4. The area of a triangle whose vertex is at the point on an ellipse x = a cos o, y = b sin ø, and whose sides pass through the foci, is 4abe sin (1 − e2 cos2ø) I - 2e2 cos 2p + et 5. Investigate the maximum and minimum values of this expression. 7. When the equation (a, b, cd, e) (x, 1)1 = o has a double root a, prove that dK 13 a = 4 dK 8. If two conics intersect in four real or four imaginary points, their common self-conjugate triangle has all its sides real? (a). In case two points of intersection are imaginary, two sides of this triangle are imaginary? 9. Find the foci of the conic given by the general equation. 10. Putting U = (a, b, c, d) (x, 1)3, V = (a1, b1, c1, di) (x, 1)3, W = (a2, b2, C2, d2) (x, 1)3, prove that the determinant 11. Find a pair of conjugate diameters of an ellipse such that the sum of the perpendiculars from their extremities on the axis major shall be a maximum. 12. Find the conditions which must be fulfilled when the equations x3 +px2+qx+r=0, x3+p2x2 + q'x + r′ = o have two common roots; find also the third root of each, and the quadratic whose roots are those common to both. where λ=(a+B-y-8)2, μ=(a+y-B-8)2, v = (a + d − B − y)3. 14. Find the condition that two circles x2 + y2 + 2gx + 2ƒy + c = 0, x2 + y2 + 2g′x + 2ƒ'y + c′ = 0, should cut orthogonally; and hence prove that the circle which cuts three circles So, S'= o, S" = o orthogonally cuts also every circle whose equation is of the form IS +mS′+nS" = o orthogonally. 15. Prove (a) that two points on an ellipse, the difference of whose eccentric angles is constant, form with the centre a triangle whose area is constant; (b) that two points, the sum of whose eccentric angles is constant, are connected by a chord of constant direction. 1. Beginning, εἰ μὴ 'γὼ παράφρων μάντις ἔφυν καὶ γνώμας, κ. τ. λ. Ending, τοῖς δρῶσι καὶ συνδρῶσιν. 2. Beginning, εἰ θέμις ἐστί μοι τὰν ἀφανῆ θεὸν, κ. τ. λ. Ending, σέ τοι κικλήσκω τὸν αἰένυπνον. SOPHOCLES, Electra, 472-498. EDIPUS, Col., 1556-1578. Antig., 816-838. 3. Beginning, ΧΟ. οὐκοῦν κλεινὴ καὶ ἔπαινον ἔχουσ', κ. τ. λ. Ending, ἔγκληρα λαχεῖν μέγ ̓ ἀκκῦσαι. 4. Beginning, ΟΔ. τί δ ̓ ἐργασείεις; κ. τ. λ. Ending, ἄφιλον ἔρημον ἄπολιν ἐν ζῶσιν νεκρόν. Phil., 1001-1018. I. Scan the following lines :- α. πιθοῦ θελήσας φρονήσας τ', ἄναξ, λίσσομαι. δ. ὅτ ̓ ἐς τόνδ' Ατρειδῶν ὕβρις πᾶσ ̓ ἐχώρει. 2. Write notes on the following : : α. ὑφ' οὗ κενοῦται δῶμα Καδμειον, μέλας δ' 3. Mr. Davies has remarked that synaphaea of this sort is only admissible in certain cases in Iambic trimeter ? β. νῦν οἱ σέθεν χρῄζοντες ἐκκαλοῦσί με. γ. σὺ δ ̓ ἐμπολήσας ἢ τεκών μ' αὐτῷ δίδως; ε. πύργοι μὲν οἵ πόλιν στέγουσιν. ζ. σπεύδειν ἄπο ρυτῆρος. Account for accentuation. θ. οὐ γάρ ἔσθ ̓ ὅπως πόλιν κείνην ἐρείψεις. What is the MS. reading ? 4. What influence had the writings of Herodotus on Sophocles? One remarkable scene in the Oedipus Rex reminds us of a passage in the first book of Herodotus ? 5. Some editors of Sophocles fall into the error of attempting to construe two constructions on the meanings in passages, where “ robust scholars,” according to Dr. Kennedy, insist on one only: can you give any instance from the Oedipus Rex? 6. What explanation of the following passage has been given by Dr. Kennedy? ἀλλ ̓ εὐτυχὴς ἵκοιτο τῇ θ ̓ αὐτοῦ πόλει ἐμοί τε. τίς γαρ ἐσθλὸς οὐχ αὑτῳ φιλος ; 7. The distinguishing feature of the poetry of Sophocles corresponds with the distinguishing feature of his character as mentioned by Aristophanes ? 8. To which play of Sophocles do you give the preference, and on what grounds? 9. Write notes on the usage of the following words in Sophocles : κεύθω πρεσβεύω, τομάω, ξενίζω, μασχαλίζω, ἐπιστροφή, στόμωσις, προμνάομαι. 