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5. Given A=135°, a = 2, b=√/2, solve the triangle.
6. Write down a formula suited for calculating the logarithms of small numbers; and apply it to find the Naperian logarithm of the base of the common system; hence prove that if M be the modulus, =2.3, nearly. 7. From the formula
sin x = r -
find sin 3° to five places of decimals.
Translate the following passages into English 1. Beginning, Βρόμιον ἔνθα τέκετο, κ. τ. λ. Ending, δεῖξεν αἰθέρος πνοαῖς.
2. Beginning, Χο. ἰὼ Γᾶ τε καὶ παμφαὴς, κ. τ. λ. Ending, δὰ θεόθεν πιτνοῦντ ̓ ἐπὶ δόμοις ἄχη.
EURIPIDES, Phanissa, 658-686.
Ibid., Medea, 1246–1267. 3. Beginning, Εκάβη δὲ παιδὸς γνοῦσα θανάσιμον μόρον, κ. τ. λ. Ending, πλήθει γυναικῶν οὐδὲν ἥνυτον τάλας.
Ibid., Hecuba, 1127-1149. 4. Beginning, οὐδὲ τότ ̓ Αἰνείαο δαίφρονος ὄβριμον ἔγχος, κ. τ. λ. Ending, ταρβήσας, ὅ οἱ ἄγχι πάγη βέλος.
HOMER, Iliad, lib. xx. 267–283.
DEMOSTHENES AND XENOPHON.
Translate the following passages into English prose :
I. Beginning, ̓Αλλὰ μὴν τὸ μὲν παρεληλυθὸς ἀεὶ παρὰ, κ. τ. λ.
3. Beginning, Ως δὲ ἐνέβαλε, πρῶτον μὲν τὴν γῆν ἐδῄου, κ. τ. λ. Ending, εἰ μὴ καὶ διοικοῖντο κατὰ κώμας.
Ibid., Meidias, 542.
XENOPHON, Hist. Grac., lib. v. C. 2.
4. Beginning, Οὔκουν δοκεῖ σοι ὁ ἐξ ἀρχῆς ποιῶν ἀνθρώπους, κ. τ. λ. Ending, ἀπορεῖς πότερα τύχης ἢ γνώμης ἔργα ἐστίν;
XENOPHON, Commentarii, lib. i. c. 4.
Translate the following passages into English:
I. Beginning, Sa. Credo, istuc melius esse: verum ego numquam adeo astutus fui,
Ending, Sy. Jamne enumerasti id, quod ad te rediturum putes? TERENCE, Adelphi, act ii. sc. i. 13–28.
2 Beginning, Ph. Nil aput me tibi...... Ending, Nobis, in re ipsa invenimus: porro hanc nunc experiamur. Ibid., Hecyra, act v. sc. ii. 1-12. 3. Beginning, Edificare casas, plostello adjungere mures, Ending, Postquam est impransi correptus voce magistri ? HORACE, Satyr., lib. ii. 247–257. 4. Beginning, Qualem commendes, etiam atque etiam aspice: ne mox.... Ending, Et neglecta solent incendia sumere vires.
Ibid., Epist., lib. i. 76–85.
5. Beginning, Si quando sedem augustam, servataque mella.... Ending, Affixa venis, animasque in vulnere ponunt. VIRGIL, Georg., lib. iv. 228–238. 6. Beginning, Haud procul inde, cita Metium in diversa quadrigæ . . . . Ending, Romuleoque recens horrebat regia culmo.
Ibid., Eneid, lib. viii. 642-654.
CICERO AND LIVY.
Translate the following passages into English:
1. Beginning, Aebutio negotium datur. Adest ad tabulam : . Ending, omnium controversiarum putat.
CICERO, Pro A. Cæcina, c. 6.
2. Beginning, O miserum et infelicem illum diem,. Ending, interposita rejectione, devenire convenerit.
Ibid., Pro P. Sulla, c. 32, 33.
3. Beginning, Ceterum parva quoque (ut ferme principia omnia)... Ending, regnis tolerabilem insaniam venerit.
LIVY, lib. vii. c. 2.
4. Beginning, Et Faliscis pacem petentibus annuas indutias dedit,.... Ending, quam peragi, accusatio ejus poterat.
Ibid., lib. x. c. 46.
