4. Prove that all equilateral hyperbolas which pass through three given points have a fourth point in common.

5. If R be the radius of a circle circumscribing a spherical triangle, prove the formula

be in harmonic progression, prove the following relation among the coefficients :

7. Find the ratio in which the line joining the points (x' y'), (x" y'") is cut by the circle

x2 + y2 2.2

= 0,

and hence deduce the equation of the pair of tangents through the point (x'y').

8. If on a fixed tangent to an ellipse two variable points A and B be taken, so that the intercept AB be constant, find the locus of the intersection of tangents from A and B to the ellipse.

9. If the chance that A can solve a certain problem in conics be, and the chance that B can solve it, what is the chance of the problem being solved when they both try?

10. Given the base of a spherical triangle, and the sum or difference of sides, and the locus of the vertex a great circle; construct the triangle.

d

MR. BURNSIDE.

11. Determine the equation of the asymptotes of a conic given by the general equation.

12. Determine the locus of the centres of equilateral hyperbolæ circumscribing a triangle.

13. Find the equations of the bisectors of the angles formed by the lines given by the equation

15. In a right-angled spherical triangle, prove ab initio that cot2p=cota + cot2b,

where p is the perpendicular on the base, the sides being a and b.

Logic.

DR. STUBBS.

1. Put the following argument of Locke into a strictly logical form :— "Whereby it is evident that the essences of the species of things are nothing else but these abstract ideas. For the having the essence of any species, being that which makes anything to be of that species, and the conformity to the idea to which the name is annexed being that which gives a right to that name, having the essence and the having the conformity must needs be the same thing; since to be of any species, and to have the right to the name of that species, is all one."

2. Give instances from the first Book of Euclid of a simple disjunctive syllogism; and of a syllogism disjunctive from the enumeration of the parts.

3. Analyse the following arguments:

"He that is of God heareth my words; ye, therefore, hear them not because ye are not of God."

"He who has a confirmed habit of any kind of action exercises no selfdenial in the practice of that action: a good man has a confirmed habit of virtue therefore he who exercises self-denial in the practice of virtue is not a good man."

"There are two kinds of things which we ought not to fret about: what we can help and what we cannot" [as a dilemma].

4. When a precept of which we see the reasons conflicts with a precept from the same authority for which we do not see the reasons, Butler argues that the strict logical way of stating and determining the matter is this "There is an apparent reason for the preference and none against it. Further positive institutions are means to a moral end; and the end must be acknowledged more excellent than the means. Nor is observance of these institutions any religious obedience at all otherwise than as it proceeds from a moral principle." Put these arguments into a logical form.

5. Expose the following fallacy:

"The chances are ten to one against a man's possessing strong reasoning powers, and ten to one against exquisite taste; therefore these qualities are incompatible."

6. What is the converse of these propositions :

Isosceles triangles have the angles at the base equal. The greater angle is opposite to the greater side.

7. To what class of fallacies does Whately reduce the following :"He who necessarily goes or stays is not a free agent; you must necessarily go or stay, therefore you are not a free agent."

"What is bought in the market is eaten raw meat is bought in the market, therefore it is eaten."

MR. ABBOTT.

1. Discuss the question to what logical form induction should be reduced.

2. Explain the circumstances which cause real questions to be mistaken for verbal.

3. Show that in the ordinary account of reduction ad impossibile, the reduction fails-i. e., the whole reasoning is not exhibited in the first figure-and, if possible, state the exact process.

4. Explain the ambiguity of some, same, law.

5. State Mr. Mill's view of the nature of syllogism.

6. What, according to him, is the true theory of predication?

7. Discuss the following arguments, and if there is a fallacy expose it:a. That called evorns, which may be thus stated:-No Cretan ever speaks truth: call this proposition C. This being so, Epimenides makes a statement, B. If B is false, then C is universally true; if B is true, C is false. Now, let B = C, and the result is, if B is false, it is also true, and if true it is also false, and an exception to the principle of contradiction is established.

b. God has said so and so; therefore if Mr. M. denies so and so, he in fact declares that he disbelieves God.

c. If A is B it is probably C. But A is not C.. it is probably not B. 8. Show that Whately's solution of the following fallacy (as a case of undistributed middle) is incorrect:-Food is necessary to life; corn is food; therefore corn is necessary to life.

