VIRGIL.

TRANSLATE two passages, - I. and either II. or III. Answer all the questions.

I.

II.

Pauca tamen suberunt priscæ vestigia fraudis,

Quæ temptare Thetim ratibus, quæ cingere muris
Oppida, quæ iubeant telluri infindere sulcos.
Alter erit tum Tiphys, et altera quæ vehat Argo
Delectos heroas; erunt etiam altera bella,
Atque iterum ad Troiam magnus mittetur Achilles.
Hinc, ubi iam firmata virum te fecerit ætas,
Cedet et ipse mari vector, nec nautica pinus
Mutabit merces: omnis feret omnia tellus.

ECL. IV.

Postera iamque dies primo surgebat Eoo,
Humentemque Aurora polo dimoverat umbram :
Cum subito e silvis, macie confecta suprema,
Ignoti nova forma viri miserandaque cultu
Procedit supplexque manus ad litora tendit.
Respicimus. Dira inluvies inmissaque barba,
Consertum tegumen spinis; at cetera Graius,
Et quondam patriis ad Troiam missus in armis.

III. Primus equum phaleris insignem victor habeto,
Alter Amazoniam pharetram plenamque sagittis
Threiciis, lato quam circumplectitur auro
Balteus, et tereti subnectit fibula gemma;
Tertius Argolica hac galea contentus abito.
Hæc ubi dicta, locum capiunt, signoque repente
Corripiunt spatia audito, limenque relinquunt,

EN. III.

Effusi nimbo similes, simul ultima signant. -ÆN. V.

1. Give a brief summary of the events in Æneid IV.

2. Divide into feet, marking quantities and ictus (or verse accent), the fifth line in I.

3. How does the metre help to determine the meaning of the fifth line in II. ?

ARITHMETIC AND LOGARITHMS.

[Give the work in full, and arrange it in an orderly manner. Reduce each answer to its simplest form.]

3. Give a proof of the process of finding any root of a quantity by logarithms. If the characteristic of the logarithm of the given quantity is negative, how is the characteristic of the logarithm of the root obtained?

rate of 8

5. A carriage, at the

a certain distance in 3

plete

hour?

miles an hour, completes of days; in how many days will it comof the same distance, going at the rate of 10 miles an

6. A merchant buys 23 hectometres of silk for $480, and sells the silk at $1.95 a yard. Does he gain or lose, and how much?

7. Find the cube root of 0.083453453.

8. Thirty-six persons buy 2766 A. 3 R. 12 P. of land on equal shares. What does one man receive, who sells of his share at 1 s. 9 d. 2 f. per square rod? [Give the answer in pounds and decimals of a pound.]

9. What is gold quoted at, when one dollar in currency is worth only seventy-five cents?

[Give the whole work clearly, and reduce each answer to its simplest form.]

2. A can do a piece of work in half the time in which B can do it, B can do it in two thirds the time in which C can do it, and all three, working together, can do it in 6 days. Find the time in which each can do it alone.

3. Find the two middle terms in the expansion of (a — x)o. What is the reason that one of these terms is negative, and the other is positive?

4. Find the fourth root of a2c2. [Fractional exponents may be used if desired.]

5. One number is 10 of another, and the product of these two numbers is 750. What are the numbers?

7. I bought a certain number of oxen for £80. Had I bought four more with the same money, each ox would have cost £1 less. How many did I buy, and what did I pay for each?

8. Find the square root of

8m

am+6a3m ch+11a2m c2 + 6am c3n + cân.

N

ALGEBRA.-Course II. and Advanced Standing.

[Give the whole work clearly, and reduce each answer to its simplest form.]

2. A man rides a certain distance at the rate of 8 miles an hour, and walks back to his starting-point at the rate of 4 miles an hour. The time employed in going and returning is 6 hours. How far does he walk?

4. Solve the equation x2+2ax = b. What will the roots be if a = 2, b = -4? If a =

5. What is the 4th term of (a

4, b=

-20?

6. The greater of two numbers is a2 times the less; the product of these two numbers is 62. Find the numbers.

7. There are 3 numbers in arithmetical progression: the sum of these numbers is 18, and the sum of their squares is 158. Find the numbers.

8. I have 4 single books and a set of 3 books. In how many ways can I arrange these 7 books on a shelf, provided the books which make the set cannot be separated?

PLANE GEOMETRY.-Courses I. and II.

1. In a triangle A B C the angle A is greater than the angle B, and B is greater than C; what is true of the sides? State

and prove.

State and prove the converse.

2. Prove that two triangles are equal if the sides of one are respectively equal to the sides of the other.

3. Prove that when two circumferences touch each other the point of contact and the centres lie in one straight line.

4. Draw two circles touching each other, and through the point of contact draw a straight line forming a chord in each circle: prove that these chords are proportional to the diameters of the circles.

5. To draw the circumference of a circle through three given points. Solve and prove. When would the problem be impossible? Why?

Given any curve, to ascertain whether it is the arc of a circle or not.

6. Prove that the perimeters of regular polygons of the same number of sides are proportional to the diameters of their inscribed or circumscribed circles. Go on to prove that the ratio of the circumference to the diameter is the same in all circles.

7. Draw, in your book, a regular hexagon of which each side shall be of this length

Explain how you do it. Now draw another having half the area of the first. Solve and prove.