10. Three consecutive numbers are such that the middle one is a prime number greater than 3 ; prove that one of the other two is divisible by 6. MR. F. PURSER. 11. Determine the dimensions of a rectangular brick, being given that its total surface is 76 square inches, its solid contents 40 cubic inches, and the perimeter of one of its faces 18 inches. 12. Solve the equation (x2 - 1)(x2 + 2x – 1) = 6x + 9. 14. If 1, M, v denote three unequal positive quantities, prove that the product of the three arithmetic means of the quantities taken in pairs is greater than the product of the three quantities. 15. Given U=VII – x2)(1 – y2) + xy VII – k+ x2)(I – k2 y2), V = V(I – 2) (1 - y2) – xy V(I – k? 22)(1 – k* y2); prove that UV contains [ – k? x2 ya as a factor, and determine the other factor. Classics. MR. L. C. PURSER. Translate into English :1. Beginning, νύν δε θεωρών και σκοπών ευρίσκω την μεν, κ. τ.λ. Ending, πόλεμον πολεμήσειν υπέρ αυτών αναδέξασθαι. DEMOSTHENES, Olynth., p. 19. 2. Beginning, προς δή ταύτα εκείνο υμάς υπολαμβάνειν δεί, κ.τ.λ. Ending, εκείνα δε τούτοις αν προσήν, ει μή διά τούτους. ID., Fals. Leg., p. 369. 3. Beginning, Έτι τοίνυν κακείνο σκοπείτε, ώ άνδρες δικασται, κ.τ.λ. Ending, τους αυτούς ήδικηκότας και αλλ' ου διά ταύτα. Ibid., p. 4ο9. 4. Beginning, σκοπείτε γάρ. άνθρωπος πολλά και δεινά, κ. τ.λ. Ending, ασφαλές υμίν δεδωροδοκηκότα τούτον αθώον εασαι. Ibid., p. 423. 5. Beginning, “Ο τι τοίνυν δύναται ταύτα ποιείν, κ.τ.λ. Ending, μή τι ποιήσαντί γε η συγκαταπραξαμένω. ID., De Chers., p. 95. 1. Translate έφη τον Σόλωνα ανακείσθαι είσω την χείρα έχοντα άναβεβλημένον. 2. How does Shilleto propose to emend υμάς εξηπάτηκεν, άδοξεί, δίκαιος απολωλέναι κρίνεται ? 3. Explain διά ταύτα έσπαθάτο ταύτα: πώμαλα : έκπωματ’ άργυρα προύπινεν αυτοίς: εν χορηγίοις αλλοτρίοις παρατρεφόμενον: ενοχλείν: αποκαλεϊν: παρεκλέγειν τα κοινά: ωτακουστεϊν: οι τα μέταλλα εωνημένοι: τη τετράδι φθίνοντος ήκκλησιάζετε. 4. Write notes on—(1) Construction of verbs of fearing ; (2) Negatives after ώστε; (3) Construction of indefinite relative sentences ; (4) Formation of desiderative verbs. 5. What policy did Demosthenes advocate in his speech for the Megalopolitans ? 6. What was the political position and influence of Eubulus, and of Phocion? 7. The Athenians were not altogether unreasonable in hesitating to apply the Theoric fund to military purposes ? Wbat course did Demosthenes take on the question ?; 8. In the negotiations for peace in 346, corrupt mendacity appears to be the only explanation of Æschines' conduct in certain respects : what respects ? Where in these negotiations is Demosthenes to blame, and what excuses may be urged for his conduct ? 9. What was the Peace of Demades ? What remarks do Polybius and Grote make on it? 10. Who were Charidemus, Diopeithes, Hypereides, Meidias, Phry. non ? MR. MAHAFFY. Translate the following passages :1. Beginning, Iam vero narrationem quod iubent veri, .... Ending, efficit non difficilius arte coniuncta. CICERO, De Orat., ii. 19. 83, 84. 2. Beginning, Ita fit, ut unum genus in eis causis, Ending, quod totum a facti controversia separatum est. Ibid., ii. 26. III, 112. 3. Beginning, Ea vi sua verba pariet, quae semper satis, Ending, quas venere et pervestiges, quod quaeras. Ibid., ii. 34. 146, 147. 4. Beginning, Atque haec omnia verbo continentur. Ending, non in re, sed in verbis posita ducantur. Ibid., ii. 64. 257, 258. 5. Beginning, Verum si a Chrysogono, iudices, Ending, sicarii iugulare non potuissent ? ID., Orat. pro Lex Roscio Amerino, 150, 151. 1. Give Cicero's sketch of Greek oratory. 5. What dominions were left to the Romans by testament ? Give dates. 6. Describe the war with the pirates. MR. GRAY. Translate into Latin Prose : When it was announced, that the detachment was bringing Syphax to the camp, the whole multitude poured out, as if to the sight of a triumph. He preceded the rest in chains, and was followed by a number of noble Numidians. On this occasion, everyone spoke in the most exalted terms of the greatness of Syphax, and the fame of his nation ; thus exaggerating the renown of their victory. “ That was the king,” they said, “ to whose dignity the two most powerful states in the world, the Roman and Carthaginian, had paid such deference; that for the sake of procuring his friendship, their own general, Scipio, leaving his province and his army, sailed with only two quinqueremes to Africa ; and the Carthaginian general, Hasdrubal, not only visited his kingdom, but also gave him his daughter in marriage. That the Roman and Carthaginian generals had been within his grasp at one and the same time. That as both parties had, by the offer of sacrifices, solicited the favour of the immortal gods, so his friendship had been equally sought for by both. That he lately possessed power so great as to enable him to expel Masinissa from his kingdom ; and to reduce him 10 such a state, that his life was preserved by a report of his death, and by lurking in concealment, while he was obliged, like a wild beast, to live in the woods on prey.” Such were the discourses of the throng, through which the king was led to the general's quarters. Translate into Greek Prose : “That you would wish, O men of Athens, to recover that power which you formerly possessed, we all know; and by what means is it more likely that this object should be effected, than by succouring, of yourselves, those who are oppressed by the Lacedæmonians ? Be not afraid of them because they rule over many states, but rather be greatly encouraged, by that consideration, to resist them; reflecting that you yourselves, when you had the greatest number of subjects, had also the greatest number of enemies. As long, indeed, as they had nobody to whom they could revolt, they concealed their enmity against you; but when the Lacedæmonians stood forward as leaders, they at once showed what their feel. ings towards you were; and be assured that if you and we, on the present occasion, appear openly uniting our strength against the Lacedæmonians, many who cherish hatred to them will openly declare it. Translate into Latin Verse : Thus pray'd Tydides, and Minerva heard, Be bold (she cry'd) in ev'ry combat shine, Translate into Greek Iambics : He sought alone the good of those for whom |