ΓΟΡΓΩ. μὴ λέγε τόν τεόν ἄνδρα, φίλα, Δείνωνα τοιαῦτα, αἰσθάνεται τό βρέφος, καὶ τὰν πότνιαν. ΓΟΡΓΩ. ἀπφῦς μὲν τῆνος τὰ πρόανλέγομες δὲ πρόαν θην ΓΟΡΓΩ. χώμὸς ταῦτά γ ̓ ἔχει, φθόρος ἀργυρίω, Διοκλέιδας· θασόμεναι τὸν Αδωνιν· ἀκούω χρῆμα καλόν τι κοσμῖν τὰν βασίλισσαν. Describe the feast of Adonis. Theocriti Idyllion, XV. 3. Translate-Τάχα δ ̓ οὖν ταῦτα μυθός σοι δοκει λέγεσθαι ὥσπερ γραὸς καὶ καταφρονεῖς αὐτῶν, καὶ οὐδὲν γ ̓ ἄν ἦν θαυμαστὸν καταφρονειν τούτων, εἴ πῃ ζητοῦντες εἴχομεν αὐτῶν βελτίω καὶ ἀληθέστερα εὑρειν· νῦν δὲ ὁρᾷς, ὅτι τρεῖς ὄντες ὑμεῖς, οἵπερ σοφώ τατοί ἐστε τῶν νῦν Ἑλλήνων, σύ τε καὶ Πῶλος καὶ Γοργίας, οὐκ ἔχετε ἀποδεῖξαι, ὡς δεῖ ἄλλον τινὰ βίον ζῆν ἢ τοῦτον, ὅσπερ καὶ ἐκεῖσε φαίνεται συμφέρων. ἀλλ ̓ ἐν τοσούτοις λόγοις τῶν ἄλλων ἐλεγχομένων μόνος οὗτος ἠρεμεῖ ὁ λόγος, ὡς ἐυλαβητέον ἐστὶ τὸ ἀδικεῖν μᾶλλον ἢ τὸ ἀδικεῖσθαι, καὶ παντὸς μᾶλλον ἀνδρὶ μελετητέον οὐ τὸ δοκειν εἶναι ἀγαθὸν ἀλλὰ τὸ εἶναι, καὶ ἰδίᾳ καὶ δημοσίᾳ· ἐὰν δέ τις κατά τι κακὸς γίγνηται, κολαστέος ἐστί, καὶ τοῦτο δεύτερον ἀγαθὸν μετὰ τὸ εἶναι δίκαιον, τὸ γίγνεσθαι καὶ κολαζόμενον διδόναι δίκην· καὶ πᾶσαν κολακείαν καὶ τὴν περὶ ἑαυτὸν καὶ τὴν περὶ τοὺς ἄλλους, καὶ περὶ ὀλίγους καὶ περὶ πολλούς, φευκτέον· καὶ τῇ ῥητορικῇ οὕτω χρηστέον ἐπὶ τὸ δίκαιον ἀεί, καὶ τῇ ἄλλῃ πάσῃ πράξει. ἐμοί οὖν πειθόμενος ἀκολούθησον ἐνταῦθα, οἱ ἀφικόμενος εὐδαιμονήσεις καὶ ζῶν καὶ τελευτήσας ὡς ὁ σὸς λόγος σημαίνει· καὶ εἰσόν τινά σου καταφρονῆσαι ὡς ἀνοήτου καὶ προπηλακίσαι, ἐὰν βούληται, καὶ ναὶ μὰ Δία σύ γε θαρρῶν πατάξαι τὴν ἄτιμον τύταην πλήγην· οὐδὲν γὰρ δεινὸν πείσει, ἐὰν τῷ ὄντι ᾖς καλὸς κἀγαθός, ἀσκῶν ἀρετήν. Platonis Gorgias. Explain Plato's doctrine of ideas, and shew what diffi culties it was intended to solve. GREEK. Examiner-C. H. TAWNEY, M. A. Translate into Greek Iambics : Neither to this interment called by me When I was perishing; but thou, who stood'st Thou showedst, put to touch, the thing thou art, (You need only attempt four of the following questions.) and illustrate your remarks by instances in which their force is discernible. 3. Distinguish between wore with the infinitive and wore with the indicative. What are the grammatical conditions of the right use of πρίν. 4. Give Aristotle's definition of happiness, showing clearly the meaning of the terms which he employs. 5. Give the various significations of διά, κατά, ὑπέρ, with the genitive and accusative. 6. Explain the terms-τὸ τριώβολον, ἀνάκρισις, σύμβολον, τίμημα, οἱ ἕνδεκα. 7. 8. What were the principal liturgies at Athens ? PURE MATHEMATICS. Examiner-MR. W. BOOTH, B. A. 1. Find the condition that the line ax + μy + v = the conic given by the general equation. (a.) Find the coordinates of the foci of the conic ax2 + 2hxy + by2 + 2gx + 2fy + c = = 0. O may touch 2. If 20 be the angle between the tangents to an ellipse from a point P and a′ and a" be major axes of the confocals through P; then will tan20= a'r 3. Prove that the anharmonic ratio of the pencil subtended at any point on a conic by four points on the same conic is constant. Hence deduce geometrically Pascal's theorem. 