16. Find the values of x which satisfy the equation

tan3x-3 tan2x-3 tan x + I = 0.

17. Prove the formula in a spherical triangle

18. Prove that in an ellipse the sum of the squares of conjugate diameters is constant.

Translate the following passages into English Prose :

1. Beginning, Πέπεισμαι τοίνυν, ἦ δ ̓ ὅς, ἐγώ, ὡς πρῶτον μέν, κ. τ. λ. Ending, τό τε ὕδωρ καὶ τὴν ὁμίχλην καὶ τὸν ἀέρα.

Phaedo, lviii.

Protag., viii.

2. Beginning, οὗτοι πάντες, ὥσπερ λέγω, φοβηθέντες, κ. τ. λ. Ending, τοιοῦτον πρὸς τοῖς ἄλλοις καὶ πανοῦργον εἶναι.

3. Beginning, Ταῦτά τε οὖν πάντα πρὸς τὸν Πιττακὸν εἴρηται, κ. τ. λ. Ending, ὡς ὄντων τινῶν, οἱ ἑκόντες κακὰ ποιοῦσιν.

Ibid., xxxi.

4. Beginning, Τὰ δὲ τῶν ἀρχῶν καὶ τιμῶν ὧδ ̓ εἶχεν ἐξ, κ. τ. λ. Ending, κατὰ κορυφὴν αὐτῆς ἔσφαττον κατὰ τῶν γραμμάτων.

Critias, xi.

1. To what sources does Grote trace the dialectic method of Socrates, and what were the objects sought by that method?

2. Show that Plato's views were such as naturally brought him into collision with the Sophists.

3. How does Grote argue that the views of Kallikles in connexion with justice could not, on Plato's own showing, have been adopted by the Sophists?

4. How does Protagoras describe the special objects of his system of instruction, in the Dialogue named from him?

5. What two important elements in dialectic reasoning does Aristotle, as quoted by Grote, state to have originated with Socrates?

6. In what respects did Socrates regard special trades or professions as analogous to Ethical Science ?

7. What was the political charge against Socrates noticed by Xenophon ? Grote notices its probable effect at Athens, and defends Socrates in reference to it?

8. What remark is made in the context as to the construction of ἑκών in the third passage in the clause πάντες δὲ ἐπαίνημι καὶ φιλέω ἑκὼν ὅστις ἔρδῃ μηδὲν αἰσχρόν ?

9. Translate the following passages, making notes where required :

α. Τί; ἔφη· ὑμῖν τὰ λεχθέντα μῶν μὴ δοκεῖ ἐνδεῶς λελέχθαι; πολλὰς γὰρ δὴ ἔτι ἔχει ὑποψίας καὶ ἀντιλαβάς, εἴ γε δέ τις αὐτὰ μέλλει ἱκανῶς διεξιέναι.

6. Οὐκοῦν αὖ ὡμολογήσαμεν ἐν τοῖς ἔμπροσθεν μήποτ' ἂν αὐτήν, ἁρμονίαν γε οὖσαν, ἐναντία ᾄδειν οἷς ἐπιτείνοιτο καὶ χαλῴτο καὶ πάλλοιτο καὶ ἄλλο ὁτιοῦν πάσχοι ἐκεῖνα, ἐξ ὧν τυγχάνει οὖσα.

ε. ̓Αλλὰ κἂν εἰ ὀλίγον ἔστι τις ὅστις διαφέρει ἡμῶν προβιβάσαι εἰς ἀρετήν, ἀγαπητόν.

d. Νῦν δ ̓ ἐστὶν ὥσπερ ἂν εἰ δέοιό μου

τῶν δολιχοδρόμων τῳ ἢ τῶν ἡμεροδρόμων διαθεῖν τε καὶ ἕπεσθαι. εἴποιμι ἄν σοι, ὅτι πολὺ σοῦ μᾶλλον ἐγὼ ἐμαυτοῦ δέομαι θέουσι τούτοις ἀκολουθεῖν.

CICERO.

PROFESSOR BRADY.

Translate, adding short notes where necessary :

1. Beginning, Utinam ille omnes secum copias suas eduxisset ! . Ending, verum etiam si edictum praetoris ostendero, concident.

2. Beginning, Quamquam me tuae litterae sustentant : Ending, ut tibi placet, Thessalonicae tenet.

In Cat., ii. 2, 3.

......

Epist. ad Att., iii. 9.
De Domitio,....

3. Beginning, De Trebonio prorsus tibi assentior. Ending, Eum, quia non videbam, abesse putabam.

4. Beginning, Laodiceam veni pridie Kal. Sext. Ending, impositae, plane non est nostrum onus.

Ibid., iv. 8.

Ibid., v. 15.

5. Beginning, Diem tuum ego quoque ex epistola quadam tua, Ending, quantum quasi sit in trientis triente.

....

Ibid., vii. 8.

6. Beginning, De Varrone loquebamur; lupus in fabula. . . . . . Ending, tamen remanserunt: ceciditque belle.

Ibid.,

xiii. 33.

1. Mention some of what you consider the most successful emendations of the text of Epist. ad Att. I. and II.

2. Translate and explain the following, and mention in what context they occur:

(α). τὸ ἐπὶ τῇ φακῇ μύρον.

(4). τίς πατέρ ̓ αἰνήσει ;

(ε). Πουλυδάμας μοι πρῶτος ἐλεγχείην ἀναθήσει.

