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4. Define and illustrate the difference between positive and negative thinking.
5. Explain the nature and origin of the scepticism of Berkeley and Hume.
6. Give Sir W. Hamilton's " analysis of the causal judgment, as the result of the mental law of the conditioned.”
7. Give the substance of Stewart's observations upon the use and abuse of general principles in politics.
8. Classify and criticize the principal theories of the association of ideas.
9. How does Stewart explain the phenomena of dreaming ?
10. In what respects do Locke, Stewart, and Mill differ respecting abstraction ?
LOGIC AND PSYCHOLOGY,
1. a. Reduce the reasoning in the following quotation to strict syllogistic form.
6. Name the mode of each syllogism.
“I suppose then that God is not extended. If so, I say there can be no external world. For if there be an external world, and if it be a creature, we must suppose that God is everywhere present and with it, for He is supposed to preserve and do every thing that is done in it. To deny this is to shut Him out of the universe, even altogether to deny His being. On the contrary, to affirm that He is thus present with every part and particle of it is to make Him co-extended, which is contrary to the supposition.”-ARTHUR COLLIER, Clavis Universalis, chap. viii.
2. State the following propositions in strict logical form; convert and contradict them.
a. Every father has been a son.
3. What evidence have we of the existence of spirit and of spirits, according to Locke?
4. How does Locke prove the necessary existence of pure space ? In what words is the element of necessity introduced ?
5. Give a summary classification of philosophical questions according to Cousin's arrangement.
6. How is the passage from Psychology to Ontology effected, according to Cousin
Translate the following passages into English Prose :1. Beginning, “Ως φάτο, κώκυσεν δε γυνή και αμείβετο μύθω, κ. τ.λ. Ending, Εσταότ', ούτε φόβου μεμνημένον ούτ' άλεωρής."
Iliad, Χxiv. 200-216. 2. Beginning, H, και κυανέφσιν επ' οφρύσι νεύσε Κρονίων, κ. τ.λ. Ending, "Εξω εγώ το δε οι κλέος έσσεται όσσον εμοί περ.”
Ibid. Σvii. 209-232. 3. Beginning, “Ως είπών, απέπεμπε δόμων βαρέα στενάχοντα, κ. τ.λ. Ending, Καπνον δ' οίον ορώμεν από χθονός αΐσσοντα.
Odyssey, Χ. 76-99. 4. Beginning, Παννύχιος φερόμην άμα δ' ήελίω ανιόντι, κ.τ.λ. Ending, Aύτις άριζήλως είρημένα μυθολογεύειν.
Ibid. xii. 428-453.
1. What is the Wolfian theory with respect to the Homeric Poems, and what are the usual arguments against it ?
2. Whence did the earliest interpolations arise ?
4. What are the distinguishing characteristics of the Odyssey as compared with the Iliad ?
5. The Iliad was not originally written ?
9. Historic Greece exhibits an improvement over Heroic Greece both in the affections and the intellect?
10. Compare the theology of Homer with that of Æschylus. 11. Why was Aletes so called ? 12. Explain the formation of the words κτέννω (for κτείνω), είχον, δώσουσα, τεκμαίρομαι, ελαύνω, σχίζω, πράσσω.
13. What traces of the participle ending in hevog have we in Latin ? 14. Analyze the words εκάτερος, πάς, and δημόσιος.
15. What was the original phonetic value of the Digamma ? What letters took its place in the various Greek dialects ?
16. Write down the dialectic variations in the declension of the personal pronouns, and account for each, if possible.
Translate the following passages into English :1. Beginning, Quod superest, quæcumque premes virgulta per agros, . Ending, Adsuescant, summasque sequi tabulata per ulmos.
Georg. ii. 346–361. 2. Beginning, Excipiunt plausu pavidos, gaudentque tuentes... Ending, Impediunt, texuntque fugas et proelia Iudo.
Æneid, v. 575-593. 3. Beginning, Non ego te, Ligurum ductor fortissime bello, . Ending, Arduus, et longa sulcat maria alta carina.
