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7. Given, of a conic, the centre and a self-reciprocal triangle; determine, geometrically, the directions of the axes, and also of the asymptotes, real or imaginary.
8. In a parabola, the circle circumscribing any circumscribed triangle passes through the focus; what does this property become by reciprocation to any circle having its centre at the focus?
9. Explain the method of forming the equation of the reciprocal of a conic, and show how it follows from the equation, that if the conic reduce to a pair of right lines, the reciprocal must also reduce similarly.
10. Being given the equation of the reciprocal of a conic, we can at once write down the equation of the tangents to it from a point; form by this method the equation of tangents from a, ß, y to
ax2+ by2+ cz2 = 0.
11. Express the area of a spherical triangle in terms of the sides, and show how it follows geometrically from this expression, that if p denote the perimeter of the triangle, and 2, 21, 22, 23 the areas of the triangle itself, and of those formed by producing its sides two by two,
tan 12. Eliminate a and ẞ from the equations, tan a + tan ẞ= a,
tan a tan ẞ (cosec 2a + cosec 2ẞ) = b,
1. Define Metaphysics. Give a few specimens of questions which properly fall within the scope of this science. In what sense is the term employed by Stewart ?
2. Stewart asserts that metaphysical studies are the best of all preparations for those philosophical pursuits which relate to the conduct of life; for what reasons?
3. "That when two subjects of thought have been repeatedly presented to the mind in conjunction, the one has a tendency to suggest the other, is a fact which will be as readily admitted by the materialist as by the Berkeleian." Explain this sentence, and point out clearly the exact points at issue between the materialist and the Berkeleian.
4. Discuss the following question-Can we attend at one and the same instant to objects which we can attend to separately?
5. The association of ideas has a tendency to warp our speculative opinions in three ways? Give some examples of each.
6. What is the "scientia perfectissima," according to Descartes ? Give Stewart's comment upon this statement.
7. What are the principal sources of the peculiar difficulty which is experienced in attending to the operations of the mind?
8. Explain the following philosophical terms-Physical cause, efficient cause, occasional cause, final cause.
9. Write a note, historical and explanatory, on the following proposition-"Entia non sunt multiplicanda præter necessitatem."
10. Subject for a short essay-The influence of Imagination on human character and happiness.
WHATELY AND BACON.
1. Show the line of argument by which the validity of Reductio ad Impossibile is proved.
2. Whately professes to reduce Baroko and Bokardo ostensively? The names proposed by Whately to indicate this reduction do not adequately describe the process?
3. When there are several distinct and independent arguments, not incompatible, and not connected, each separately proving the probability of the same conclusion, how do you estimate their cumulative force?
4. State the various points on which logicians are at issue with respect to the nature of Induction.
5. "He that is of God heareth my words: ye therefore hear them not, because ye are not of God." Reduce this to the syllogistic form, and show that the reasoning is valid.
6. Give a brief statement of Bacon's doctrine of Idols.
7. "Syllogismus cum intellectu humano magnam habet sympathiam"? 8. "Inventio argumentorum inventio proprie non est"?
9. What is the philosophical character of the Venatio Panis? and what is the origin of the expression?
10. State the true functions of the Intellect, the Imagination, and the Will.
1. "It is for want of reflection that we are apt to think that our senses show us nothing but material things." How does Locke develope this remark, and for what purpose does he make it?
2. In what does Identity consist in general, and the identity of a man in particular? How does Locke arrive at the latter, and why does he object to placing it in the identity of the soul?
3. He puts the following objection to his theory of personal identity :Suppose I wholly lose the memory of some parts of my life, yet am I not the same person that did those acts, &c." How does he reply to
4. By what instances does Locke show that brutes have memory?
5. Wherein does he suppose that the species of brutes are discriminated from men, and what are his reasons?
6. How does he show that thinking is the action, not the essence, of the soul?
7. Show that ideas of mixed modes are arbitrary.
8. "Many a man," says Locke, "who was pretty well satisfied of the meaning of a text of Scripture, or of a clause in the code, has by consulting commentators quite lost it." State fully and clearly Locke's explanation of such facts.
9. Give instances of the abuses of setting words for what they cannot signify, and of supposing that they have a certain signification.
10. To what source does Locke trace the disputes about materia prima?
I. Beginning, Καὶ τὸ βραδὺ καὶ μέλλον, κ. τ. λ.
Ending, κράτιστον δὲ εἶναι ὅστις ἐν τοῖς ἀναγκαιοτάτοις παιδεύεται. Lib. i. 84.
2. Beginning, καὶ τὴν εἰωθυῖαν ἀξίωσιν τῶν ὀνομάτων, κ. τ. λ. Ending, τὸ φιλονεικεῖν καθισταμένων τὸ πρόθυμον.
Lib. iii. 82.
