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b. καίτοι πόσα χρήματα τοὺς ἡγεμόνας τῶν συμμοριῶν ἢ τοὺς δευτέ ρους καὶ τρίτους οἴεσθέ μοι δίδοναι.

C. καὶ βοᾷς ῥητὰ καὶ ἀρρητὰ ὀνομάζων, ὥσπερ ἐξ ἁμάξης.

Write explanatory notes.

2. a. εἶτ ̓ οἶμαι συμβέβηκε τοῖς μὲν πλήθεσι..... τὴν ἐλευθερίαν ἀπολωλεκέναι, τοῖς δε προεστηκόσι καὶ τἄλλα πλὴν ἑαυτοὺς οἰομένοις πωλεῖν πρώτους ἑαυτοὺς πεπρακόσιν αἰσθέσθαι.

b. ἄντι γαρ φιλων καὶ ξένων, νῦν κόλακες καὶ θεοῖς ἐχθροὶ καὶ τἆλλα ἃ προσήκει πάντ' ἀκούουσιν.

Translate these sentences, explain the constructions, and quote similar idioms from Milton and Horace.

3. Write in Greek the usual form of a photoμa. Why are the documents quoted in the De Corona supposed to be spurious?

4. How were the days of an Attic month denoted?

PHILOLOGY AND COMPOSITION.

TIME: THREE HOURS.

A. Translate into Latin: Upon Cæsar's political sins I need not express any judgment; they are patent on the face of history: but to the humanity of our times the merit of his clemency is not equally obvious: I may fairly urge the reader once more to contrast it with what he has read and has yet to read in the pages before him. If in private life Cæsar's gallantries exceeded even the license of his time, what else, the Romans might have asked, was to be expected of the comeliest son of Venus? If charges still more scandalous are freely advanced against him, the earnestness with which he repelled them in an age disgracefully indulgent to the worst iniquities, bespeaks perhaps the dignity of conscious innocence; and the authority on which they rest is at least avowedly worthless.

But Cæsar has other claims on history besides that of political preeminence. As the historian of his own exploits, he was reputed second to no writer of his own class who had then arisen at Rome; as an orator, to none perhaps but Cicero. He wrote on grammar; he wrote tragedies and verses of Society; he wrote a satire in prose which he called his Anti-Cato.

B. (N. B.-Try only six questions.)

1. Every science passes through three stages. Illustrate by the case of astronomy.

2. Describe as fully as you can the first stage in the Science of Language.

3. What error long retarded the advance of this science? What was the immediate result of the removal of this error?

4. Give some account of Leibnitz and his services to the study of language.

5. Languages have been grouped together on various principles. What are the scientific methods? Apply one of these methods and show the results.

6. What is the meaning of the name Arya? Where does M. Müller find traces of this name?

7. 'How can you prove that Sanskrit literature is so old as it is supposed to be? What answer does M. Müller give to this question?

C. N. B.-Try only six questions.

1.

Show by examples the various forms the verbal stem-suffix ya assumes in Greek and in Latin.

2. What words are derived from the root SPAR and its by-forms

3.

4.

5.

Give varied examples of Reduplication.

What is the rule for accentuation in Latin? On what grounds does Corssen assume an older law.

Shew the changes the Digamma has undergone.

6. Give examples of Labialism.

7. Shew that the aspirate in Greek is often not original.

8. Illustrate the use of the particles used to denote the superlative in Greek and Latin, and account for such forms as: fortissimus, fucillimus, extremus, summus.

CLASSICAL LITERATURE,

TIME: THREE HOURS,

N. B.-Try only the questions marked*, and two more in each part.

A. 1. a.

What parts of the Iliad are believed to be interpola tions? Give the reasons for this belief in any one important instance, b. Horace quotes from the Odyssey: give the quotation and state his object in quoting.

2. Give some account of humorous poems previous to Achilochus, Describe the language of Archilochus, and quote Horace's references to him.

* 3. The origin of Tragedy and its development by Thespis.

4. Sophocles won his first prize under peculiar circumstances. His earliest extant play gained him political honours. What changes did he introduce into the composition and representation of plays.

* 5. A sketch of Plato's life. What was Plato's object in introducing Socrates into all his dialogues. How have they been classified ?