(α). πρόσθε λέων ἔπιθεν δὲ—

(ε). ἑλικτὰ καὶ οὐδέν.

3. Explain - litteras attulerunt non tam exploratas a timore— superficiem consules ex Senatus consulto aestimabunt-Itaque oratio iuventuti nostrae deberi non potest viaticum Crassus praeripit — Balbτns mea-hic Abdera.

4. What do we read in I.-IV. of Catilina; Tadius; eopávns; Vettius; Milo; Tyrannio?

5. What are the Latin equivalents for the following epistolary phrases?-(a) "to send, deliver, a letter." (b) "My son sends you his love." (c) "do please come." (d) "letters of the same purport." (e) as to your saying that, &c." (f) "in your note of the 7th inst." (g) so believe me yours, &c." (h) much obliged."

66

6. By what considerations was Caesar guided in his treatment of the vanquished party? His greatest difficulties began only after the

victory?

7. Show that it was not the object of Caesar to establish a military despotism.

8. Describe some of the most characteristic features of social life at Rome at the close of the republican period.

9. The idea of an Helleno-Italic state did not originate with Caesar? 10. In what respects are Sisenna and Cornelius Nepos representative writers in Roman historical literature?

11. What do you understand by Alexandrinism?

12. Describe the educational system at Rome in the last century of the Republic. What were the seven liberal arts ?

MR. PALMER.

Translate the following into Greek Prose:

"Domestic discord," answered she, "is not inevitably and fatally necessary; but yet it is not easily avoided. We seldom see that a whole family is virtuous: the good and evil cannot well agree; and the evil can yet less agree with one another: even the virtuous fall sometimes to variance, when their virtues are of different kinds, and tending to extremes. In general, those parents have most reverence who most deserve it: for he that lives well cannot be despised.

"Many other evils infest private life. Some are the slaves of servants whom they have trusted with their affairs. Some are kept in continual anxiety to the caprice of rich relations, whom they cannot please,

and dare not offend. Some husbands are imperious, and some wives perverse: and, as it is always more easy to do evil than good, though the wisdom or virtue of one can very rarely make many happy, the folly or vice of one may often make many miserable."

"If such be the general effect of marriage," said the prince, " I shall, for the future, think it dangerous to connect my interest with that of another, lest I should be unhappy by my partner's fault."-JOHNSON.

Translate the following into Latin Prose:

66

I will also relate another anecdote, all vanity to myself, but you will partake of it. A person sent me a letter, and directed as follows, "Horatio Nelson, Genoa." On being asked how he could direct in such a manner, his answer, in a large party, was, Sir, there is but one Horatio Nelson in the world." The letter certainly came immediately. At Genoa, where I have stopped all their trade, I am beloved and respected, both by the Senate and lower order. If any man is fearful of his vessel being stopped, he comes and asks me; if I give him a paper, or say, "All is right," he is contented. I am known throughout Italy; not a Kingdom, or State, where my name will be forgotten. This is my Gazette.-NELSON.

Translate into Latin Elegiac Verse:-
:-

O, open the door, some pity to show;
Keen blows the Northern wind:
The glen is white with the drifted snow,
And the path is hard to find.

The hare is crouching in her form,
The hart beside the hind;
An aged man, amid the storm,
No shelter can I find.

You hear the Ettricke's sullen roar,
Dark, deep, and strong is he;
And I must ford the Ettricke o'er,
Unless you pity me.

The iron gate is bolted hard,

At which I knock in vain;

The owner's heart is closer barred,
Who hears me thus complain.

Farewell! farewell! and Mary grant,
When old and frail you be,
You never may the shelter want
That's now denied to me.

The ranger on his couch lay warm,
And heard him plead in vain ;
But oft, amid December's storm,
He'll hear that voice again :

For, lo! when through the vapours dank,
Morn shone on Ettricke fair,

A corpse amid the alders sank,

The Palmer weltered there.

Translate into Greek Tragic Iambics :

EMIL. [Within.] What! ho! my lord! my lord!

Отн.

Who's there?

EMIL [Within.] O, good my lord, I would speak a word with you. Yes;--'tis Emilia ;-by-and-by--she's dead.

Отн.

'Tis like she comes to speak of Cassio's death;
The noise was high. Ha! no more moving?

Still as the grave. Shall she come in? Were't good?

I think she stirs again :-No.-What's the best?

If she come in she'll sure speak to my wife.

My wife! my wife! what wife?-I have no wife :
Methinks it should be now a huge eclipse

Of sun and moon, and that the affrighted globe
Should yawn at alteration.

Logics.

MILL. BOOK II.

DR. SHAW.

1. (a). Mill enumerates three species of apparent but not real inference?

third.

2.

(8). Show that there is a close analogy between the second and

One of the masters of chemistry was Berzelius;

Berzelius was a Swede:

One of the masters of chemistry was a Swede.

(a). On what grounds does Bain deny that there is any real deductive inference in this form of syllogism?

(8). On what grounds does Mill dissent ?

3. (a). What sort of arguments fall most naturally into the 2nd, 3rd, and 4th figures, respectively?

(8). Lambert exhibits the conclusiveness of these three forms without reducing them to fig. I; how?

4. (a). If p per cent. of A are B, and 9 per cent. of A are C, what is the least percentage of A that those individuals make up which are both B and C ?