3. Beginning, καὶ εἴ τις ἰδίᾳ τινὰ δεδιὼς ἄρα, κ. τ. λ.
Lib. iv. 86.
4. Beginning, Τοὺς μὲν ̓Αθηναίους ὅστις μὴ βούλεται, κ. τ. λ. Ending, πόλεις τοσαῦται καὶ οὕτω μεγάλαι.
Lib. vi. 36.
I. Describe the events that led to the exile of Thucydides; and discuss the question as to how far that sentence was merited by his conduct.
2. What are the Episodes in the history of Thucydides, and where placed in his work?
3. The Speeches afford much essential information of a particular kind?
4. For once in his history he has availed himself of the form of dialogue? A comprehensive view of the history will suggest to us the explanation of this drama?
5. What was the real object of the Spartan ɛvnλaoía?
6. State the object and probable origin of the Ephori: it is a mistake to compare them with the Roman tribunes ?
7. What corresponded at Athens to the jus Cæritum at Rome ?
8. What is the difference between the subjunctive and optative when they both depend upon a verb in a determinate tense? and illustrate this difference by a passage in the 3rd Book of Thucydides ?
9. A passage in the 1st Book shows clearly the distinction between ἄρχομαι and ἄρχω ?
ro. What is the force of ἐπὶ in ἐπιχρῆσθαι ? and mention other examples of it.
11. Explain πρύμναν κρούεσθαι, ἀνάκρουσις, αποσιμοῦν, παραποιεῖσθαι σφραγῖδα, and ὅσα μή with a participle.
12. Translate, οἷς τὸ μὴ ἐπιχειρούμενον ἀεὶ ἐλλιπὲς ἦν τῆς δοκήσεώς τι πράξειν. αὐτοκράτωρ μάχη. τῆς γνώμης τὸ μὴ κατὰ κράτος νικηθέν.
Translate each of the following passages :
1. a. Beginning, Prima Vari castra, lato ambitu,... Ending, attrectare feralia debuisse."
b. Beginning, Nec multo post adfertur,.
Ann. i. 61-62.
Ann. iv. 25-26.
Translate any two of the three following passages:
2. a. Beginning, Non referrem vulgatissimum Senatusconsultum,.. Ending, qui animum etiam levissimis adverterent." Ann. xiii. 49.
b. Beginning, Sustinuit labantem aciem Antonius, ....
Hist. iii. 23.
c. Beginning, Deorum maxime Mercurium colunt,.. Ending, secundam impressam ante notam, interpretatur. De Mor. Germ., 9-10.
1. Give the names of the principal Roman prose authors of the first century of the empire, and some account of the works of each.
2. State accurately the periods comprised in the extant portions of the Annals and Histories of Tacitus.
3. Give the dates of the defeat of Varus, the invasion of Britain by Claudius, the fall of Jerusalem, and of the accession of the Emperors Tiberius, Nero, Galba, Domitian, and Trajan.
4. What real advantages did the emperors gain by the assumption of the title princeps? How was the title princeps senatus expressed by Greek writers ?
5. What were the successes celebrated by Augustus in the triple triumph alluded to by Virgil-Æn. viii. 714:
"At Cæsar triplici invectus Romana triumpho
By what significant innovation was this triumph marked? What event did he commemorate by the erection of the temple to Mars Ultor on the Capitol ?
6. Narrate briefly the circumstances of the fall of Sejanus?
7. What was the subject of the Apocolocyntosis of Seneca?
8. State some particulars of the battle of Bedriacum.
9. Detail the chief military exploits of Trajan.
10. In what cases in Latin do two negatives in a sentence not destroy one another ?
II. Point out the different ways of expressing in Latin without followed by a present participle in English.
12. Give the derivations of the words gnarus, fastigium, procax, obedio, sodalis, flagitium, exauctoro, alumnus, contio.
Translate the following passage into Greek Prose:
I do not mean to commend either the spirit in this excess, or the moral causes which produce it. Perhaps a more smooth and accommodating spirit of freedom in them would be more acceptable to us. Perhaps ideas of liberty might be desired, more reconcilable with an arbitrary and boundless authority. Perhaps we might wish the colonists to be persuaded, that their liberty is more secure when held in trust for them by us, than with any part of it in their own hands. The question is, not whether their spirit deserves praise or blame, but, what shall we do with it? You have before you the object, such as it is, with all its glories, and all its imperfections on its head. You see the magnitude; the importance; the temper; the habits; the disorders. By all these considerations we are strongly urged to determine something concerning it. We are called upon to fix some rule and line for our future conduct, which may give a little stability to our politics, and prevent the return of such unhappy deliberations as the present. Every such return will bring the matter before us in a still more untractable form.-BURKE,