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ΑΔ. όρθου πρόσωπον, μὴ λίπῃς παῖδας σέθεν.
ΑΛ. οὐ δῆθ ̓ ἑκουσά γ', ἀλλὰ χαίρετ ̓, ὦ τέκνα.
ΑΔ. βλέψον πρὸς αὐτοὺς βλέψον. ΑΛ. οὐδέν εἰμ ἔτι.
(δ) Καὶ ἐν τούτῳ ὁ Μενέξενος πάλιν ἧκε, καὶ ἐκαθέζετο παρὰ τὸν
2. Translate into Greek
Thus Cyrus learned that Croesus was a good man and dear to the gods: and, causing him to descend from the pyre, he questioned him thus:-"Croesus, who of men persuaded you to invade my land and make me your enemy instead of your friend?" And he replied, "O King, I acted thus for thy happiness indeed, but for my own misery: and the cause thereof was the god of the Greeks, who roused me to the invasion. For no one is so foolish as to choose war before peace for in this, children bury their fathers, but in that, fathers their children. But as for my fate, perchance it was God's will, that it should befall."
GREEK-PRELIMINARY CLASS* (FIRST YEAR PASS.)
1. Translate into English, extracts from Plato, Apologia and
2. Translate and Explain
(α) Εδόκει τις μοι γυνὴ προσελθοῦσα καλὴ καὶ εὐειδὴς λευκὰ ἱμάτια ἔχουσα καλέσαι με καὶ εἰπεῖν· ὦ Σώκρατες,
ἤματί κεν τριτάτη Φθίην ἐρίβωλον ἵκοιο.
(δ) απιόντες ἐνθέντε ἡμεῖς μὴ πείσαντες τὴν πόλιν πότερον κακῶς
(ε) οὐδὲ χρήματα μὲν λαμβάνων διαλέγομαι, μὴ λαμβάνων δὲ
3. Translate into English, extracts from Homer, Odyssey, Books V. to VIII.
4. Translate with notes
(α) αἱ δ' ἱστοὺς ὑφόωσι καὶ ἡλάκατα στρωφῶσιν
καιροσέων δ' ὀθονέων ἀπολείβεται ὑγρὸν ἔλαιον.
(ε) οὐ μὲν γὰρ τοῦ γε κρεῖσσον καὶ ἄρειον,
ἢ ὅθ ̓ ὁμοφρονέοντε νοήμασιν οἶκον ἔχητον
ἀνὴρ ἠδὲ γυνή
πολλ ̓ ἄλγεα δυσμενέεσσι,
χάρματα δ' εὐμενέτῃσι μάλιστα δέ τ' ἔκλυον αὐτοί.
*For First Year Houour papers see "Greek, Junior Class," under Second Year.
(α) ἀλλ' ὅτε δὴ ὄγδοόν μοι ἐπιπλόμενον ἔτος ἦλθε,
ARITHMETIC AND ALGEBRA.
(TWO HOURS AND A-HALF.)
1. A ladder 13 feet long is placed with its upper end resting against a vertical wall and its lower end on the ground level with the foot of the wall. The bottom of the ladder is distant 5 feet from the wall. If the ladder slip down till its lower end is 6 feet from the wall, find through what distance the upper end has slipped.
2. If £100 amounts to £109.2 in two years at compound interest, what will it amount to in three years at the same rate of interest?
5. If a, ẞ are the roots of the quadratic equation ax2—bx+c=0, express a+ß, aß in terms of a, b, c.
Hence or otherwise shew the sum of the squares of the roots of the equation 9.2+27x+20=0 is equal to the sum of the squares of the roots of 9.2+33x+40=0.
8. Find the sum to n terms of a series in geometrical progression.
The first term of a G.P. is 2, the second term is 2-√2; find the sum of the series to infinity.
9. If a, b, c are in harmonic progression, shew that 2a-b, b and 2c-b are in geometric progression.
10. By selling a parcel of shares for £80, I make a gross profit of a pounds: had I sold them for £78 15s. I should have made a profit of x per cent. on the transaction; find x.
GEOMETRY AND MENSURATION.
(TWO HOURS AND A-HALF.)
1. If three parallel straight lines make equal intercepts on a straight line which cuts them, they will make equal intercepts on every straight line which cuts them.
2. Divide a given straight line so that the rectangle contained by the whole and one of the parts shall be equal to the square on the other part.
3. The tangents drawn to two circles from any point in the straight line joining their points of intersection are equal to one another.
4. Inscribe a regular pentagon in a given circle.
5. If ABCDE be a regular pentagon, prove that the straight lines AC, AD, BE, BD, CE will by their intersection also form a regular pentagon.
6. Give Euclid's definition of proportionals and illustrate it by shewing that the ratio of 3 pence to 4 pence is not equal to the ratio of forty seconds to one minute.
7. Triangles of the same altitude are to one another as their bases.
8. Similar triangles are to one another in the duplicate ratio of their homologous sides.
9. Find the diameter of a cylindrical pipe, two feet long, containing a volume of 600 cubic inches.
10. A regular hexagon is inscribed in a circle of fifteen inches radius; find the area contained between them in square inches correct to three places of decimals.
1. Define a radian.
TWO HOURS AND A-HALF.
Which is greater, 126° or 2-3 radians?
2. Define the tangent, cotangent and cosecant of an angle. Find the tangent and cotangent of an angle whose cosecant is 1.25.
3. Find by geometrical constructions the sine of 45° and the cosine of 30°.
(sin 45°-sin 60°) (cos 150°-cos 45°) = sin2150°.
4. Prove the following, and in the case of (i.) state clearly what restrictions you make as to the magnitude of the angles. (i.) cos(A-B) = cos A cos B+ sin A sin B,
(ii.) tan A-sin2A= tan2A sin2A,
sin 2+ sin 2y
5. Solve the equations
(i.) 3-2 sin2x — 3 cos x=
(ii.) sin 5a cos 3x=sin 9x cos 7x.
6. In any triangle prove the following, proving (i.) from a figure
(i.) a sin B-b sin A = 0,
COS 2A cos 2B
7. Two sides of a triangle are 1 foot and 2 feet respectively, and the angle opposite to the shorter side is 30°. the triangle completely.
8. The shadow of a stick placed vertically in a horizontal piece of ground is observed at one instant to be equal in length to the stick. How much must the sun go down before the shadow will have increased in the ratio of 1/3 to 1?