2. Translate, distinguishing in each case the dialect: (α) Συμμαχία κ ̓ ἔα ἑκατὸν Γέτεα. (3) ποίεε ὅκως ἐκείνην θεήσεαι. (α) Εῤῥει τὰ καλα· Μίνδαρός τ ̓ ἀπεσσύα· Πεινῶντι τὤνδρες ἀπορίομες τί χρὴ δρῆν. Transpose each into Attic Greek. 3. Write a short history of agrarian legislation at Rome. 4. Illustrate from Greek history the political use of religion. 5. Restore and translate, with comments on the orthography CONSOL CENSOR· AIDILIS HIC FVET· A Give some account of the metre in which the inscription is composed. 6. Explain the following terms:—ζευγῖται, συμμορίαι, οἱ ἕνδεκα (at Athens), νομοθέται, κληρουχία, litium aestimatio, lex satura, usucapio, praevaricatio, duumviri perduellionis. 7. Give a full account of the methods of dating according to the Athenian calendar. 8. Derive the Roman alphabet, accounting for the number and forms of its letters. 9. Draw a map of Sicily, showing the distribution of races at the time of the Athenian invasion (B.C. 415), and distinguish between Ionian and Dorian settlements. SCHOOL OF MATHEMATICS. MATHEMATICS.-PAPER I. The Board of Examiners. 1. The arithmetic mean of any number of positive quantities which are not all equal is greater than their geometric mean. 2. Shew that any quadratic surd is equal to a recurring continued fraction. If Z be any integer not a perfect square, and if Z be converted into a continued fraction two, .... i complete periods, each period terminating with k be denoted by P1, P2, .... Pi, prove that 3. Prove Newton's theorem concerning the sums of the powers of the roots of an equation. (x .... If f(x)=(x — α1) (x — α2) (x — α3) an), prove that the sum of all the homogeneous products of the degree of the n quantities a1, a2.... an is 4. State and prove the rule for forming the product of two determinants of the same order. where are A31, A32, A33 + λ, &c. &c., &c., &c. aer, shew that the roots of the equa tion 4 (X) = 0 are all real. 5. If there be n angles a, b, c, d, &c., prove that 2n cos a cos b cos c cos d .... is equal to the sum of the cosines of all the angles included in the expression 6. If Hence find an expression for cos " in terms of cosines of multiples of 0 and deduce an expression for sin "0 in terms of sines or cosines of multiples of 0. a2 x2 where A, is equal to the value of a2 — 002 xp (x) If a, ß, y be the arcs joining the middle points of the sides of a spherical triangle, prove that 4 cos a COS b = sin с 2 COS 8. Find the locus of the feet of the normals drawn from a fixed point conics. to a system of confocal Shew that the foot of the perpendicular from O on the polar of O with respect to any one of the conics lies on the locus. 9. If a triangle be self conjugate with respect to a parabola the centre of the circumscribed circle of the triangle lies on the directrix and the nine point circle of the triangle passes through the focus. 10. If a system of conics be such that the pencil of tangents drawn from any point is in involution, then the system of conics has four common tangents. MATHEMATICS.-PAPER II. The Board of Examiners. 1. Define a differential coefficient. Find the differential coefficient of u with respect to x (i) When u is a function of У and function of x. y is a (ii) When u is a function of x, y, z, and y, z are functions of x. |