IX.

EUCLID, I. AND II.

1. Define the term "plane rectilineal angle.”

How is the size of an angle measured? What is the test, for instance, that one angle is twice as great as another? or that two angles are equal?

2. Quote Euclid's postulates.

3. Write out the propositions of which the following are the enunciations :

(i.) From a given point to draw a straight line equal to a given straight line.

(ii.) To bisect a given rectilineal angle, that is, to divide it into two equal angles.

(iii.) If two straight lines cut one another, the vertical, or opposite, angles shall be equal.

(iv.) If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.

(v.) Parallelograms on the same base, and between the same parallels, are equal to one another.

(vi.) In any right angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.

(vii.) If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.

(viii.) To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

4. Use propositions iii. and iv. of questions 3 to prove that, if from any point perpendiculars be drawn to two straight lines, the angle between the perpendiculars is equal to the angle between the straight lines.

5. If the distances of a point from two given straight lines be known, prove that the point must be one of the four angular points of a certain parallelogram.

X.

FOR LATIN PROSE.

The soldiers who composed the legion were distinguished by a helmet with the figure of a lark or a tuft of its plumage on the crest, from whence it derived its name Alauda. The Gauls admired the spirit and vivacity of the bird, and rejoiced in the omen. Fond of the excitement of a military life, vain of the consideration attached to the profession af arms, they found united in Cæsar's service all the charms which most attracted them. No captain ever knew better how to win the personal affection of his soldiers, while he commanded their respect. The general severity of his discipline enhanced the favour of his indulgence.

For Honours in Classical and General Literature.

I.

ETHICS.

1. Explain the terms and show the bearing of the statements :

(α) ὧν δ' εισί τέλη τινὰ παρὰ τὰς πράξεις ἐν τούτοις βελτίω πέφυκε τῶν ἐνεργειῶν τὰ ἔργα.

(6) ἡ μὲν οὖν μέθοδος τούτων ἐφίεται, πολιτική τις οὖσα. (c) μὴ λανθανέτω δ ̓ ὑμᾶς ὅτι διαφέρουσιν οἱ ἀπὸ τῶν ἀρχῶν λόγοι καὶ οἱ ἐπὶ τὰς ἀρχάς.

2. For what reasons would Aristotle ignore the opinion of a young or a bad man on moral questions? On what grounds does he accept the verdict of language? Give instances of appeals to it.

3. Give the definition of Happiness. Trace the steps by which it is reached. What is there in it in common, and what at variance, with previous views of the ***chief good?

4. By what arguments does Aristotle combat Plato's view of an Ideal Good? Explain the view, and criticise the answer.

5. In what sense can Happiness be predicated of the living? How did this question arise? What is meant by Happiness being πάντων αἱρετωτάτη μὴ συναριθμουμένη ?

6. Can a man be virtuous without a proper motive? 7. What are the component elements of προαίρεσις ? 8. Οἱ ἀνδρειά and συφροσύνη, which better answers to the test of (α) ἕξις, (β) μεσότης, (c) τὸ ἑκούσιον?

9. Is Virtue innate? Is Vice compulsory? Is Happiness improvable?

10. Give a list of the Virtues.

Illustrate in three of

them the assertion that Virtue is a mean.

11. Translate Ethics i., ch. 9, §§ 1-7.

Translate :

II.

GREEK AUTHORS.

Hom. Od. iii., 184-197.—From ὡς ἦλθον, φίλε τέκνον .to ἐτίσατο πατροφονῆα.

Æsch. Cho., 332-352.—From ΗΛ. κλύθι νυν ὦ πάτες ..to τάφον διαποντίου γᾶς.

Æsch. Eum., 734747.—From ἐμὸν τόδ' ἔργον.........to ἢ πρόσω τιμὰς νέμειν.

Soph. Ο. Τ., 463479.—From τίς ὅντιν ̓ ἁ θεσπιέπεια to ποδὶ χηρεύων.

