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 corresponding to P which is to the left of the line NN'. of the two," read, "the same Page 455, line 21. For the sentence "but if 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 Oh read 6h. 3 Also of (2x + y) (2x + 3y), when x = 2, y = 3. 5. Also of (x + y + ≈) (x + y − ≈) (x + x − y), when the following expressions: (2a+3b) (4c - d), (a + b + c − d) (a − 2c + 4d), (2b3d) (a + b − 3c + d), a2 − b2 + c2 − d2, (a3 +b3) (a2b+b°c + c2d), and (a + b + c + d) 3 − a3 — b3 — c3 — d3. 9. Find the value of x3 3x2 + 3x 1, when a 3. 10. when ∞ = Find the value of √2-a + √2x - 3 √1 - 4x, 1 12 11. Replace the radical signs in the following expressions by fractional indices: √ (x+y)3, √ a3 x + √/b3æ°+Vc*æ3‚√√√a,√ √ √ c. 2 -2 2. Add together TM+4axTM-1+a2x2, 3x + 2 a2x2+a", 3. Add together 2 (a + b) − c + d, a + (b −c) - d, 5. Add together a3 + a2b-ab2 + b3, a3 - (a2b+3ab3)-2b", and 2 a3 - a2b + 2 ab2 + b3. 6. Add together a (b + c − d), b (a + d −c), c(a + d − b), and d (b+ca). 7. 8. 9. Add together a2 {b - (c - d)}, ab {b + (a − c)}, Add together (3a + 2b + c) x, (2a3b4c) x, Add together ax-by, x-y, and (a 1) + (b + 1) y. 10. 11. 12. 13. 14. 15. 16. Add together 2x2 + 3 (xy − y2), x2 − y (2x + 3y), Add together (a+2b)x−(3 a−4b)y,2a(x+y)+b(x−y), and 4ax + 3by. Add together a-{b-(c-d)}, a−b (c-d), a+b-c+d, (b + c − d.) and a Add together 2a3+3a2b− ac2 + c3, a3 +2 ac2 − b3 + 3c3, 3a2b+4ab2 – b3c, and b3 3ab2 - 5a2b - 4c3. Add together 3a2-4a3b+ab3+7a2 b2, 2a+a3b-6ab3+b1, and 3a3b+5 a b3 - 6a2 b2. Add together a2b2c2-a1b2+3ab3 c3, abc1+4a2b*+ a*b*, and ab3 c2 + 2 a2b1 — bo. Add together a2 - (ab+b2), 2 a2 - (3ab-4b2), and 4ab+8b". 17. Add together 17 a3 + 25bab - 71ab2 + 2863, 18. Add together 121 a 31 a3b + 60 ab2 + 28 a b3 — 40b+, 37 ab3 + 12b*, 52 ab3 +7b*, Subtract a (x + y − ≈) + b (x − y + x), from (a + b) x + (2 a + 3b) y + (a − b) z. |