Write notes explaining the sentences printed in italics. Obvii inter se Nero Britannicum nomine, ille Domitium salutavere.

....

•quam imperatore genitam sororemque ejus qui rerum potitus sit et conjugem et matrem fuisse unicum ad hunc diem exemplum est. III. From Hæc, et quæ poterunt reditus. ...

to

...rege temperante cælitum.

HORACE, Epod. xvI. 35–56.

IV. From Sed vatem egregium cui non sit..... .... nihil gemeret grave buccina.

to

Juvenal, vii. 53–71. Quote from Virgil and Horace the passages to which allusion is here made. Does Juvenal's assertion agree with what Horace says of himself, and is it generally true? Give examples.

1. For Latin Prose:

III.

The philosophy which affects to teach us a contempt of money does not run very deep; for, indeed, it ought to be still more clear to the philosopher than it is to ordinary men, that there are few things in the world of greater importance. And so manifold are the bearings of money upon the lives and characters of mankind, that an insight which should search out the life of a man in his pecuniary relations would penetrate into almost every cranny of his nature. He who knows, like St. Paul, both how to spare and how to abound, has a great knowledge: for if we take account of all the virtues with which money is mixed up,honesty, justice, generosity, charity, frugality, forethought, selfsacrifice, and of their correlative vices,-it is a knowledge which goes near to cover the length and breadth of humanity: and a right measure and manner in getting, saving, spending, giving, taking, lending, borrowing, and bequeathing, would almost argue a perfect man.

2. For Latin Hexameters :

They couch'd their spears and prick'd their steeds and thus,
Their plumes driv'n backward by the wind they made
In moving, all together down upon him

Bare, as a wild wave in the wide North-sea,
Green-glimmering toward the summit, bears, with all

Its stormy crests that smoke against the skies,
Down on a bark, and overbears the bark,
And him that helms it, so they overbore
Sir Lancelot and his charger, and a spear
Down-glancing lamed the charger, and a spear
Prick'd sharply his own cuirass, and the head
Pierced thro' his side, and there snapt, and remained.

3. For Greek Prose:

But then, this happy temper and these good faculties rather preserved him from having many enemies, and supplied him with some well-wishers, than furnished him with any fast and unshaken friends; who are always procured in courts by more ardour, and more vehement professions and applications, than he would suffer himself to be entangled with. So that he was a man rather exceedingly liked, than passionately loved: insomuch that it never appeared, that he had any one friend in the court, of quality enough to prevent or divert any disadvantage he might be exposed to. And therefore it is no wonder, nor to be imputed to him, that he retired within himself as much as he could, and stood upon his defence without making desperate sallies against growing mischiefs; which, he knew well, he had no power to hinder, and which might probably begin in his own ruin. To conclude; his security consisted very much in the little credit he had with the King; and he died in a season most opportune, and in which a wise man would have prayed to have finished his course, and which in truth crowned his other signal prosperity in this world.

IV.

1. Make a triangle whose sides shall be three given straight lines any two of which are together greater than the third. Whence arises the necessity for this limitation? Where, in your investigation, do you make use of it?

2. Find, as Euclid does, the difference between the square of the side of a triangle subtending one of the acute angles and the squares of the sides containing it.

3. Draw a straight line touching two given circles. 4. Is a ratio of greater inequality increased or diminished by adding the same quantity to both its terms?

see this at once by taking an extreme case?

Can you

5. Explain the difference between interest and discount;

and find the difference between the interest of £350 for 15 months at 4 per cent. and the discount on £350 for the same time at the same rate of interest.

6. In an arithmetical progression, given a, s, d; find n. Explain the double answer in the cases when n being integral has two positive values, or one positive and one negative. If n is fractional, what is its meaning? Illustrate by the following instances: find the number of terms of the series 3, 4, 5...which make 18, and of the series 7, 6, 5...which make 22.

7. Find the sum of n terms of the series

1.2.3 + 2.3.4 + 3.4.5 + &c.

8. Having given in a triangle, b = 9.5, c = ·5, A = 36°; find the remaining angles,

=

log tan 16°.18' 9.4660078,

log tan 16°.19' = 9.4664765,

=

log cot 18° 9.5117760,

log 34771213.

9. Assuming Demoivre's theorem for an integer, prove it for a fraction; and apply it to find the values of (1)3.

10. The section of a right cone made by a plane which is parallel to a plane touching the cone along its slant side, is a parabola.

