18

H.—l6.

"Je m'en vais, mon cher Cardinal; je sens que je m'en vais a Dieu; je m'affaiblis de jour en jour ; ni l'ete, ni lair dv midi, ne mont rendu mes forces." " Je precederai Votre Majeste," repondit le ministre ; "la inort a deja conquis mes jambes, vous le voyez, mais tant qu'il me restera la tel:e pour penser, et la main pour ecrire, je serai bon pour votre service." —"Et je suis sur que votre intention etait d'ajouter le coeur pour m'aimer," dit le roi.—"Votre Majeste en peut-elle douter?" repondit le cardinal, en froncant le sourcil, et se mordant les levres par l'impatience que lvi donnait cc debut. —" Quelquefois j'en doute," reprit le prince; " tenez, j'ai besom de vous parler a co3ur ouvert, et de me plaindre de voua a vous-meme. II y a deux choses que j'ai sur la conscience, depuis trois ans ; jamais je ne vous en ai parle, mais je tous en voulais en secret; et meme, si quelque chose cut etc capable de me faire consentir a dcs propositions contraires a vos interets, c'eiit etc cc souvenir." 2. Write in French —(«) each with a definite article, five names of animals ; (5) with an indefinite article, five names of flowers; (c) with & partitive article, five names of metals or minerals. 3. Distinguish between an and anne'e; connaitre and savoir; dans and en; sur and dessus; en eampciqne and a la campagne. 4. Render into French — (a) " Did you ask for me ?" (V) "I am not very rich." (c) "Let us go and take a walk." "No ; I can't just now. I must learn my lessons first; but I shall be very glad to go with you presently." 5. When is the preposition de used before the verb in the infinitive mood ; when the preposition a ? TRIGONOMETRY. 1. The angles of a triangle are in arithmetical progression, and the number of grades in the least is to the circular measure of the greatest as 30 to it. Find the angles. 2. Define the cosine of an angle ; and show how it changes in magnitude and algebraic sign as the angle increases from 0° to 180°. 3. Divide, by a geometrical construction, a given angle into two parts whose cosines shall be in a given ratio. 4. Prove the following formulae : — (1.) Sin (w+o) = —Sin'o. (2.) Sin A-Sin B= 2 Sin A-^ B . Cos^t?. (3.) Cot A . Cot B + Cot B . Cot C + Cot C . Cot A=l,_where A+B + C = 180°. 5. Prove that Sin (A+B) = Sin A. Cos B + Cos A. Sin B, when A+ B is greater than a right angle, and less than two right angles. 6. Define a logarithm, and show that the decimal part of a log. is independent of the position of the position of the decimal point in the corresponding number. 7. Given log. 71968=4-8571394 ; diff. for I=6o. Find the value of VW19686. 8. Express the cosine of an angle of a triangle in terms of the sides. If the sides of a triangle be xz + x+l, 2# +l, a; 3—l, show that the greatest angle is 120°. 9. Find the radius of the escribed circle which touches one side of a triangle and the other two sides produced. 10. Solve the triangle AC=sll'76; 8C=317-09; A=s6° 31' 14". 11. A fortress was observed by a ship to bear E.N.E., and, after sailing due E. for four miles, it was found to bear N.N.E. Find the distance from the fortress at each observation. ALGEBRA. 1. Simplify (2o —3J)*— («-l) .r— {a — 2b)x —x. 2. Divide 4a™— 3%"> by 2a mx m. 3. From (a — V) (e — d) take (b — a) (c — d), and show what the result would be if a=2b, and </=2c. 4. Express in fractional form a — l-\- c- —^ 5. From the sum of |a + -j5 + ie, \a —|^ + ie, and-ya + iS — \c, take c — a-\-\h. 6. Solve the following equations : — 5" +2a? 5 2x 2x f ax + by—c. \px + qy — d. a; 3 + 6.r = 2-4# + 5005. 7. John is half as old again as Harry, and Tom is five years older than both their ages added together. The sum of their ages is 55. How old are they each ? 8. Express with fractional indices Vx''+ Vx 2+ (Vx)1; with negative indices, so as to remove all x* 4i powers from the denominators, -, + —„- +—;; with negative indices, so as to remove all power from the i x x% cc* y y y numeratcrs,- + -~ 3 + p - T +- tv a v o 9. Some friends gave a picnic, agreeing to share all expenses, which came to £10 ; but three did not pay, and the others had to pay 15s. each additional. How many were there in the party ? 10. Decompose into two equal factors ns 2—4 aS —6«c+4J 3 + 12Jc + 9c 2 ; find the «th power of 3ax m; and expand! m+ 1 — ) . 1 x in) 11. What number is that to which, if 24, 12, and 312 be severally added, the first sum will be to the second as the second to the third ? 12. Two persons invest £900, and gain £125 by the speculation. Of this gain, one person is entitled to £35 more than the other. How much did each invest ?