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4. If a man can perform a journey of 170 miles in 4} days of 11 hours each, in how many days of 8 hours will he perform a journey of 470 miles ? 5. Extract the square root of :
. 964.226704 6. What sum of money will produce £43 interest in 31 year, at 21 per cent. simple interest ? 7. Prove that:+ _
- xs y _
y = 1 y x + y x2 y - y2 8. Divide :
as + xe® by a + c Multiply 1 y + y} by yt 9. Solve the following equations :
1 3 y +- =9
3 10. A post is a fourth of its length in the mud, a third of its length in the water and 10 feet above the water, what is its length ?
1. (a.) square,
(6.) Every rectangle is a parallelogram. Is it true that every parallelogram is a rectangle? Give reasons for your answer.
c.) Two triangles that have three sides of the one equal to three sides of the other, each to each, are equal in every respect. Two triangles that stand on the same base and between the same parallels are likewise equal. Is there any difference between the equality of the triangles in these two cases ? If so, what?
(d.) In the first book of Euclid, what properties are shown to belong to triangles ?
2. Given two equal and parallel straight lines A B and D C; prove that A C and B D bisect each other. Under what circumstances will A C equal B D ?
3. The angles at the base of an isosceles traingle are equal to each other. Give Euclid's proof of this proposition. How might it be proved if you were permitted to bisect an angle ?
4. Three straight lines meet in a point. Draw another line cutting them so that the segment of it intercepted between the first and second shall be equal to that intercepted between the second and third.
5. If a straight line be divided into any two parts, the square of the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts.
To what algebraical proposition is this equivalent ?
6. Describe a square that shall be equal to a given triangle.
7. (a.) Equal chords in a circle are equally distant from the centre.
(6.) How do you measure the distance of a straight line from a point ?
(c.) What is the locus of the middle points of equal straight lines in a circle ?
8. The opposite angles of any quadrilateral figure described in a circle are equal to two right angles.
9. A tangent is drawn parallel to a chord. Show that the intercepted arc is bisected at the point of contact.
10. Inscribe in a circle an equilateral and equiangular pentagon. Is it necessary to say equilateral and e quiangular?
First Examination in Arts.
Examiner.-Rev. J. RICHARDS, M. A. ' 1. Give the argument of the sixth book of Paradise Lost.
2. Explain the following passages :-
And roll’d, o'er labour'd works, the attentive eye;
They mark'd the spacious margin with their own." (b) “She makes the vile to virtue yield applause,
And own her sceptre while they break her laws;
(c) “So fast he flies, that his reviewing eye ·
Has lost the chasers, and his ear the cry;
Their disproportion'd speed does recompense.” (d) “So promised he ; and Uriel to his charge
Return’d on that bright beam, whose point now
Of planets, and of fix'd, in all her wheels
Then most, when most irregular they seem.” (f) “All night the dreadless angel, unpursued,
Through heaven's wide champain held his way;
Unbarred the gates of light.” 3. How do you distinguish between conjunctions and prepositions and between adjectives and adverbs ?
4. In what sense does Milton use these words- ,
Fare, eminent, error, lithe, reform, uncouth, slope, procinct, obvius, idol. 5. Ah! gentle pair, ye little think how nigh
Your change approaches, when all these delights
Long to continue, and this high seat your heaven
Henceforth. 6. Give the etymology and meaning of these words : -wanton, lethargy, polemics, subtile, verdurous, limi. tary, intelligential, puissance, surceased, enamoured, primeval, sheer, griding.
7. What affixes are used in English to express diminutiveness ?
8. Explain allusions :-
Hung forth in heaven his golden scales, yet seen
“So down they sat,