9. Reduce the following propositions to the simplest logical type:I was happy once.

He reaped in fame an ample reward.

Things which resemble the same resemble each other.

Misit qui dicebant; Misit qui dicerent.

DR. TARLETON.

1. Describe the method of distinguishing the conclusion of a legitimate syllogism from the premises, and prove the principles employed. Arrange in regular order the three propositions of the following syllogisms:

2. If the conclusion of a legitimate syllogism be substituted for one of the premises in order that the new premises should be legitimate, what conditions must be fulfilled by the retained and by the suppressed premiss?

3. If the contradictory of one of the premises of a legitimate syllogism be substituted for it, and a new legitimate syllogism result, its conclusion cannot contradict that of the original syllogism?

4. From two given propositions, can a third ever be deduced by a valid process of Reductio ad impossibile when the introduced opposition is Subcontrariety?

In deducing the rules of syllogisms from Aristotle's Dictum, and the process of Reductio ad impossibile, the introduced opposition may always be considered to be Contradiction?

5. In Reductio ad impossibile if Contradiction be introduced, prove that Subcontrariety will not result; the reducend and reduct being each legitimate, whether the reduct conclusion be compared with the suppressed premiss, or with its converse.

6. If a conclusion be drawn from two negative premises by regarding one or both as affirmative, prove that it can assert only that two classes taken together do not make up the universe.

7. Determine the syllogistic modes in which Contrariety results from the application of Reductio ad impossibile, the introduced opposition being Contradiction.

8. Show how Reductio ad impossibile is to be applied to the received syllogisms in the second, third, and fourth figures; and prove that the process is valid in each case.

1

Classics.

PLATO.

MR. GRAY.

Translate the following passages :—

I. Beginning, ̓Απὸ δὴ θαυμαστῆς, ὦ ἑταῖρε, κ. τ. λ.
Ending, δέον ξυνδεῖν καὶ ξυνέχειν οὐδὲν οἴονται.

2. Beginning, Επισκεψώμεθα δὴ αὐτὸ κοινῇ ἅπαντες, κ. τ. λ. Ending, ῥήματος διὰ παντὸς τοῦ ᾄσματος.

Phædo, xlvii.

Protagoras, xxix.

3. Beginning, ΣΩ. Φέρε δή σοι, ἐὰν δύνωμαι, κ. τ. λ. Ending, τοῦ οἰκείου τοῦ διὰ τῆς γυμναστικῆς ἀμελεῖν.

Gorgias, xix.

1. Plato appears to give the stamp of authenticity to the Apology and not to the Phædo?

2. For what purpose may Plato be supposed to have written the Crito?

3. What question is discussed in the Protagoras, and how is it determined? Give a sketch of the argument. What estimate may we fairly form of Protagoras from a study of this dialogue? In what light may we regard the long and curious speech in which Socrates defends the poem of Simonides?

4. How does Grote explain the hostility of Plato to the Sophists ? It is he, and not Socrates, who was peculiarly hostile to them?

5. Review at length the three leading peculiarities of Socrates as given by Grote, comparing him in each point with previous philosophers.

CICERO.

MR. PALMER.

Translate the following passages :—

1. Beginning, Epigrammatis tuis, quae in Amaltheo posuisti,...... Ending, Nihil erat absoluti.

2. Beginning, Primum, ut opinor, εvayyέλia.... Ending, quod sine sumptu corrigi possit.

3. Beginning, Dolabellam video Liviae testamento cum Ending, σύγχυσιν τῆς πολιτείας fore.

Att., i. 16.