11. Turn into Oratio Obliqua:

"Regna autem non merito accidunt, sed sorte variantur. Ceterum imperium ante tenuerunt et Assyrii et Persae, et Graecos et Aegyptios regnasse cognovimus. Ita, vicibus potestatum, Romanis imperandi tempus obvenit. Ceterum, si ad originem redeas, erubescendum erit. Populus de sceleratis et nocentibus congregatur, et asylo constituto facit numerum impunitas criminum.”

III.
Arithmetic.

1. Find the value of half an acre of land at 94d. per square foot.

3. Multiply 000215 by 0732; and divide 46.729 by 3.125. Express the results both in decimals and fractions.

4. Multiply 8.3 by 519, and find the value of

•3 of a £+ of a shilling + of a guinea+.25 of a penny.

5. How much will 75 cwt. I qr. 16 lbs. of sugar cost at 27. 48. 11d. per cwt. ?

6. If the keep of 6 horses be a guinea a day, when oats are at 288. per quarter, how much will the keep of 16 horses be, when oats are at 328. per quarter?

7. Find the square root of 37249 and of 99.8001.

8. At what rate per cent. will 6257. amount to 7657. 12s. 6d. in 5 years, simple interest?

9. How much paper will be required to cover a box all over 3 ft. long, 24 ft. wide, and 1 ft. high, leaving space for a lock 6 in. long by 3 in. wide, the paper being 9 in. in breadth ?

10. A person buys 700l. Stock at 961, and sells out at 1023; what does he gain by the transaction?

11. A bankrupt owes his creditors 1520l., and his assets amount only to 3481. 6s. 8d. How much can he pay in the pound?

12. A boat rowing 40 strokes a minute rows 1 mile 280 yds. in 6 minutes 48 seconds. How much water is cleared at each stroke?

IV.
Euclid.

[Two Propositions at least from the Second Book are
required.]

1. Define-a superficies, a diameter of a circle, an obtuse-angled triangle, an oblong, a diagonal.

2. From the greater of two given straight lines to cut off a part equal to the less.

3. On the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise those which are terminated at the other extremity equal to one another.

4. The angles which one straight line makes with another straight line on one side of it, either are two right angles, or are together equal to two right angles.

5. Parallelograms on equal bases, and between the same parallels, are equal to one another.

6. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

7. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square on the whole line.

8. If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

9. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side

produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.

10. Describe a square that shall be equal to a given rectilineal figure.

b+ca, c+1a−b, a+b-c.

2. Subtract 2 (a—b) — 3 (b−c) from 2 (a+b) + 3 (b+c). 3. Multiply 13a2-17a-45 by -a-3.

4. Divide

(1) ab2 — ac2+c2b—b3 by (b+c)(a—b);
(2) a3+3ab+b3—1 by a+b−1.

6. Find the G. C. M. of

(1) a2-4a+3 and 4a3-9a2-15a+18;
(2) 12a2+7ab+b2 and 28a2+3ab—b2.

7. Find the L. C. M. of

(1) a2+6a+8 and a3+5a2+7a+2;

(2) (x2+4x+3), (x2+3x+2), (x+2) (x2+7x+12).

8. Extract the square root of

(1) x2+4xy +4y2+9z2+6xz+12yz;

10. (1) At the general election of a constituency abstained from voting, and voted for the successful candi

voted

date. At a subsequent election abstained, and for the successful candidate. The minority in the latter election was 40 less than in the former. Find the number of voters in the constituency.

(2) A father had two children. When the Census was taken one of the children was four times as old as the other, and the father was five times as old as the two children conjointly. Ten years hence the father's age will be twice the combined ages of the children. How old was each at the time of the Census ?