4. Given five points on a conic, construct geometrically its centre, and the lengths and directions of its axes. 5. Find the locus of a point such that its polars with respect to three conics may be concurrent. (a) What is the locus if the three conics be three circles. 6. Form the equation of a plane passing through a given point and perpendicular to two given planes. In determining a surface of the second degree, to how many conditions is it equivalent to be given a point and its polar plane? To how many to be given a self-conjugate tetrahedron ? 7. If u=0 represent a quadric, its asymptotic cone is represented by the equation u = What is the geometrical signification of D = 0, of ▲ = 0. 8. Any two circular sections of a quadric of opposite systems lie on the same sphere. 9. Prove Meunier's theorem. 10. Find the locus of points on a surface where the indicatrix is an equilateral hyperbola. 11. If Q be the foot of the perpendicular dropped from the centre O of the ellipsoid upon a tangent plane at P, and if OQ = p and OP = r, also if a, B1 Y, be the angles made with the axes by the bisector of the angle POQ prove that 12. If the eccentric angles a B 8 of three points on an ellipse be connected by the relation = Sin (a + B) + Sin (8 + d) + Sin (8 + a) 0, shew that the normals at these points are concurrent. 1. If P = PURE MATHEMATICS. (a—b)2 + (b—c)2 + (c—a)2 express a-b2 (a + b-2c)2 + (b−c)2 (b + c−2a)2 + c- 12 (c + a−2b)2 in terms of P. 2. If√(1−x) (1 + y + y2) — √√ (1−y) (1 + x + x2) = C (x—y) and 1-√/1—y3 = (x—y) ✔a-x-y express C in terms of a. 3. Exhibit the result of eliminating a from the equations the form of a determinant. (a.) Write down the three roots of the equation 4. Express in its simplest form the product of the squares of the n -1=0. differences of the roots of the equation "— 5. If ac-b70 then will the sign of a2d2-6 abcd + 4aca -36°c + 4b3d be positive. 6. Solve the system of equations (a) Express x + y + z + u = p xy + yz + zx + xu + yu + zu = q xyzxzu + yzu + xyu =r ay= = zu. αβγδ (α + β + γ + δ)-(αγδ + αγβ + β γδ + αβδ as the product of three quadratic factors. (b.) If a, B, y, 8, be the roots of the equation (a.) State the corresponding relation between these determinants when the number of rows is n. 8. If the second term be removed from the equation ax + 4bx3 + 6cx2 + 4dx + e = 0 the result is (az)* + 6 λ (az)2 + 4 μ (az) + a3v 3 λ2 =0 3 abc2b3ae4 bd + 3 c2. that the result of eliminating x from the equations ax+ + 4 bx3 + 6 cx2 + 4 dx + e = 0 where A and have the same values as in (8) and pace + 2bcd — ad2 — b2e — c3. 10. Form the equation whose roots are the cubes of the roots of x2 + px2 + qx + r = 0 and shew that the equation whose roots are the cubes of the roots of and hence calculate the coefficients of the first five terms in the expan. sion of u in a series of ascending powers of x. |