II. Grammar. 1. Give Gen. and Accus. Sing., Nom. and Dat. Plur. of νεανίας, ἀνήρ, εὐγενής, ἑστώς, ὅστις; domus, abies, dives, celer, alius. 2. Give the Comparative and Superlative of τλýμwv, píλos, aλyew@s, aureus, graviter, male; and the Positive and Comparative (if any) of κáλλiota, éyyvtátw, acerrime, plurimum. 3. Translate into Greek and Latin-six thousand, thirtyfifth, two hundred and first, fifty, ten times. 4. Write out in full: Fut. indic. active of p0elpw. Imperative of ingredior. 5. Give the 2 aor. active in all moods of náoɣw, ààíoκομαι, βαίνω, γιγνώσκω, φέρω. 6. Give the Perfect, Supine, and Present Infinitive of tollo, scindo, lacesso, aufero, texo, comperio, pessundo, avello, emo, intelligo. 7. Translate into Latin: (1) Dionysius begged them to receive him into their friendship. (2) He died on the first of March, in the year of the city eight hundred and sixty-three, leaving his children ten thousand sesterces apiece. (3) Metellus said that he would not place garrisons in the towns which had yielded to him. (4) He asked me to come to him to be taught whenever I wished. (5) The soldiers were too weak to prevent the enemy from escaping. 8. Translate and distinguish Si quid habeo, dabo. Si quid haberem, darem. : Si quid habuissem, dedissem. Also turn each of these sentences into Oratio Obliqua (after dixit.) 9. Translate into Greek, using the words given :- (1) The ships go down the river to the sea. κάθημαι ἐπὶ πυργὸς βλέπω εἰς (2) The women were sitting on the tower looking into the city. κατὰ νόμος κρίνω περὶ (3) According to the laws no one is judged twice about the same things. 10. Distinguish between : (2) ἕστηκα, ἔστησα, ἔστην. (3) metere, metare, metiri. (4) μὴ κλέπτε, μὴ κλέψῃς. (5) quisque, quisquam, quisquis, quicunque, quivis. 11. Explain the terms Mood, Supine, Accusative Case, Deponent Verb, Subjective Genitive. III. Arithmetic. 1. Find the value of (1 × 1 × 3) × ( 1 + 1 + }) × ( 1 − 1 − }). 2. Divide 375 by 37.5, by 3.75, and by .000375: and find the value of 822-(.8+.02 + .002). 1000 3. Find the cost of carpeting a room 16 feet wide by 21 feet long, with carpet yard wide, at 58. 3d. a yard. 4. What is the interest on 666l. 138. 4d. for 4 years at 5 per cent.? 5. Reduce 27. Is. 8d. to the fraction of 100l., and of a quart to the decimal of a gallon. 6. How many oxen at 247. 108. each can be bought for 10047. 108.? 7. A man has 1000l. in Three-and-a-Half per Cent. securities he sells at 95, and re-invests in Three per Cents. at 76. Find the difference in his annual income. : 8. If Moira coal costs 31s. per ton, and Wallsend coal 46s. per ton, how much do I gain or lose by buying 24 tons of Moira, supposing 3 tons of Wallsend to last as long as 4 tons of Moira ? 9. Find the square root of 1974.8136. 10. If 5000 bricks four inches thick are required for a wall 125 feet long, how many bricks 5 inches thick will be required for a wall 80 feet long? IV. Euclid. [N.B. Two Propositions at least from the Second Book are expected.] 1. Define-a superficies, a line, a diameter of a circle, and a scalene triangle: and state the three postulates. 2. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other, the base of that which has the greater angle shall be greater than the base of the other. 3. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. 4. From a given point draw a straight line equal to a given straight line. 5. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 6. Describe a square that shall be equal to a given rectilineal figure. 7. Draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. 8. If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. 9. The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel. 10. Parallelograms on the same base, and between the same parallels, are equal to one another. V. Algebra. 1. If a=b=c=1, find the numerical value of a2. - (x + a) (2 x + b) (x —α) (2x—b). - amx — 2m2x2 + 3 mnx3-n2x2 by a+mx—nx2, I by 1- to 4 terms. and |