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I take this opportunity of correcting some errors which I have detected, or which have been pointed out to me, in the “Elementary Course of Mathematics.”

Page 195. In the figure the weight W is made to act upon the right hand side of the wheel, instead of the left.

Page 224, line 17. For first read here.

In the figure of page 417, the arrows should point in the opposite direction, in order to shew the true direction of the Earth's motion; and in the figures of pp. 418, 423, and 462, the ecliptic and equator ought to change places; but the explanations are not at all affected.

Page 436, line 1. For great read small.

In figure of page 445 insert P' at the point corresp onding to P which is to the left of the line NN'.

Page 455, line 21. For the sentence “but if ..... of the two,” read, “the same will be the case when the sun and moon are on opposite sides, or the moon in geocentric opposition; when the moon is halfway between opposition and conjunction the effect may be considered to be the difference of those due to the lunar and solar action."

Page 465, line 10. For Ob read 65.

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3

Also of (2x + y) (2x + 3y), when x = 2, y = 3.

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5.

5.

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If a = 1,

Also of (x + y + x) (x + y - x) (x + x - y), when 1, y 3, Z = 6. Prove that 30 - {y-(x – u)} = x – y +% - u. 7.

6

2, C = 3, prove that
a + 6+ c? + 2ab + 2ac + 2bc 6 abc a+ b3 + c",
a2 + b + c 14(a + 2c),
ab + 65

11c,
a? ab + 62

C,
(a + b)(a + c)(b + c) = 10 abc.
8.

2, b. 3, C = 5, and d = 6, find the value of the following expressions : (2a + 36) (4c - d), (a + b + c-d) (a – 2c + 4d), (2b 3d) (a + b - 3c + d), a' b + c - d?, (a3 + b)(a*b+boc+cd), and (a + b +c+d)3 - q- 63-(3- d.

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If a =

=

9.

Find the value of 203 – 3x2 + 3x

1, when x = 3.

10. when x =

Find the value of $ - + 2x - V1 – 4x,
T

11.

Replace the radical signs in the following expressions by fractional indices : V(x+y), Vdo+Vb+x+Ve*x*, NV Va, Navove.

ADDITION

1.

Add together 2012 a x + a, 2 x + 3a x 2 a,

and x2 + ax + 3a?.

2.

Add together w+4 a x-'+a??, 3x" + 2 a* x*–2 +a", and a xm

6a".

m - 1

+ axm-2

3.

Add together 2(a + b) - c+d, a + (6 c) d,

and a + b - (c d).

4.

Add together a + 2c + d, 2a - (6 - c)-d,

and 3a + b - (3C + d).

5.

Add together a2 + ab - ab + b}, as – (a*b+3 ab)2b",

and 2 a3 a b + 2ab + b3.

6.

Add together a (b + c - d), b(a + d - c), c(a + d - b),

and d (b + c - a).

7.

Add together q* {b – (c d)}, ab {b + (a – c)},

and b? (c + d a).

8.

Add together (3a + 2b + c) X, (2a 36 40) X,

and (a + b - c) x.

9.

Add together a x - by, x - y, and (a – 1) x + (6 + 1) y.

10.

11.

12.

Add together 20* + 3 (ry - y'), x - y (2x + 3y),

and x (y - 3x) + y. Add together (a +2b)x – (30–46)y, 2 a(x+y)+b(x-y),

and 4 a 2 + 3by. Add together a-{6-(c-d)},a-b-(c-d), a+b-c+d,

and a

(b + c - d.) Add together 2a + 3 a'

bac +c, a + 2 ac 6 + 30%, 3 ab + 4ab-boc, and 63 - 3ab - 5ab - 4c?. Add together 3a* -4ab+ab3 +7a*b*, 2a* +ab-6ab' +6*,

and 3ab + 5ab3 - 6ab.

13.

14.

15.

Add together a'bc-a*b*+ 3 abc', abc +4 a'b'+ a*b*,

and a b c + 2 a 64 - 6'.

16.

Add together aź– (ab+b), 2 a? – (3ab-4b2),

and 4 ab+362.

17.

Add together 17 a3 + 25 ba'b 71 ab? + 286",

161 a? - 13aRb + 14 ab? - 51 b,
19a - 146 a' b + 317 ab - 8063,
and 6 a 23 aob 200 ab + 11263.

18.

Add together 121 a' - 31ab + 60 ahe + 28 a b3 - 405*,

30 a* + 27 a'b 15 aob? + 37 ab3 + 126*,
17 a' - 15ub - 40 ab - 52 a b3 + 764,
a' - 3a'b + 43 a 6 - ab3 + 296",
and 6 a* + ab – 29 ab% + 8ab3 1664.

SUBTRACTION.

1.

Subtract a b + C-d, from 2a + b-C + 3d.

2.

Subtract 2a

3 (b + c), from a

2b + 2c.

3.

Subtract a (x + y - %) + b (x y +%),
from (a + b) x + (2a + 3b) y + (a - b)x.

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