Soph. Ο. C., 728 739. - From ἄνδρες χθονὸς τῆσδ .to ἐς πλεῖστον πόλεως.

Arist. Birds, 638-653.From καὶ μὴν μὰ τὸν Δί' ......to ἀετῷ ποτέ.

Arist. Plutus, 802-817. From ὡς ἡδὺ πράττειν, ώνδρες .to ἀρτιάζομεν χρυσοῖς.

Thuc. i., c. 120.—From ̓Ανδρῶν γὰρ σωφρόνων μέν ἐστιν .....to ἐν τῷ ἔργῳ ἐλλείπομεν.

Thuc. ii., c. 51.—From Τὸ μὲν οὖν νόσημα........to ἐς τοῦτο ἐτελεύτα.

Herod. vii., c. 210.—From Ταῦτα λέγων, οὐκ ἔπειθε τὸν Ξέρξεα............to ἡ συμβολὴ δι' ἡμέρης.

Herod. viii., c. 77.—From Χρησμοῖσι δὲ οὐκ ἔχω ἀντιλέγειν ..to σβέσσει κρατερὸν Κόρον.

III.

LATIN.

Translate into English :

Hor. Od. I., xxxviii.

Hor. Od. III., xxii.

Liv. I., c. ii., §§ 5-8.-From Eneas, adversus tanti bellli ..to Jovem indigetem appellant.

Liv. II., c. xl., §§ 3—6.—From Ubi ad castra ventum est ...to longa servitus manet.

Tac. Ann. II., c. lii.--From Valida ea gens....... .to impune fuit.

Tac. Ann. III., c. xxvii.-From Pulso Tarquinio......to plurimae leges.

IV.

ANCIENT HISTORY.

1. By what arguments was Darius persuaded to appoint Xerxes as his successor? and Xerxes induced to undertake the expedition against Europe?

2. Relate the stories of Pythius and Eurytus.

3. Describe the conduct of the Argives and Corcyreans, and of Gelon at the commencement of the Persian invasion.

4. Show from the narrative of Herodotus the influence of Oracles on the Greek, and of Visions on the Persian mind.

5. Give an account of the expedition into Phocis, its causes and results.

6. Compare the characters of Xerxes and Themistocles. 7. Describe the mode of communication called Angarion. 8. Map or describe the relative positions of Athos, Potidæa, Thermopyla, Artimisium, Salamis, Athens, and Corcyra.

9. Who were Epialtes, Sinicus, and Artemisia?

10. What were the occasions of the saying-" My men have fought like women and my women like men.' "Your year shall have no spring. "They who

falter in the race win no crown.'

11. Give the dates of the beginning and close of the Persian and Peloponnesian wars, and an account of the real and avowed causes of the latter.

12. Explain the mutual demands of Athens and Sparta for the removal of "the accursed."

13. Detail the incidents of the first year's campaign. 14. Relate the history of Cleon.

V.

ROMAN HISTORY.

1. Give a short account of Livy. Who were his chief contemporaries, and what the state of government în his time?

2. What materials had Livy for his history? What previous writers does he mention by name, and what criticisms does he pass upon them severally?

3. What views have been mainly held as to the credibility of early Roman History? Do you consider Romulus-Numa-Tullus Hostilius to be real or mythical personages? Give reasons for your answer. 4. Sketch in outline the beginnings of Rome. What is meant by saying there had been a σvvolkiσpós in very early times? Was the people of one origin, or were they a mongrel race?

5. Some account of the religion of Rome.

6. Some account of the Servian Constitution.

7. What do you know of Rome's system of colonization? Compare with that of Greece.

8. What was the date, and what the leading incidents of the first Volscian war?

9. Explain precisely :

Comitia Centuriata-Lex Publilia-Consul-Rex Sacrificulus-Roman Republic-Provocare ad-appellare-Lex Valeria-reus-Tribuni Plebis.