2. Deduce from the Dictum the conclusiveness of the received modes, and show that we are naturally led to the operations indicated by the significant letters in their names.

3. Given the three propositions of a Syllogism, show how to construct it.

4. Show the conclusiveness of Reductio ad impossibile as applied to any of the received modes not in the first figure.

5. Prove that if the reducend mode violate any of the general rules, Reductio ad impossibile will lead to a reduct which also violates them.

6. If a sorites be resolved into a number of legitimate syllogisms, determine how far it is true that the conclusion of the last syllogism is the same as that of the sorites.

7. From what sort of a proposition can the greatest number of deductions be made? Determine the number.

8. Point out the fallacies in the following arguments :

a. "A quantity, say a foot, has an infinity of parts. Any part of this quantity, say an inch, has also an infinity. But one infinity is not larger than another therefore an inch is equal to a foot."-Sir W. Hamilton's Metaphysics.

b. Whatever body is in motion must move either in the place where it is, or in a place where it is not. Neither of these is possible: therefore there is no such thing as motion.

c. Of two contradictory propositions one is always true: hence matter is either divisible to infinity, or is made up of certain absolutely smallest parts.

d. No cat has two tails. Every cat has one tail more than no cat: therefore every cat has three tails.

Classics.

PLATO.

MR. MAHAFFY.

Translate the following passages

I. Beginning, "Αν οὖν τύχῃ ὁ ἐρόμενος ἡμᾶς ὑβριστὴς ὤν, κ. τ. λ.
Ending, ἐὰν δὲ τὰ ἡδέα ὑπὸ τῶν ἀνιαρῶν, οὐ πρακτέα.

Protagoras, sec. cxi.

2. Beginning, ΣΩ. Ὦ μακάριε, οὐκ οἶσθ ̓ ὅτι τὰ πρῶτα, κ. τ. λ. Ending, ἐπὶ τήν κορυφὴν δεῖ τῶν εἰρημένων ἐλθεῖν.

Cratylus, sec. xxviii.

3. Beginning, Οὐκοῦν οἶσθα, ἦν δ' ἐγώ, ὅτι οἱ βαφεῖς, κ. τ. λ. Ending, παντὸς ἄλλου ῥύμματος.

d

De Republica, lib. iv.

1. Give an outline of Mr. Grote's remarks on the literary and scientific characteristics of early Greek philosophy.

2. He contrasts the early history of the Platonic school with that of Aristotle? Give some account of both.

3. Give an account of the life and literary labours of Demetrius Phalereus.

4. Discuss the value of the Thrasyllean canon.

5. By what considerations does Mr. Grote attempt to determine the dates of the Dialogues?

6. What are the peculiar philosophical principles discussed in Plato's Epistles?

7. Explain, on Mr. Grote's principles, the discrepancies between the Phado and the Apology, and refer them to their respective places in the canon of Thrasyllus.

8. What reasons may be assigned for Plato's adopting the form of dialogue in his compositions?

CICERO.

MR. PALMER.

Translate the following passages into English :

1. Beginning, Noster autem status est hic. Apud bonos iidem sumus,.. Ending, Tionpacías sine ulla pastoricia fistula auferebamus.

Epistola, xxi. 6.

2. Beginning, A scribendo prorsus abhorret animus... Ending, Quando te proficisci istinc putes, fac, ut sciam.

Ibid., xxii. 2.

3. Beginning, Parva sunt, quæ desunt, nostris quidem moribus, . Ending, quam omnes leges, omnesque judices.

......

Ibid., cxli. I.

4. Beginning, Interim rejectis legationibus in Idus,.. Ending, Clodiani nostros consputare cœperunt.

Ibid., xcix. 3.

1. Write explanatory notes, where necessary, on the first three pas

sages.

2 Draw out a chronological table giving the dates of the chief events of Cicero's life.

3. When did Cicero make use of the following expressions, which are quoted by Forsyth and Mommsen from his letters, and what does he mean by them?—

Scito me asinum germanum fuisse.

Clitella bovi sunt impositæ.

Vellem Idibus Martiis me ad coenam invitasses: reliquiarum nihil fuisset.

1

4. From what period does Livy date the decay of the Roman aristocracy?

5. What evil consequences are traceable to the Galatian war?

6. What was the occasion of the foundation of Aquileia?

7. What date does Polybius assign to the beginning of the universal empire of Rome? Mommsen notices a great change in her foreign policy from this time?

8. Explain the following:-prensare, divisores, prævaricatio, sententiam excedere, attribuere: solvere ab argentario.

MR. FERRAR.