B. 1. Mention some of the oldest specimens of Latin. What reference is made by Horace to one of them,

2. What shape did the first literary efforts of the Romans take?

3. When were histriones first brought to Rome? What account does Livy give of the introduction of the regular drama?

*

4. Ennius and his works. Horace quotes from them.

5. Compare the Prologues of Plautus, Terence and Euripides. What part of a Greek play do those of Plautus most resemble? What were the reasons of his popularity? What compliment was paid to his style by A. Gellius?

* 6. Why did Tragedy not flourish at Rome?

C. * 1. Discuss the following questions (a.) The number of Dioysia at Athens. (b.) The time of the year at which each festival was held. (c.) The peculiar circumstances and regulations affecting the audience and the performance at each festival.

* 2. Give a description of the Theatre at Athens, naming the different parts in Greek.

3. Distinguish τραγῳδος and τρυγῳδός. Horace seems to have confused them.

4. Describe the preparations necessary for producing plays at Athens.

5. Explain fully the meaning of the following terms:-Terpahoyía; χορυφαῖος, προσωπεῖον, περίακτος, αἴωραι,

6. Quote any passages you have met in Latin authors, that refer to the stage or the scenic arrangements of a theatre.

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1. O is a point within a triangle at which the three sides subtend equal angles. Given OA, OB, OC, = α,ß,y, respectively. Find the sides.

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3. Express cos" in terms of descending multiplies of 0, n being a positive integer, Illustrate, when n=7.

2n

4. The roots of the equation, x sion. Shew, independently, that no

+1=0, are in geometrical progrestwo of them are equal.

5. Decompose the above equation into its quadratic factors, and find factorials by giving x the values

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successively.
(2n − 1)π

tan

4n

From these

6. To what purpose is the decomposition you have just made applied in the Integral Calculus. Give a step or two of the process.

7. By the method of sum and difference of compound angles, sum the series, cos 0 + cos 20+ +cos n 0. Shew also how this

summation can be applied to sum the two series
sin20+sin22 0+
+ sin2no, and cos20+ cos220+

8. Shew that the sum, to infinity, of the series

cos 0 + § cos 3 0 +† cos 50+ &c., = log (cot (2)

+ cos2no.

9. State the mutual properties of co-polar triangles; hence from

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sin

explaining any paradox that may present itself in the investigation.

a

2'

10. In an equation with rational co-efficients, imaginary roots enter in pairs.

11. If a be the root of the equation ƒ x)=0, and ƒ'(x) be the first derived function, and if x increase continuously through a; then f(x) and f'(x) have contrary signs just before the passage of the root a, and the same signs just after the passage.

12. Apply Sturm's functions to find what can be known from them respecting the roots of the equation, x3-3x2+x-4=0.

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1. In the equation to a straight line, y=mx+c (oblique coordi nates), what is the Geometrical meaning of m? Shew by a figure.

2. If &=0, ß=0, y=0, be the equations to three straight lines, shew that la+mẞ+ny=0 may be made to represent any line passing through two given points.

3. Give the investigation for the change of the coördinates of a point from rectangular to oblique, origin unchanged.

4. Find the equation to the chord of contact in any curve of the second degree you choose, tangents being drawn from (h,k).

5. Prove that the equation to the normal of a parabola in terms of the angle it makes with the axis of X, is y = mx - 2am - am3. If the three normals are possible, deduce from this equation a conspicuous inference respecting the angles they make with the axis of X.

6. Shew that, the axis being rectangular, the locus represented by ax2 + bxy + cy2+f=0, becomes a,x2+by2+f0, when the axes are turned through an angle 9, such that tan 20

b
а - с

7. If two lines, moving parallel to themselves, cut a conic section, the ratio of the rectangles of their segments, measured from their point of intersection, is constant. Prove for the ellipse or the hyperbola.

8. Find the equations to the three tangents to the curve, 3x2 - 4xy + x - y2- 5y=0, (1) at the origin: (2) and (3) at the points where the axes cut the curve.

9. In the ellipse, conjugate semiaxes are in different quadrants: in the hyperbola, in the same quadrant.

10. The asymptote bisects the line joining the points where the conjugate axes meet the hyperbola and its conjugate.

11. Tangents to an ellipse meet at a constant angle. Shew that the locus of their intersection is generally a curve of the fourth degree: but if the angle is a right angle, the locus is a circle.

12.

Prove that, if a particle move in an orbit that is a conic section, the centre of force being in the focus and x the sum of the

1

(dist)2

squares of the velocities at the extremities of a focal chord is constant. h (You may assume, without proof, that v≈ -.

p

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