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4. According to Paley, two faults may fairly be attributed to Euripides?

5. What reason does Paley assign for the enmity shown towards him by Aristophanes ?

6. Compare ancient and modern Tragedy. 7. The worship of Bacchus was twofold ?

MR. GRAY.

Translate the following passages into English Prose :1. Beginning, Mes. In scirpo nodum quæris. Quin nos hinc domum .... Ending, Ubi nil habebis, geminum dum quæris, gemes.

PLAUTUS, Menachmi, act 11. sc. i. 22–32. 2. Beginning, Mes. Sciti'n' quid ego vos rogo? ...... Ending, Vix (credo) tota auctione capiet

quinquagesies.

PLAUTUS, Menachmi, act v. sc. ix. 92-99. 3. Beginning, Con. Cense'n' talentum magnum exorari potesse ... Ending, Solet ire coctum.

PLAUTUS, Aulularia, act 11. sc. iv. 30-46. 4. Beginning, Nunc illud est, quom me fuisse, quam esse, pimio ma

velim :. Ending, Nugas ineptiasque incipisso. Hæreo.

PLAUTUS, Capteivei, act Ill. sc. iii. 5. Beginning, G. Nullus 's, Geta, nisi aliquod jam consilium celere re

pereris :... Ending, Convasavissem, atque dehinc me protinam conjicerem in pedes.

TERENCE, Phormio, act II. sc. ii. 1-13. 6. Beginning, Gn. Di immortales, homini homo quid præstat? stulto in

tellegens. Ending, Vocabula, parasiti item ut Gnathonici vocentur.

TERENCE, Eunuchus, act 11. sc. ii. 1–33.

1. Write brief notes on the above passages wherever you think them necessary

2. Give the derivation and meaning of the following: cerritus, intercus, glaber, ciniflo, baxea, confuto, protelo, scapula.

3. Give the rules for Latin accentuation.

4. Rome, in the time of Terence, seems to have been divided into two literary factions ?

5. Give an account of the life and literary position of Livius Andronicus.

6. Give an account of the life and writings of the three oldest Roman comic writers of note.

7. Explain fully the distinction between fabulæ prætextate, fabula palliate, and fabulæ togatæ.

MR. ABBOTT.

Translate the following passage into Greek Verse :Beginning, Then am I doubly hopeless. What is gone,. Ending, Is such my doom? Nay, speak it, if it be.

TAYLOR, Philip Van Artevelde, act III. sc. ii.

Translate the following passage into Greek Prose :Beginning, Paternal authority, and the order of domestic life, , Ending, be entirely or abruptly withdrawn.

PALEY, Moral Philosophy, book vi. c. 7.

Translate the following passage into Latin Hexameters :Beginning, He look’d, and saw wide territory spread .. Ending, On each hand slaughter, and gigantic deeds.

Milton, Paradise Lost, book xi.

Translate the following passage into Latin Prose :Beginning, Envy and cavil are the natural fruits of laziness and igno

rance, Ending, who not only knows, but scrupulously observes them.

SPECTATOR, No. 592.

SENIOR FRESHMEN.

Mathematics.

DR. SALMON.

1. Prove that in a plane triangle (cos A + cos }B +cos ?C) (cos}B+cos C - cosA) (cos įC+ cosA

cos B) (cos A+ cos?B - cos įC) = 4 cos 2 ? A cosa} B cos }C. 2. Transform the equation a? cos 44 A + B2 cos ^{B + y2 cos 4C-2aß cos 24 cos ? B

- 2By cos * { B cos 2C – 2ya cos ? C'cos 2A into the form (la + +ny) (a sin A + B sin B+ y sin C)

=p (By sin A + ya sin B + sin C), and determine the values of l, m, n, p.

=0

3. Find in trilinear co-ordinates the equation of the circle passing through the middle points of the sides. 4. Find the equations of the common tangents to the circles

(x – 3)2 + (y - 4)2 = 25, x2 + y2 = 9. s. Find the equation of the locus of the vertex of a triangle whose sides pass respectively through points d'y', &"y", and which makes on the axis of x a given intercept a. 6. Find the sum of the series

1 + 1 + $+ to + &c.

DR. SHAW

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7. Divide an arranged algebraical equation by its first term xr, and take the log of the quotient i + P by the formula,

log (I +P) = P-{P9 + {P3 - &c. Show that the coefficient of x-m in this series, when multiplied by - m, is the sum of the mth powers of the roots of the given equation; and apply this principle to find the sum of the fifth powers of the roots of the equation x2 - 5x+6=0. 8. Show that the product of the determinants ai bici

αι βι γι az b2 C2 and αν β2 γο a3 bz cz

аз Bз үз is itself a determinant.

