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3. Write a life of Miltiades, or of Themistocles, or of Pausanias, or of Alcibiades. (N.B.-One only of these lives to be attempted.)

4. What do you understand by the term Triumvirate in Roman History? Triumvirates were there? Describe briefly the fortunes of the men who formed one of those Triumvirates.

5. What Barbarian tribes had most share in the overthrow of the Empire of the West ?

MODERN HISTORY.

1. How many dynasties ruled in France before the House of Capet came to power ? Mention the names of those dynasties, and that of the greatest monarch in each.

2. When do we first hear of Hungary in the History of Europe ? When did Hungary become attached to the Austrian Empire ?

3. Write a short life of Louis XI. of France.

4. Describe the course of events which placed the Bourbons on the thrones of Spain and Naples.

5. What do you understand by the Germanic Confederation ? What Princes have most weight in that Confederation ?

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MATHEMATICS.

Morning Paper.

Rev. Canon HEAVISIDE, M.A.

OBLIGATORY PORTION.

(The Questions in the remainder of the Obligatory

Portion will be set in the Afternoon Paper.]

Arithmetic.

1. The sum of 551. 6s. 10 d. is to be equally divided among 35 persons, how much will each person receive ?

2. If a soldier step of a yard, how many steps will he take in 3 miles ?

3. If with a capital of 5001. a tradesman gain 501. in 7 months, in what time will he gain 601. 10s. with a capital of 3851. ? 4. If 4 of the cargo of a ship be worth

a 7141. 148., what is the value of the whole cargo ?

5. Find the simple interest on 49681. 15s. for 3 years at 44 per cent. per annum.

6. Add together 2, 3, 5%, and explain why fractions are reduced to a common denominator in addition,

7. Express 12s. 6 d. and 41. 12s. 62d., each as decimals of a pound sterling.

8. A quantity of matting 37 feet 9 inches in length and 7 feet 6 inches wide, will just cover a

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room; what width of matting that is 75. feet long, will be required to cover the same room.

9. Extract the square root of (1) 154:157056, (2) 13 to four decimal places.

Euclid.

1. Define a right angle ; prove that the angles which one straight line makes with another upon one side of it, are either two right angles or are together equal to two right angles.

2. Describe a parallelogram which shall be equal to a given triangle and have one of its angles equal to a given rectilineal angle.

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VOLUNTARY PORTION.

1. About a given circle describe a triangle equiangular to a given triangle.

If the triangle circumscribing the circle be equilateral, find its area when the circumference of the circle is 60 feet.

2. Upon a given straight line describe a rectilineal figure of four sides, similar and similarly situated to a given rectilineal figure of four sides.

Show how to find the area of a trapezium two of whose opposite sides are parallel.

3. Prove, by means of algebra, the rule for finding the greatest common measure of two numbers. Reduce to its lowest terms :

ab( x2 y2) + xy(a62)
ab(x2 + y2) + xy(a? +62)

X,

(7)"

4. Find by means of the logarithmic tables :
1. (14.276)
2. The value of if =700

3 3. The sum of the series 12 + 36 + 108 + &c. to 7 terms.

5. A hemispherical basin holds a gallon of water;

find the diameter of the hemisphere, it being given that a gallon contains 277.27 cubic inches.

Afternoon Paper.

Rev. Canon HEAVISIDE, M.A.

OBLIGATORY PORTION.

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Algebra. 1. Account for (ab) and (6-a) having the same value when a = ý and b= 3; what is the

a-bo value of if a = 7 and b = 3,

a + b 2. From a® + 3a2b + 3ab2 + b3 take a? - 3a2b + 3ab2 13. Simplify

3.x2 + 2xy = {4x2 + y2} {xy - x2). 3. Multiply

2003 – 3x+y + 4xy – 3y by (2x + 3y). Divide the product obtained by (2x2 xy + 3y”).

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4. Reduce
2x + 3y 2x

3y
2x – 3y

2x + 3y.
Prove

(a + b - c)? (a - b + c)2 = 4a (b-c).
5. Solve the following equations :
2x – 7

3

62
(1)
3

5

X

X

5

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X - y

= 13 3

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X Y

4

x + y

2
(3)
x + y

8} 3 6. A General, after losing a battle, found that he had only rds of his army left fit for action; žth of the army were wounded, and the remainder, 2000 men, were either killed or missing; of how many did his army consist before the battle?

Euclid.

1. If a straight line be divided into two equal and also into two unequal parts, the squares of the two unequal parts are together double of the square of half the line and of the square of the line between the points of section.

2. If a point be taken within a circle, from which there fall more than two equal straight lines to the circumference, that point is the centre of the circle.

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