3. Give an account of the pronominal eccum, and decline ecquis. Distinguish the genitives nostrum and nostri. guish, alius-alter. Distin 4. Write seven hundredth in Latin. In the sentence, legionariis ccc numum millia viritim dedit, write ccc at length. 5. How may the Latin conjugations be reduced to one? Define a verb transitive, and explain "olet unguenta." State what verbs take a double accusative; and explain, Socratem philosophum appellant. 6. What is the Latin for I sent you a letter? Correct the expressions :-laborem parcere-tribunos obedire-principi adire. When we find ludos Circenses eburna effigies præiret, how do we guide ourselves in ascertaining the government of compounded verbs?-Maledicimur et benedicimus: criticise the Latinity. 7. Give examples of passive deponents. Give instances of the interchange in etymology between Z and D. 8. Distinguish aut from an; and explain the following:Illic fugam tentans an ficto crimine interficitur. V.-Greek Grammar. 1. WHEN We have a word ending in a, must we decline it like μοῦσα, or like φιλία, or like σῶμα? 2. Decline, ἱππεὺς-πατὴρναῦς-ὑγιής. 3. Compare, φίλος-κλέπτης. 4. How do the Greeks express the two articles of the English? 5. Explain, ὅτου-νίν-σφε. 6. Give the syncopated forms of the moods and persons of έστηκα 7. What is the meaning of Terapraîos? 8. Express in Greek, self-same-he. 9. Name the four dialects, and the authors in each. FIRST CLASS MATHEMATICAL SCHOLARSHIP. I. Euclid and Trigonometry. II.—Algebra. THE questions upon these subjects were the same as those set for the Junior Mathematical Scholarship in the Department of General Literature and Science. SECOND CLASS MATHEMATICAL SCHOLARSHIP. I.-Euclid. 1. DESCRIBE an isosceles triangle, having each of the angles at the base double of the third angle. 2. Shew that the base of the triangle is a side of a decagon inscribed in the large circle, and a side of a pentagon inscribed in the small circle. 3. In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. 4. If squares be described on the sides of any triangle, and the angular points be joined, the sum of the squares of the hexagonal figure thus formed, is equal to four times the sum of the squares of the sides of the triangle. 5. If from a point P, in the diameter AB of a circle, PQ, PR be drawn to the extremities of the chord QR, which is parallel to AB, then shall AP+PB2 P Q2 + PR2. 6. Triangles upon equal bases, and between the same parallels are equal to one another. 7. Let ABC, ABD be two equal triangles on the same base AB, and on opposite sides of it; join CD, cutting AB in E; then shall CE = ED. 8. In a circle, the angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. 9. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. 10. If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle so as to have their homologcus sides parallel to one another; the remaining sides shall be in a straight line. 11. If ABCD be a parallelogram, and P and Q two points in a line parallel to AB, and if PA, QB meet in R, and PD, QC in S; prove that RS is parallel to AD. 12. A lamp elevated 32 feet from the ground is just seen by a man six feet high at the distance of 10 miles; determine the earth's radius. II.-Algebra. 1. Ir four quantities be proportionals according to Euclid's definition, prove that they will be so according to the algebraic definition. 2. If a: a b b1 :: c : c1, &c. &c., then shall 1 1 a: a1 :: am + b n + cp+ &c. : a ̧m + b1n + c1p + &c. 3. Two clocks point to 12 at the same instant; one of them gains 7", and the other loses 6" in 12 hours. When will one have gained half-an-hour on the other, and what time will it show? 4. If x2 (9 +5√/3) + ≈ (15 +7 √/3) + 6 = 0, find z. 5. If x45x3y-3x2y2+5 xy3+y1= 379, and x* — 3 x3y + 5 x2 y2 — 3 x y3 + y2 = 43, find x and y. 6. If a, b, c, d be in geometric progression, then (a + b + c + d)2 = (a + b)2 + (c + d)2 + 2 (b + c)2. 7. The sum of the squares of two numbers, divided by their ratio, equals 10; the difference of their squares, multiplied by their ratio, equals 24. Find the numbers. 8. A passenger in a railway carriage observes a train moving in the opposite direction to pass him in 2"; and also that another train moving in the same direction as his, with the same speed as the former train, but twice its length, takes 40′′ to pass him compare the speed of the two trains. 9. Exhibit as binomial surds the square root of ; 12 −8√√/2+6√/3 — 4/6, and the cube root of 2√√/7 +3√3: 10. If a be the first and be the last of a series of numbers in geometric progression, prove that the continued product of the terms is (a l)2. 12. There are two vessels A and B, each containing a mixture of water and wine, A in the ratio of 2: 3, B in the ratio of 3:7. What quantity must be taken from each in order to form a third mixture, which shall contain 5 gallons of water and 11 of wine? |