Translate the following passage into Latin Prose
Eternally that fable is true, of a choice being given to men on their entrance into life. Two majestic women stand before you: one in rich vesture, superb, with what seems like a mural crown on her head and plenty in her hand, and something of triumph, I will not say of boldness, in her eye; and she, the queen of this world, can give you many things. The other is beautiful, but not alluring, nor rich, nor powerful; and there are traces of care and shame and sorrow in her face; and (marvellous to say) her look is downcast and yet noble. She can give you nothing, but she can make you somebody. If you cannot bear to part from her sweet sublime countenance, which hardly veils with sorrow its infinity, follow her: follow her I say, if you are really minded so to do; but do not, while you are on this track, look back with ill-concealed envy on the glittering things which fall in the path of those who prefer to follow the rich dame, and to pick up the riches and honours which fall from her cornucopia.—HELPS, Companions of my Solitude.
Translate the following passage into Latin verse :
The glories of our blood and state
Are shadows, not substantial things;
Death lays his icy hand on kings:
And in the dust be equal made
And plant fresh laurels where they kill:
They stoop to fate,
And must give up their murmuring breath
Then boast no more your mighty deeds;
See where the victor-victim bleeds :
Only the actions of the just
SHIRLEY, Death the Leveller.
Translate the following passage into Greek Prose:
Compertum ege habeo, milites, verba virtutem non addere; neque ex ignavo strenuum, neque fortem ex timido exercitum oratione imperatoris fieri. Quanta cujusque animo audacia naturâ, aut moribus inest, tanta in bello patere solet: quem neque gloria, neque pericula excitant, nequidquam hortere; timor animi auribus obficit. Sed ego vos, quo pauca monerem, advocavi: simul uti caussam consilii aperirem. Scitis equidem, milites, socordia atque ignavia Lentuli quantam ipsi cladem nobisque attulerit; quoque modo, dum ex urbe præsidia opperior, in Galliam proficisci nequiverim.-SALLUST, Bell. Catil., c. 58.
Translate the following passage into Greek Tragic Trimeters :
Antony. Good friends, sweet friends, let me not stir you up
They that have done this deed are honourable;
That made them do it; they are wise and honourable;
I come not, friends, to steal away your hearts:
But as you know me all, a plain blunt man
GRECIAN HISTORY, GEOGRAPHY, AND GRAMMAR.
1. The rise and fall of the great Asiatic monarchies have been characterized by the same features in ancient and modern times?
2. The reign of Darius, the son of Hystaspes, forms an important epoch in the Persian annals?
3. The trial of the Ten Generals after the Battle of Arginusæ illustrates various points in Attic Law?
4. In the literary history of Greece the Athenians were at first outstripped by their colonists in Asia Minor?
5. Give a short history of the Lamian War.
6. In the case of Greece Proper the physical configuration of the country exercised an important influence upon the political destinies of the people?
7. Trace a Map of Greece, showing the general direction of the mountain ranges which were of political importance in the Persian and Peloponnesian Wars.
8. Trace a Map of the chief Greek Colonies in Sicily.
9. In the case of contracted Verbs Homer inflects the a-Stems in three ways?
10. The relation of the Present-Stem to the Verbal-Stem produces four classes of Verbs, with some subdivisions?
II. Decline νεώς, λᾶς, ναῦς, οὖς, υἱός; giving the dialectical varia
tions and the accents.
12. Go through the different tenses of the verb sido in the sense of knowing which were in common use.
13. Explain and exemplify the use of the Gnomic Aorist.
14. By the addition of the particle av the Participle may be resolved in two ways?
15. Οἷος, and sometimes ὅσος and ἡλίκος, have a peculiar attraction :
ROMAN HISTORY AND GEOGRAPHY, AND LATIN GRAMMAR.
1. Trace the steps by which the Plebeians acquired the same privileges as the Patricians.
2. Name the chief battles fought by the Romans with the Samnites.
3. Who fought the battles of Asculum, Aquæ Sextiæ, Zama, and Munda?
4. Who were the chief conspirators against Julius Cæsar? Give the subsequent history of each of them.
5. What was the treaty of Brundusium?
6. What were the duties and privileges of the Dictator, and how was his power restricted?
7. Draw a map of the coast of Africa from Egypt to Carthage, and give both the ancient and the modern names of the chief towns.
8. What were the ancient names of the rivers, Guadalquiver, Guadiana, and Guadalete; and of the towns, Badajoz, Zaragossa, Orleans, Beja, Autun, Loudon, Friuli, Forli, and Frejus ?
9. What is the construction of opus?
10. What cases do the following verbs take:-Circumsono, induo, intercludo, invideo, and arceo?
11. What is meant by the "oratio obliqua"? What are its rules?