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5. Give the etymology of moneo, terreo, sopio, ploro, lavo.
7. How does it appear that the tendency of events in the latter period of the Republic was towards monarchy?
8. How was the despotism of the emperors practically limited ? M. Merivale compares the working of the Roman Constitution under the empire with that of the British Constitution at present; in what respect are they similar.
9. Give an account of the administration of the senatorial and imperial provinces respectively.
Translate the following passages into Latin Hexameters :-
Translate the following passage into Latin Prose :Beginning, There lurks, perhaps, in every buman heart...... Ending, an airy temper and a quick apprehension.
DR. JOHNSON to Boswell.
Translate the following passage into Greek Prose :Beginning, The members of the Government. Ending, and arranged all other matters concerning the forces as he pleased.
Franslation of Thucydides.
Translate the following passage into Greek Iambics :-
KIRKE WHITE, Instability of Human Glory.
1. If a conic pass through three fixed points, and cut a given finite line harmonically, it passes through a fourth fixed point ?
and bring the result to the simplest form. 3. Integrate
and x2 sin x dx.
cos*x 4. Given a self-conjugate triangle with regard to a parabola, three tangents to the curve are given?
5. The portion intercepted between the axes of a tangent to an ellipse is a minimum; find its length.
6. Find an expression for the length of the line joining two feet of perpendiculars of a spherical triangle.
7. Find the limit to which
TT x tan x
approaches, as x approaches
r 8. Find the envelope of all the ellipses having the length of the line joining the extremities of their semiaxes constant, the axes being coincident. 9. Find the parameter of the parabola
9x2 – 12xy + 4y2 – 36x – 244 + 36 = 0, the axes being rectangular.
10. Prove that in a parabola the distances of any point on the curve and its centre of curvature from the directrix are in the ratio of 1: 3.
11. A teetotum of eight sides, numbered 1, 2, &c., is spun three times consecutively; what is the chance that it will fall on the numbers 2, 4, 7 in any order whatever ?
12. Apply Horner's method to find to three places of decimals the root lying between 1 and 2 of the equation
23 - 3% – 1=0.
13. Find the maximum and minimum values of
tan 43 14. Find the integrals
✓ 1 + x - 1 y=tan 1
dt 16. Find the common root of the equations
** +223 – 822 – 7% + 14 = 0,
act + 3x3 – 16x9 +152 – 6=0. 17. Find the locus of the centre of a circle which makes given intercepts on two fixed lines.
18. Apply the method of projections to the following question :
Through a given point a transversal is drawn cutting a conic, and the points of section are joined to two fixed points on the curve; find the locus of the intersection of the joining lines.
1. Find the locus of the vertex of a triangle whose sides touch one conic, and whose base angles move on another.
2. The two parabolas which can be described through four given points, a, b, c, d, have as common tangents the lines joining the middle points of the sides of the triangle (ab, cd), (ac, bd), (ad, be)?
3. By the ruler alone draw a tangent at any point on a conic.
(1 – x2)/1-6222 3. If y= a +ä sin y, expand sin y in powers of x.
6. If T and T'' are the feet of the perpendiculars from the foci on the tangent at any point P of an ellipse, determine P so that PT2+ PT"? shall be a maximum.
7. Find in trilinear co-ordinates the equation of a conic touching the lines a, b, y, and having its centre at a given point a'B'y'.
8. Prove the general expression in polar co-ordinates for the radius of curvature, namely,
do d02 and apply it to find the radius of curvature of the spiral r=ad.
9. Find the envelope to the series of parabolas determined by the equation
122 y=mx –
- (1 + m2) where m is the variable parameter.
10. Show that the absolute term in the equation to the squares of the differences of the roots of a biquadratic is
11. Find either of the integrals, do
xndx (a + b cos 0)2 12. Find the locus of the point in which the focal radius vector of an
b ellipse intersects the line drawn from the centre to the point x', ; y'.
sca + bx + (x2)
13. Integrate the expression
(a + 8 cos &+ c sin 2) da
a+b cos x + csin 14. Find the equation whose roots are aß + yo, ay + B8, and By + ad, where a, b, y, d are the roots of the biquadratic equation
204 + pr3 +qx2 + ræ+8=0; and show that the result is the same as the reducing cubic in the ordinary method of solving the biquadratic.
15. Given of a conic one focus, two points, and a tangent, show that another tangent can be constructed; and hence the second focus found. State the number of solutions of the problem.
16. Determine the value of the radius of curvature at the origin to the curve
3y = 42 — 1522 — 323 + x4, find also at what points the radius of curvature is infinite.
17. Find the whole area of the curve
18. Prove that the equation of a conic inscribed in a quadrilateral may be written in the form
I - H
STEWART'S DISSERTATION, AND BACON.
1. The optimism of Leibnitz was necessary from his system? State its defects as compared with that of other philosophers.
2. State Spinoza's conception of the Deity as explained by Stewart; and the leading points of difference in it from that acknowledged by Christians ?
3. What is Laplace's explanation of the sufficient reason? He misapprehends the Epicurean views according to Stewart. Explain the principle as applied to man's conduct.
4. How does Stewart state Kant's argument for man's free will, who rests his proof on two grounds ? What is the condition of man's responsibility, according to Kant?
5. Locke says, “The next thing to be considered is how bodies produce ideas in us: and that is manifestly by impulse, the only way in which we can conceive bodies to act.” Show that this may be explained without contradicting the fact of Locke being a conceptualist. The principle involved is one admitted by many philosophers ?
6. Show that the system of metaphysical inquiry chiefly pursued involves the dangers arising from idola specus; and point out how this may be to some extent avoided.
7. State the curious views of Leibnitz on the subject of knowledge, as noticed by Stewart, which seem closely to resemble those of Plato.
8. Show that Idealism, in the English sense of the word, is the natural result of Kant's system.
9. To what sciences, according to Bacon, is syllogism applicable? Why does he reject it in the case of some other sciences ? and what difference, which he alludes to, exists in the two classes ?
10. State Bacon's instances of idola tribus ; and the special cases which he adduces to illustrate each.
STEWART AND MANSEL.
1. State at length the views of the Realist and the Nominalist respecting Ideas. Mention the principal philosophers of these two sects, both ancient and modern, noting the opinion peculiar to and distinctive of each.
2. On what grounds does Mansel exclude the principle of the sufficient reason from the laws of thought?
3. How do the views of Stewart and Mansel differ respecting Perception, Conception, and Imagination ?