9. A series of circles touch the same right line at a fixed point, and are cut by a fixed circle; take the common tangent and the perpendicular to it as your axes of co-ordinates, and express the locus of the point which is with respect to the fixed circle the pole of the varying chord of intersection.

10. A variable circle cuts two fixed circles at constant angles; show, both by analytic and plane geometry, that it will also touch two fixed circles.

11. In an oblique-angled spherical triangle, if one side (c) vary, show that the corresponding variation in the adjacent angle A is AA= Ac.(cot A cot c - cot b cosec A).

2e (I –n) 12. If t=no - (1-n) sin mo and the coefficient small, show that, quam proxime,

sin (= sin ne (1-n) {sin (n + m) 0 – sin (n – m) @}

2e

be very

m

m

e

m

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MR. WILLIAMSON.

13. A right line touches two fixed circles in points T and T"; from a fixed point 0 on it any secant is drawn cutting the first circle in points A, B, and the second in A', B'. Find the locus of the intersection of lines TA and T'A'; and determine in what case the locus becomes a right line.

14. Prove that the roots of the cubic

(x - aj (x -- 6) (x c) – a'2 (x – a) 52 (x 6) 62 (7 —c) za'b'c' =0 are all real, and investigate the conditions that it should have equal roots.

15. The construction of a quadrilateral of maximum area, being given three of its sides, is reducible to the solution of a cubic equation; find the cubic, and prove that its roots are all real.

16. Taking two sides of a triangle inscribed in a circle for axes of coordinates; express the co-ordinates of the centre in terms of the lengths of these sides, and apply them to find the equation of the locus of centre of circumscribing circle, when two of the sides are fixed in position, and the third passes through a given point. 17. In a spherical triangle, if

%C

26 sin sin

+ sin

2 prove that C= A + B. 18. Find the sum of n terms of the series

cos a + cos (a + d)+cos (a +2d) + &c.

2 a

2

2

DR. SALMON.

1. Find the co-ordinates of the intersection of the perpendiculars of the triangle (2, 4), (3, 5), (6, 1).

2. Find the equation of the circle circumscribing the triangle, (0, 3), (4, 0), (1, 1). 3. Find the locus of vertex of a triangle, being given the base, and

cot A + 2 cot B. 4. Find the condition that the following cubic may have a pair of equal roots :

ax3 + 36x2 + 30% + d=o. 5. If A, B, C be angles of a plane triangle, prove

sin 2 A + sin 2B + sin 2C = 4 sin A sin B sin C,

sin A + sin B + sin c = 4 cos A cos B cos C. 6. Express the area of a spherical triangle, being given two sides and the included angle.

DR. SHAW.

7. From the equations of two circles show that every secant drawn through the intersection of common tangents is cut similarly by the circles.

8. Form the equation of the circle exscribed to the base of the triangle

a=0, p = 0, y = 0. 9. Given the three angles of a spherical triangle, deduce the expressions for the sine and cosine of half one of the sides.

10. In a right-angled spherical triangle, where C is the right angle, and A is invariable, find the change on the hypothenuse e consequent on a small change in the side b. 11. Resolve into partial fractions the expression

112% – 26x + 107

23 – 22 – 213 + 45 the denominator of which has two equal roots.

12. Calculate to three places of decimals the root lying between s and 6 of

203 – 2x2 – 23% – 70=0.

MR. WILLIAMSON.

13. Prove that the sum of the radii of the circles inscribed in a spherical triangle and circumscribing its polar is equal to a quadrantal arc.

14. One angle of a triangle is fixed in position, and the sum of m times one adjacent side and n times the other is given; find analytically the locus of the centre of the circumscribing circle.

15. Find the equation of the line which passes through the intersection of the lines, +

3x + 2y = 34 ) 16. If a +b+c=0, prove that

(a+ b2 +c2)2 = 2 (a* + 24 + c4). 17. The lines OC and OC" are divided in the same anharmonic ratio in the points, 0, A, B, C and 0, A', B', C'; prove by analysis that the lines AA', BB', and CC" pass through the same point.

18. Transform a cubic whose roots are a, ß, y into another whose roots

*+ 2y=3} and of 1–4 = 4 i

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1. What circumstances give rise to the belief that there are different kinds of reasoning ?—and how does Archbishop Whately answer this opinion in the two forms in which it appears?

2. What remarks does he make on the observation, “that it is difficult to prove a negative"?

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