Cos. What! shall I slay all, then, that I suspect? Translate the following passage into Latin Verse : How has kind heaven adorned the happy land, her blooming mountains, and her sunny shores, Logics. KYD. ADDISON. 1. What two fundamental principles lie at the basis of every Syllogism, according to Mill? These may be reduced to one? 2. What does he hold to be the major premiss of the Syllogism? and what are the real logical premises from which the conclusion is drawn? 3. How far is a Science experimental, and how far deductive? 4. What are the discoveries which generally change the method of a Science from experimental to deductive? 5. Invent an example to show that from false premises a true conclusion may be deduced. 6. Supply premises to the following conclusions:-(a) Some logicians are not good reasoners; (6) Party government exists in every demo cracy. 7. Examine the validity of the following argument:-Suicide is not always to be condemned, for it is but voluntary death, and this has been gladly embraced by many of the greatest heroes of antiquity. Ꭰ Ꭱ . SHAW. 1. Mill proves by a sorites the necessity of a chapter on the Categories, to a treatise on Logic? 2. Quote from Hobbes some passages in which the true theory of predication is recognised. 3. What did Logicians make of differentia as soon as they found that essences were undiscoverable ? 4. Why, and how far, is a chapter on Classification necessary to complete the theory of general names and of their employment in predication ? 5. The nature of mathematical postulates helped to keep up the notion that definitions are the principles of demonstrative science. How so? 6. What mistake did the Aristotelians make as to the ordinary purposes of definitions? MR. PANTON. 1. X is the name of a class of objects, each of which possesses, in addition to the attributes of another class Z, certain attributes peculiar to its own class; Y is the name of a different class similarly related to Z. It is required to construct all the true propositions, affirmative and negative, which may be formed with any one of the terms, X, Y, Z, as subject, and any other as predicate. 2. Give examples of true and false hypothetical propositions. How is a hypothetical proposition converted? Find, by converting the special rules of the fourth figure, the modes in the following cases : (a). When the major is particular. 3. State Aristotle's dictum, and show that it is immediately applicable to prove the validity of conclusions in the first figure when the two special rules are observed. Show also that its applicability to a Sorites requires that the two rules of Sorites should be observed. 4. Supply the missing premiss in the following enthymemes; and distinguish, among the resulting syllogisms, those whose mode and figure are determined from those which may belong to two figures:— 5. Show that the substitution of its contradictory for a premiss in any legitimate mode never gives rise to legitimate premises except in the third and fourth figures, and then only when the retained is the minor premiss and A. When the substitution is legitimate, determine the relation between the new and old conclusions. Determine whether the substitution of its subcontrary for a premiss ever gives rise to legitimate premises; and find, in that case, the relation between the new and old conclusions. 6. Determine the modes in which, in reduction ad impossibile, when contradiction is introduced, contrariety necessarily results. Determine all the modes in which the introduction of sub-contrariety leads to resulting legitimate premises in the first figure. Show that the latter kind of opposition is never valid in reduction ad impossibile. 7. Determine the mode in each of the following cases :— (a). When the conclusion is A. (b). When the major premiss is 0. (c). When the minor premiss is 0. (d). When an extreme has different quantity in premiss and conclusion. JUNIOR FRESHMEN. Mathematics. A. MR. WILLIAMSON. 1. Given the base and the vertical angle of a triangle, find the locus of the intersection of its perpendiculars. 2. A, B, C, D are four points on a right line, taken in order, prove that the rectangle under AC and BD is equal to the sum of the rectangles under AB and CD, and under AD and BC. 3. Describe a circle touching two given lines, and passing through a given point. 4. The sides of a triangle are 200, 187, and 123, respectively; find the length of its least perpendicular. 5. Solve the equation √2x + 1 + √2x + 10 + 4 √ 2x + 3 = 3. What ought the 6. A man and his son, working together, can do a piece of work in 12 days; the man by himself could do it in 20 days. son's wages to be, if his father gets 5s. a day? MR. BURNSIDE. 7. Show how to inscribe a square in any given triangle. 8. The perpendiculars drawn from the vertices of a triangle to the opposite sides meet in a point. 9. Prove that the sum of the squares on the diagonals of a parallelogram is equal to the sum of the squares on the sides. 10. Determine x, y, z from the equations II. The sum of two numbers is 20, and the sum of their cubes 2060; find the numbers. 13. Cut off the corners of a square so as to form a regular octagon. 14. Construct a triangle, being given the bisectors of the sides. 15. Show how to draw a line to touch two circles. 17. A sum of money amounts to a after 4 years, and to b after B years; find the sum and rate of simple interest. 18. Extract the square root of 10 + 2√21. B. MR. WILLIAMSON. 1. If a circle touch two fixed circles, prove that its radius bears a constant ratio to the distance of its centre from the radical axis of the given circles. 2. ABC is an equilateral triangle, find the locus of the point P when PA = PB + PC. 3. A right line touches a circle at a point A; if, from two other points B, C on the circle, perpendiculars BL, CM be drawn to the tangent, prove that BL: CM = BA2: CA2. 4. Solve the equations x2 + xy = 77, xy-y3 = 12. 7. Draw a right line ẞ from the vertex of a triangle to the base dividing it into segments σ, o', so that σα B2 be given. 8. If a circle cut two circles at constant angles, it will also touch two fixed circles. 9. Determine the locus of a point, such that the area of the triangle, formed by joining the feet of the perpendiculars drawn from the point to the sides of a given triangle, may be constant. 10. Determine x, y, z from the equations 12. Find three numbers in geometrical progression such that their product may be 64, and the sum of their cubes 584. √x2 + 2ax - b2 + √x2 + 2bx − a2 = a + b. 15. Construct a right-angled triangle having its sides in continued proportion. 16. Show how, by geometric construction, to divide a circle into any number of concentric rings of equal area. |