^yJ
\ a + b / y^= Sly*- 4a;*/
5. A railwaytrain travels from A to C passingthroughB
where it stops7 minutes. Two minutes afterleaving^, it meets
an express train which started from C when the former was
28 miles on the other side of J3, The express tra
of the campaignas many as two whole garrisonasnd half of another
died of an epidemic,and all the rest except 84 invalids,who
returned to head-quarterwser,e equallydivided among the ftorer-sses
as before. But, the reduced garrisons provingtoo weak for