A parabola being traced on paper, shew how its axis and directrix may be found.

11. Find the locus of the middle points of all chords in an ellipse at a given distance (p) from its centre.

12. Trace the curves = =

y x (x-1)

and y2

=

x(x-1)

a (x-2)(x-3)

a2 (x-2)(x-3)*

13. A Norman window consists of a rectangle surmounted by a semicircle. Having given the periphery, determine the height and breadth of the window when the quantity of light admitted is the greatest possible.

14. Find the equation to the curve in which a chain acted on by gravity will hang.

V.

1. Give Euclid's constructions for inscribing a circle in a given triangle, and describing a circle about a given triangle. If R, r be the radii of the circumscribed and inscribed circles of a triangle, the square of the distance between the centres R2-2Rr.

=

2. Similar triangles are to one another in the duplicate ratio of their homologous sides.

3. A clock is right at mid-day to-day, but it gains one ninute per day. What will be the true time when it points o mid-day to-morrow?

4. Divide 01 by 0002 and 00001 by 03; find also a ourth proportional to 999, 33.3 and 03.

5. Solve the equations:

(1) x + y = 4, x* + y* = 82;

(2) cose + sin = +

√(2)

and shew that if ax2 + bx + c = 0 and a ̧æ3 + b1x + c1 = 0, then will (ab ̧ - α ̧b) (bc1 − b1c) = (ac1 − α ̧c)2.

6. There are n things of which p are alike and the remaining n -p different. Shew how to find the number of permutations of them taken r together. Ex. n = 7, p = 3, r = 3. 7. Find by the Binomial Theorem the coefficient of x” in (1 - 2x)2 (1 - x)'

the expansion of (1 - x) and

;

and find when the series for (1+1) begins to converge.

8. The probability of A solving a problem is, and of its being solved when both A and B try it is 2. Find the probability of B solving it.

9. A person walking along a straight road observes the greatest angle a subtended by two objects in the same plane with the road. He then walks a distance a along the road, and the objects appear in the same direction making an angle ẞ with the road. Shew that the mutual distance of the objects 2a sin a sinẞ

=

cosa + cosß

10. Define a rectilinear asymptote. Prove the property of the hyperbola RP. Pr = CB2, and shew hence that the lines CR, Cr are asymptotes.

11. If y = e cos x, shew that

d'y

+ 4y = 0, and find the

dx

logx logx

12. Explain the action of an oar in rowing. If a man pulls an oar 12 feet long with a force of 120 lbs., the distance from the handle to the rowlock being 3 feet, what is the effective force to propel the boat?

13. Define the centre of gravity of a body. Mention how it is shewn that every body has a centre of gravity.

Eight equal bodies are placed at the angular points of a cube. If one be taken away, where will the centre of gravity of the remainder be?

14. Two bodies are projected vertically upwards from the same point with equal velocities u at an interval of one second. When and where will they meet?

MINOR SCHOLARSHIP EXAMINATION.

ST. JOHN'S COLLEGE. June, 1861.

2. From Καὶ τάδε ἄλλα Αἰγυπτίοισί....
to ....κατα ταυτὸ νομίζουσι ἀποβήσεσθαι.

3. From Αἰσχρὸς ὦ ἄνδρες Ἀθηναῖοι.... to . . . μηδαμώς, ὦ ἄνδρες Αθηναῖοι.

HEROD. II., 82.

DEMOSTH., C. Leptin., p. 505, Reiske.

Translate into Greek Prose:

The historian to whom we are indebted for the most ample and authentic information we possess concerning Alexander, Arrian of Nicomedia, takes this occasion to remark, that in this respect the Macedonian hero had indeed been singularly unfortunate; since even the expedition of the younger Cyrus, and the return of the ten thousand, had been rendered by Xenophon's pen more renowned than the incomparably greater actions which he himself was about to record. The remark itself strikes us as somewhat strange, when we reflect on the immense mass of historical writings, which in Arrian's time were still extant, relating to Alexander's reign, and that among the contemporary authors who treated this subject, two were eminently qualified by their station and opportunities to do it justice. Two of his generals, Aristobulus, and Ptolemy, who held one of the highest posts in the army, and afterwards became king of Egypt, undertook the office of relating his conquests; and they both wrote after his death, when they were no longer subject to the strongest of the motives that might before have induced them to swerve from the truth.