Ibid. x. 185–197 4. Beginning, Contra ego vivendo vici mea fata, superstes.... Ending, Nec fas; sed nato Manes perferre sub imos.
Ibid. xi. 160-181. 5. Beginning, Diripuere aras; it toto turbida cælo...... Ending, Concurrunt Itali, spoliantque calentia membra.
Ibid. xii. 283-297.
1. In what light does Merivale regard the Georgics and Æneid of Virgil ?
2. What reason does he suggest for Virgil's desiring that his unfinished poem should be destroyed ?
3. What, according to Conington, is the true relation of Virgil to Homer? 4. Trace the influence of the Greek drama on the Æneid.
5. In one passage there is a distinct mention of Greek legends as they are treated in Greek tragedy ?
6. Describe the organization of the provinces of Spain and Gaul by Augustus.
7. From whence are the modern titles of the chief cities of France derived ? Give instances.
8. At the foundation of the empire of Augustus the communities of the world might be massed in three principal families ? State the political characteristics of each.
9. What were the elements of variety and of unity within the Roman empire ?
Translate the following passage into Latin Prose :Beginning. The distinction here pointed out... Ending, the sight or knowledge of his conduct might corrupt or mislead.
Mill, On Liberty, ch. 4.
Translate the following passage into Latin Verse :-
MILTON, Samson Agonistes.
Translate the following passage into Greek Prose :-
HEEREN, Ancient Greece, ch. 3.
Translate the following passage into Greek Verse :-
Scott, Marmion, canto iv, 20, 21.
1. If a, b, c, d be the sides of a quadrilateral inscribable in a circle, prove that the radius of the circle is given by the expression
(ab + cd) (ac + db) (ad + bc) 4r=.
(8-a) (8-6)(8-c)(8-d)) 2. Find the condition that two of the roots of the equation
23 – pza +q2 – p=0 should be connected by the relation aß= kể; and hence find the condition that
go -pic +1x2 – x = 0 should represent right lines two of which are at right angles to each other.
3. If a, b, c be the lengths of the sides of a triangle, and d, e, f the lines joining the vertices to any assumed point, prove that
a? (42 - ) (42 - 12) + 6° (e2 - d) (el - f2)+(f2-d') (-2) +ä?d? (a2 – 62 – (2) + b2e2 (62 – a? – c?)+c2f? (c2 – – 62) + a2b2c? = 0.
4. Let the distances of the point P from the points y=0, x= ţa, be pop'; by what relation are p,p' connected if P be anywhere on the line v=mx + m ?
5. Given the equations of two circles, find the co-ordinates of a centre of similitude.
6. Given the four sides of a quadrilateral, and that the sum of two opposite angles is o, find an expression for the length of the diagonal opposed to these angles.
DR. SHAW 7. Show that
sin 10° sin 30° sin 50° sin 70° = . 8. Show, by trigonometry, that the roots of
2x3 – 3X – I=0 are – 1, }(I +V3). 9. Solve the equation
24 – 2*3 203 + 3522% - 85% + 16 =0, the roots of which are in geometrical progression. 10. Find the value of the symmetric function
bc of the roots of the equation
23 – 2x2 + 4x - 78=o. 11. Show that the area of the quadrilateral included between the four lines y=ax, y=ax', y= mx + c, y= m*x + c', is
c2 1 (a' – a)
(a – m) (a' – m') (a – m) (a' – m) 12. Determine the inclination of the co-ordinate axes, in order that the equation
x2 - xy + y2 – ax — ay=0 may represent a circle; and find its radius in magnitude.
13. Prove that the equation
2x2 + xy - y2– 2y - 11x +15=0 represents two right lines, and find their equations.
14. If the sum of the squares of the perpendiculars from a point on the sides of a quadrilateral be constant, find the condition that the locus shall be a circle. 15. Prove, geometrically or otherwise, that if
sin A + sin B + sin C= j, and A+B+C = 90°, the only real solution is A=B=C. 16. Prove the trigonometrical identity,
sin 5 A cos 5A - Cos 5A sin 'A= f sin 2 A cos 32 A.