Translate the following passage into Greek Prose :

The sentiments, in an epic poem, are the thoughts and behaviour which the author ascribes to the persons whom he introduces, and are just, when they are conformable to the characters of the several persons. The sentiments have likewise a relation to things as well as persons, and are then perfect when they are such as are adapted to the subject. If in either of these cases the poet endeavours to argue or explain, to magnify or diminish, to raise love or hatred, pity or terror, or any other passion, we ought to consider whether the sentiments he makes use of are proper for those ends. Homer is censured by the critics for his defect as to this particular in several parts of the Iliad and Odyssey, though, at the same time, those who have treated this great poet with candour have attributed this defect to the times in which he lived. It was the fault of the age, and not of Homer, if there wants that delicacy in some of his sentiments which now appears in the works of men of a much inferior genius. Besides, if there are blemishes in any particular thoughts, there is an infinite beauty in the greatest part of them. In short, if there are many poets would not have fallen into the meanness of some of his sentiments, there are none who could have risen up to the greatness of others.

ADDISON.

Translate the following passage into Greek Verse:—

Wol.

What should this mean?

What sudden anger's this? how have I reap'd it?
He parted frowning from me, as if ruin

Leap'd from his eyes: so looks the chafed lion
Upon the daring huntsman that has gall'd him;
Then makes him nothing. I must read this paper:
I fear, the story of his anger.-'T is so :
This paper has undone me: 'T is the account
Of all that world of wealth I have drawn together
For mine own ends; indeed, to gain the popedom,
And fee my friends in Rome. O negligence,
Fit for a fool to fall by! What cross devil
Made me put this main secret in the packet
I sent the king? Is there no way to cure this?

No new device to beat this from his brains?
I know 't will stir him strongly; Yet I know
A way, if it take right, in spite of fortune
Will bring me off again. What's this "To the Pope?"
The letter, as I live, with all the business
I writ to his holiness. Nay then, farewell!
I have touch'd the highest point of all my greatness:
And, from that full meridian of my glory,
I haste now to my setting. I shall fall
Like a bright exhalation in the evening,
And no man see me more.

SHAKSPEARE.

Translate the following passage into Latin Prose :—

If a superior mind should assume the protection of others just beginning to move among the dangers I have described, it would probably be found, that delusions springing from their own virtuous activity were not the only difficulties to be encountered. Even after suspicion is awakened, the subjection to falsehood may be prolonged and deepened by many weaknesses both of the intellectual and moral nature; weaknesses that will sometimes shake the authority of acknowledged truth. There may be intellectual indolence; an indisposition in the mind to the effort of combining the ideas it actually possesses, and bringing into distinct form the knowledge, which in its elements is already its own: there may be, where the heart resists the sway of opinion, misgivings and modest self-mistrust in him who sees that, if he trusts his heart, he must slight the judgment of all around him :-there may be too habitual yielding to authority, consisting, more than in indolence or diffidence, in a conscious helplessness and incapacity of the mind to maintain itself in its own place against the weight of general opinion; and there may be too indiscriminate, too undisciplined, a sympathy with others, which by the mere infection of feeling will subdue the reason.-COLERIDGE.

Translate the following passage into Latin Verse :-

She is far from the land where her young hero sleeps,
And lovers are round her sighing;

But coldly she turns from their gaze, and weeps,
For her heart in his grave is lying.

She sings the wild song of her dear native plains,
Every note which he lov'd awaking;-
Ah! little they think, who delight in her strains,
How the heart of the Minstrel is breaking.

He had liv'd for his love, for his country he died,
They were all that to life had entwin'd him;
Nor soon shall the tears of his country be dried,
Nor long will his love stay behind him.

Oh! make her a grave where the sunbeams rest

When they promise a glorious morrow;

They'll shine o'er her sleep, like a smile from the West,
From her own lov'd island of sorrow.

1. If a quadrilateral be inscribed in a circle, the rectangle under the diagonals is equal to the sum of the rectangles under the opposite sides. 2. Prove the converse of this: that if the rectangle under the diagonals of a quadrilateral be equal to the sum of the rectangles under the opposite sides, it is circumscribable by a circle.

3. In a given segment of a circle inscribe the rectangle of maximum

area.

4. A circle described through the feet of the perpendiculars from the angles of a triangle on the opposite sides bisects the sides.

5. Prove from the twelfth and thirteenth Propositions of Euclid, Book II., the formula for determining the area of a triangle in terms of the sides.

6. When, of a quadrilateral inscribed in a circle, two opposite sides touch a second circle, the remaining two touch a third circle coaxal with the first and second, and the four points of contact with the two circles touched are in a straight line.

MR. TOWNSEND.

7. Find the locus of a point P, the sum of whose distances from any number of given lines A, B, C, D, &c., shall be given.

8. Find the envelope of a line L, the sum of whose distances from any number of given points A, B, C, D, &c., shall be given.

9. For two triangles whose vertices and sides correspond in pairs, prove that when the connectors of corresponding vertices are concurrent the intersections of corresponding sides are collinear, and conversely.

10. Show that every two triangles, one inscribed and the other circumscribed to a circle at the same three points on its circumference, are connected as in the preceding question.