1. SHEW, by an analysis of Plato's Apology, (1) the nature of the different charges against Socrates; (2) the line of defence which he adopted in each case ; and (3) the circumstances and probable causes of his condemnation. 2. Explain the Socratic mode of disputation. How is the effect of it described in the Meno of Plato? Translate and illustrate the following: Καὶ γὰρ οὖν καὶ τοῦτο ἐν τοῖς πρώτοις παρέλιπον, ὅτι καὶ οἱ λόγοι αὐτοῦ ὁμοιότατοί εἰσι τοῖς Σειληνοῖς τοῖς διοιγομένοις. εἰ γὰρ ἐθέλει τις τῶν Σωκράτους ἀκούειν λόγων, φανεῖεν ἂν πάνυ γελοῖοι τὸ πρῶτον· τοιαῦτα καὶ ὀνόματα καὶ ῥήματα ἔξωθεν περιαμπέχονται, Σατύρου ἄν τινα ὑβριστοῦ δοράν. ὄνους γὰρ κανθηλίους λέγει καὶ χαλκέας τινὰς καὶ σκοτοτόμους καὶ βυρσοδέψας, καὶ ἀεὶ διὰ τῶν αὐτῶν ταὐτα φαίνεται λέγειν, ὥστε ἄπειρος καὶ ἀνόητος ἄνθρωπος πᾶς ἂν τῶν λόγων καταγελάσειε. · διοιγομένους δὲ ἰδων ἄν τις καὶ ἐντὸς αὐτῶν γιγνόμενος πρῶτον μὲν νοῦν ἔχοντας ἔνδον μόνους εὑρήσει τῶν λόγων, ἔπειτα θειοτάτους καὶ πλεῖστα ἀγάλματα ἀρετῆς ἐν αὑτοῖς ἔχοντας καὶ ἐπὶ πλεῖστον τείνοντας, μᾶλλον δὲ ἐπὶ πᾶν ὅσον προσήκει σκοπεῖν τῷ μέλλοντι καλῷ κἀγαθῷ ἔσεσθαι. (PLATON. Sympos.) 3. Give a short sketch of the manner in which Socrates, in Xenophon's Memorabilia, has stated the argument for the being of a God derived from Final Causes. 4. Into how many sects did the school of Socrates divide itself, and who were their respective founders? From which did the Stoics arise? How did the Stoics define Virtue? in what respect did they differ from the Peripatetics. 5. What did Epicurus consider as the End of Being? By what train of reasoning did he arrive at that conclusion? in what manner did his moral system include the Virtues? in what did its defects consist? what were its practical effects? 6. To what sect did Cicero profess to belong? What school did he chiefly follow in his treatise De Officiis? What is the date of that treatise, and under what circumstances was it written? 7. Shew in what manner St Paul, in the 15th Chapter of the First Epistle to the Corinthians, connects the Resurrection of Christ with the doctrine of the General Resurrection of the Dead: and compare the terms in which the Apostle refers to his belief in a Future State with the language of Heathen Philosophers on the same subject. 8. Εἰ οὖν συνηγέρθητε τῷ Χριστῷ, τὰ ἄνω ζητεῖτε, οὗ ὁ Χριστός ἐστιν ἐν δεξιᾷ τοῦ Θεοῦ καθήμενος. Τὰ ἄνω φρονεῖτε, μὴ τὰ ἐπὶ τῆς γῆς. Ἀπεθάνετε γὰρ, καὶ ἡ ζωὴ ὑμῶν κέκρυπται σὺν τῷ Χριστῷ ἐν τῷ θεῷ. “Οταν ὁ Χριστὸς φανερωθῇ, ἡ ζωὴ ἡμῶν, τότε καὶ ὑμεῖς σὺν αὐτῷ φανερωθήσεσθε ἐν δόξῃ. (Col. ii. 1.) How do you explain the above passage? Give examples, from early Christian writers, of the change of moral character in the first converts; shew the difficulty of producing such a change, and the evidence resulting from it. 9. Translate and explain the following passages: Beginning, (1) Ὁ δὲ Φαρισαῖος ἰδὼν ἐθαύμασεν ὅτι οὐ, κ.τ.λ. (Luke xi. 38-42.) Beginning, (2) Ἄνδρες Εφέσιοι, τίς γάρ ἐστιν ἄνθρωπος, κ.τ.λ. (Acts xix. 35-40.) Beginning, (3) Σὺ δὲ παρηκολούθηκάς μου τῇ διδασκαλίᾳ, κ.τ.λ. (2 Tim. iii. 10-17.) 10. State the date and occasion of the letters of Pliny the Younger to Trajan respecting the early Christians. Translate the following, and add short explanatory notes: Affirmabant autem, hanc fuisse summam vel culpæ suæ, vel erroris, quod essent soliti stato die ante lucem convenire: carmenque Christo, quasi Deo, dicere secum invicem : seque sacramento non in scelus aliquod obstringere, sed ne furta, ne latrocinia, ne adulteria committerent, ne fidem fallerent, ne depositum appellati abnegarent: quibus peractis morem sibi discedendi fuisse, rursusque coeundi ad capiendum cibum, promiscuum tamen, et innoxium: quod ipsum facere desiisse post edictum meum, quo secundum mandata tua hetærias esse vetueram. Quo magis necessarium credidi, ex duabus ancillis, quæ ministræ dicebantur, quid esset veri et per tormenta quærere. Sed nihil aliud inveni, quam superstitionem pravam, immodicam. Ideo, dilata cognitione, ad consulendum te decurri. Visa est enim mihi res digna consultatione, maxime propter periclitantium numerum. Multi enim omnis ætatis, omnis ordinis, utriusque sexus etiam vocantur in periculum, et vocabuntur. Neque enim civitates tantum, sed vicos etiam atque agros superstitionis istius contagio pervagata est: quæ videtur sisti et corrigi posse. Certe satis constat, prope jam desolata templa cœpisse celebrari, et sacra solemnia diu intermissa repeti: passimque vænire victimas, quarum adhuc rarissimus emtor inveniebatur. Ex quo facile est opinari, quæ turba hominum emendari possit, si fiat pœni tentiæ locus. TRANSLATE into ENGLISH (with short explanations when requisite): Beginning, AT juveni oranti subitus tremor occupat artus,.... Beginning, Mænius, ut rebus maternis atque paternis..... Hon. Epist. 