10. Mention any words which have different quantities in choral odes from their ordinary one. 11. State some of the more remarkable instances of prolepsis in Sophocles. PLAUTUS AND TERENCE. PROFESSOR BRADY. Translate: 1. Beginning, Dum haec loquimur, interea loci ad macellum ubi aduen ...... tamus, Ending, Vocabula, parasiti ita ut Gnathonici uocentur. TERENCE, Eun., act ii. 255-264. ...... 2. Beginning, Texentem telam studiose ipsam offendimus, Ending, Ancillas primum, ad dominas qui adfectant uiam. Ibid., Heaut. Timor., act. ii. 285-301. 3. Beginning, Nam ego ad Menaechmum nunc eo, quo iam diu Ending, Menaechmum eccum ipsum video; progreditur foras. PLAUTUS, Menaech., act 1. sc. i. 20–33. 4. Beginning, Ubi illae armillae [sunt], quas una dedi? Ending, ut, quantum possit, quamque liceat, ueneant. Ibid., act III. sc. iii. 13-25. 5. Beginning, Miser homo est, qui ipse sibi, quod edit, quaerit, et id aegre inuenit;...... Ending, neque ridiculos iam terunci faciunt; sese omnes amant. 1. What alterations have been made in the following lines by modern editors, and for what reasons? (a). Satis mihi id habeam supplicii dum illos ulciscar modo. Adelp. (b). Mi. Quid tristis es? De. Rogas me ubi nobis Aeschinus Ibid. (c). Qui omnia sibi post putavit esse prae meo commodo. Ibid. (d). Ita eum tum timidum ibi obstupefecit pudor. Phor. (e). Senex obsonari filiai in nuptiis. (ƒ). Si id palam fecisset. Exemi ex manu manubrium. Aul. Ibid. Graecia 2. (). Translate and explain:-Quid me vobis tactio est? exotica. Tribus vide quod sit satis. Ita fugias ne praeter casam. Una iniuriast tecum. Stataria fabula. Defugere auctoritatem. (b). What special senses attach in Plautus to-Vae capiti tuo! Haud uidi magis. Sed quid ais ? 3. Scan the following lines, and notice the peculiarities of metre or prosody which they illustrate: (a). Nam expedit bonas esse vobis; nos, quibuscum est res, non sinunt. (b). Et ad portitores esse delatam; hanc petam. (c). Per oppressionem ut hanc mi eripere postulat. (g). Ilico res foras labitur, liquitur. 4. Nam quod isti dicunt maliuoli, homines nobiles Prol. Adelph. Write a note on this passage, and remark on the way in which Terence meets the alleged charge. 5. (a). Quote and comment on Horace's criticisms of Plautus. (b). Give the well-known epigram of Caesar on Terence. 6. To what circumstances may we attribute the want of originality in Roman Comedy? In what points did the Roman adapters principally deviate from the originals? 7. Quote some of the political allusions in the plays of Plautus. 8. Nam quod rumores distulerunt maliuoli Multas contaminasse Graecas dum facit Prol. Heaut. Illustrate this practice from what is known of the construction of several plays of Terence. 9. Certain analogies may be remarked between Plautus and Shakspere? 10. Sketch in a brief essay a Plautine "Parasitus" or "Miles gloriosus." How does the latter character reappear in modern dramatic literature? MR. POOLE. Translate into Greek Prose : The empire of the Arabs, which had been the work of a military fanaticism, verged to its decline, as soon as their ardour received a new direction towards the refinement which adorned the triumph of their arms: the suddenness too of its vast acquisitions had hindered them from being consolidated into one firmly united dominion, and the empire sunk under the weakness of its manifold divisions. Another instrument was accordingly brought into action, not fitted indeed for the splendid destinations of the Arabian empire, but possessing in its rudeness a character of greater stability, and not rendered unwieldy by an excessive magnitude. When the vigour of the southern conquerors had been dissolved in the luxury of empire, it seems to have been even necessary that the rougher nations of the north should be brought down upon the corrupted warriors of the south, to arrest the progress of their depravation, and to fix them in a stationary barbarism.-MILLER. |