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11. Find the roots of the equation
23 – 3x2 +4=0. 12. A general orders two men by lot out of 100 mutineers to be shot : the real leaders of the mutiny being ten, find the chance (i.) that one or (ü.) that two of them will be taken.
13. Given three tangents and a focus of a conic, find its centre by a geometrical construction.
14. Given two conjugate diameters of a conic in magnitude and position, determine its axes geometrically. 15. If a, b, c, d be the roots of the biquadratic
2c4 +px3 + qx2 + rx+8 = 0, find the value of £ (a + b) (c+d). 16. If a, b, y be the roots of a cubic, find the value of
a2 + B2 a? + y2 B2 + y2
+ a + ß
aty in terms of its coefficients. 17. Prove that 0= w is a solution of the equation
sin 0 - cos 0 - 4 sin 0 cos 20 =0. 18. Find the condition that the line lx + my+n=o should touch a conic given by its general equation.
1. Stewart points out a circumstance which might seem an objection to education; state this, and show that it is not really so.
2. How does he show that a knowledge of the existence of the material world is not required in order to the exercise of the faculties of the mind?
3. Stewart argues against a distinction made by Reid between perception and imagination ; how does he reason ? He accounts for the appearance of truth in Reid's opinion; and quotes from Reid's views elsewhere in opposition to his opinion?
4. State the views of Plato and Aristotle as to what is expressed by a generic term; and how they differ, according to Stewart, on the subject of ideas.
5. To what circumstances does Stewart trace the origin of the opinion of Plato as to the true method of scientific inquiry?
6. Whence does the pleasure derived from wit chiefly arise ?-and tate the facts which prove this.
7. Give an accurate statement of Stewart's arguments to prove that the phenomena of dreaming arise from the suspension of that power of the will over the faculties of the mind and members of the body which it possesses when men are awake.
8. State the various ways in which the knowledge of the philosopher is more extensive than that of other men; and the different advantages to him of a hypothetical theory, and of one founded on induction.
1. If the new premisses be legitimate after substituting the conclusion for the minor premiss, investigate the mode and figure.
2. Reduce Dariï to Celarent.
3. Given three propositions which form a syllogism, construct it; and show that only one legitimate syllogism can be formed of them.
4. What inconsistency is involved in Locke’s speaking of building morals into a demonstrative science ?
5. Give the substance of Locke's proof that Relations terminate in simple ideas.
6. How does Locke's account of perception differ from Stewart's ?
7. How does Bacon divide Artes Logicæ ? What are the grounds of his division
8. What example does Bacon give of compulsio experimenti, and why does he consider the method valuable ?
9. What method of those enumerated by Bacon was employed by Archimides to detect the fraud committed respecting Hiero's crown?
10. Enumerate and explain the several kinds of Idola ?
Translate the following passages into English Prose :1. Beginning, οι δε Αθηναίοι εν τη Σηστή δυοϊν δεούσαις, κ. τ.λ. Ending, ώς oύ προσεχώρει, απέπλευσαν ες "Αβυδον.
Lib. viii. c. 102.
2. Beginning, 'Εγώ μεν ούν και αυτός είμι τη γνώμη, κ. τ.λ. Ending, από τών λόγω καλώς επιτιμησάντων:
Lib. ii. c. 38. 3. Beginning, Αυτόθεν δη διανοήθητε ή υπακούειν πρίν τι βλαβήναι,
Ending, προσέτι και θαλάσσης είργόμενοι
κ. τ. λ.
Lib. i. c. 141.
4. Beginning, "Απιστα μεν ίσως, ώσπερ και άλλοι τινές, κ. τ.λ. Ending, μήτε απιστήσαντες του ξύμπαντος αμελήσετε.
Lib. vi. C. 33.
1. What materials had Thucydides for the composition of his History?
2. Show that he had only a partial view of what should be embraced in a History of Greece.
3. Discuss the question of the genuineness of his eighth book. 4. When and with what success was Petalism tried at Syracuse ? 5. What were the two chief objects of the Hermokopidae ? 6. How does Thucydides treat the siege of Melos, and with what ob
7. Draw a map of Syracuse and of the Athenian lines during the siege.
8. What were the chief events of the year 424 B.C. ? 9. When and where was Mindarus slain ? 10. In what capacity did Lysander gain the battle of Egos Potami ?
11. What changes were effected in the Athenian constitution in 411 B. c.
12. How may the irregular constructions that occur in Greek be accounted for ?
13. Show clearly, by examples, what are meant by primary, secondary, and tertiary predicates.
14. What were the three great centres of Art in Greece, and what were the characteristics of each !
15. Explain the formation of the words, πάς, έκαστος, όπως, μέλαινα, and έχιδνα.
16. What changes does the Digamma undergo in Greek ?
17. There is only one certain example of an original gh becoming 0 in Greek ?
18. What are the derivations of the words, Aáovn, 'Aria, and Δελφόι ?
Translate the following passages into English Prose :-1. Beginning, Multa sine dubio sævaque Augustus de moribus...... Ending, ut non aliter ratio constet quam si uni reddatur,
Ann. lib. i. c. 6. 2. Beginning, Tum Cn. Pompeius tertium consul, ...... Ending, legis nexus modicum in præsens levamentum fuere.
Ann. lib. iii. c. 28. 3. Beginning, Festis Saturno diebus inter alia æqualium ludicra.... Ending, sive temperamentum inerat ne statim sæviret.
Ann. lib. xiii. c. 15. 4. Beginning, Haudquaquam erecto animo eas voces accipiebat, Ending, Sabinus non insultans et miseranti propior.
Hist. lib. iii. c. 65.
1. Enumerate the principal tribes mentioned by Tacitus as inhabiting Britain ; stating also where their settlements were situated.
2. What were the boundaries of Germany, as conceived by Tacitus ? 3. Give some account of the achievements of Arminius.
4. State the most important provisions of the following laws :- Lex Papia Poppæa, Cincia Muneralis, Juliæ Sumtuariæ.
5. What were the first measures of Caligula ?
6. Give some account of Vespasian up to the time of his accession to the empire ?
7. What were the last words of Nero ?
8. Explain the formation of such futures as, alevoovuar, and the Doric in σιω. .
9. What was the original form of the genitive termination ov of the 2nd declension:
10. What was the cause of the frequent occurrence of hiatus in Greek?
11. What are the peculiarities of Greek and Latin with respect to their consonant systems!
12. What are the Latin affinities of τέφρα, σφόγγος, σφενδόνη, βόρα πος, ίπτομαι, ιός ?
Translate the following passage into Latin Prose :-
MERIVALE, History of the Romans under the Empire, c, xlii.
Translate the following passage into Latin Lyric Verse :-
Translate the following passage into Greek Prose :-
Translate the following passage into Greek Iambic Verse .Beginning, Your coming, friends, revives me; for I learn,. Ending, These two, proportioned ill, drove me transverse.
Milton, Samson Agonistes.
1. Given three points or rays of an harmonic system, determine the fourth without the aid of a circle.
2. Given two arcs of a circle, determine the arc that cuts both harmonically without the aid of a second circle.
3. Given two circles in magnitude and position, place a third circle of given magnitude so as to cut both orthogonally.
4. Given a segment or angle in magnitude and position, place a second segment or angle of given magnitude so as to cut it in a given anharmonic ratio.
5. If two of six lines intersect the remaining four equianharmonically, every two of the six intersect the remaining four equianharmonically?
6. If six lines pass three and three through four points, the six perpendiculars upon them from any fifth point determine a pencil of six rays in involution