1. xv. 25-46. Beginning, Est aqua Mercurii portæ vicina Capenæ;.... OVID, Fast. v. 673-692. TRANSLATE into ENGLISH (with short explanations when requisite): Beginning, Καὶ οἱ μὲν Συρακόσιοι εὐθὺς αὐτῶν, κ.τ.λ. THUCYD. VII. 50. Beginning, Πολλὰ τοίνυν ἀπορηθεὶς πρὸς τῷ, κ. τ. λ. TRANSLATE into ENGLISH (with short explanations when requisite): Hom. Οd. ΧΙΧ. 215231. Beginning, Ἀλλ ̓, ὦ φίλη, τούτων μὲν ὧν ἔχεις χεροῖν, κ.τ.λ. SOPH. Elect. 431-452. Beginning, ' πᾶσιν ἀνθρώποισιν ἔχθιστοι βροτῶν, κ. τ.λ. Ending, 1. In an isosceles triangle the angles at the base are equal to each other; and if the equal sides be produced the angles below the base shall also be equal. Prove this also without construction, by superposition. 2. In a quadrilateral figure in which the adjacent sides are equal two and two, prove that the diagonals are at right angles to each other. Also if the sides be given, construct the figure which has the greatest area, 3. Prove that all the internal angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides; and that all the external angles are together equal to four right angles. In what sense are these propositions true of the polygon formed by joining in any order a number of points taken at random in a plane? 4. From a given point without a given circle it is required to draw a tangent to the circle. 5. In a given right line it is required to find a point such that the tangents drawn from it to two given circles exterior to each other shall be equal. 6. If two right lines be drawn bisecting the vertical angle of a triangle and its supplementary angle respectively, and be produced to cut the base or base produced, the distances of either point of section from the extremities of the base will be as the adjacent sides. Given the base of a triangle and the ratio of the sides, find the locus of the vertex. 7. By what proposition of Euclid may it be proved that if one of the sides of a right angle revolve about the other it will describe a plane? Give the proof. 8. Shew how to find the least common multiple of a set of integers; and find that of 299, 420, 3157, and 6006. 9. Find what fraction of 2 cwt. 3 qrs. 3 lbs. 8 oz. is of a ton, the fraction being expressed (1) as a vulgar fraction in its lowest terms, (2) as a decimal. 10. Find the cost of 1 ton, 3 cwt. 2 qrs. 12 lbs. at 7s. 13d. per stone, the price per lb., to the nearest half-penny, at which it must be sold to gain 10 per cent., and the exact percentage gained by selling at that price. 1. EXPRESS " + y" in terms of x + y and xy; and solve the equations: x+y-2z+3=0, x+y=4, (1) (x2 + y2) (x3 +y3) = 280. (2) 2x-3y-3z + 13 = 0, 2. Shew how to extract, when possible, the square root of a+√√b, where a and b are integers, under the form √x+√y, where x and y are rational. Find {73+√2304}. 3. A wants to pay B the sum of £1. 0s. 6d. but has only 8 half-crowns and 2 shillings about him, while B has 5 half-crowns and 12 shillings; in how many ways may the payment be effected? 4. Find the number of permutations of the letters a, b, c, &c. taken all together, and repeated, a, r times, b, s times, c, t times, &c. 5. Find the sines and cosines of 18° and 54o, and the sine of 3o. 6. Shew how to solve the equation a sin x+b cos x = c, by means of a table of logarithmic sines and cosines, a, b, and c being given by their logarithms. 7. In terms of the sides of any triangle, express the radii of the circumscribed circle, the inscribed circle, and the circle described so as to touch one side and the produced parts of the two others. 8. A person standing on the top of a hill observes the angular elevation of another hill-top, and the angular depression of its image in a lake; find the heights of the hills above the lake, the horizontal distance between their summits being known. 9. In the parabola, the chord of curvature at any point P is equal to 4SP. 10. Given the asymptotes of a hyperbola, a point in the curve, and a point in one of the asymptotes, required a geometrical construction for drawing through the latter point a tangent to the curve. 11. Find the condition that two straight lines whose equations, referred to rectangular axes, are given, shall be perpendicular to each other. Prove that the perpendiculars let fall from the angular points of a triangle on the opposite sides meet in a point. |