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Mais de sa vie éteindre le salpêtre,
Savoir se vaincre, et réprimer les flots
De son orgueil, c'est ce que j'appelle être

Grand par soi même ; et voilà mon béros !
d. Lorsque le chantre de la Thrace

Dans les sombres lieux descendit,
On punit d'abord son audace
Par sa femme qu'on lui rendit.
Mais bientôt, par une justice
Qui fit honneur au dieu des morts,
Ce dieu lui reprit Eurydice

Pour prix de ses divins accords. 3. La route, etc. Give the English equivalents of attendre, hisser, route, plaisant, éditeur; and the French of to attend, to hiss, the rout, pleasant, an editor.

4. Quoique la route n'atteigne, etc. Why is the verb in th subjunctive? What conjunctions always take this mood ?

5. L'attelage à la téte baissée, etc. Translate : The girl with blue eyes. The men with grey hats. The wineglass. The glass of wine.

6. What is the rule for the gender of words in -&, -age, and -ment ? Give a few exceptions. 7. Translate into French :

a. She is kindness itself.
b. The Romans borrowed much from the Greeks.
c. It is three years since their only son died.
d. These last two months I have been learning to skate.

e. We have beeu much mistaken.
8. Translate into English :

a. Cela vaut-il la peine que j'y aille ?
b. Je fais des chateaux en Espagne.
c. Je n'ai jamais eu le mot de l'énigme.
d. J'en ferai bien autant.

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GERMAN.

Time : three hours. 1. Give the nominative plural of: Aas, Adverb, Bestreben, Bett, Individuum, Joch, Kapital, Kraut, Kreuz, Laut, Rand, Tod.

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2. Give the gender and the meaning of each of the following words : Abscheu, Absicht, Andacht, Bericht, Demut, Feier, Feiertag, Feuer, Gegenteil, Genie, Genius, Gesicht, Hochmut, Nachricht, Rückkehr, Scheu, Teil, Verdacht, Verkehr.

3. Give the third person singular of the present indicative of heben, stossen, fahren, lesen ; the first person singular of the perfect indicative of genesen, geniessen, stehen, schreiten; and the first person plural of the present conditional of bringin, helfen, messen, empfehlen.

4. Give the second person singular of the preterite (imperfect) of springen, vorausgehen, anerkennen; the past participle of bitten, schweigen, veranstalten ; and the second person singular and plural of the imperative of essen, stehlen, schwellen.

5. Write down the adjectives which are derived, by means of prefixes, from Glück, Gunst, Horn, Recht, Stern, Treue, Sitte ; denken, dulden, laufen, nehmen, trauen, warten, wissen.

6. Give the German equivalents for the following geographical terms and phrases : a plain ; a lowland ; a plateau ; a mountain range ; a spur; the river rises ; the basin of a river; the mouth of a river; a tributary; a watershed; the river empties itself into the sea ; a strait ; an isthmus ; a bay; an island ; a peninsula ; a promontory.

7. Explain, by examples, how ordinal and fractional numbers are formed in German.

8. Translate, by the use of the gerund (or future passive participle), the following sentences :

a. This is the problem to be solved.
b. There came to him a joy never to be forgotten.
c. I know no one who is more to be despised.
d. You expressed a wish difficult of fulfilment.
e. The harvest to be looked for will be a mediocre one.
f. It is a matter to be determined hereafter.

9. Translate into German :

It was a dull winter's morning. It seemed as if day would never break. Harshly a bell rang out amid the mist, and when it ceased, a voice was heard boarsely singing one single verse of a funeral hymn. It was a poor old man, who, as he had led a dull and tuneless life, was as' unmelodiously laid in his grave. But now his spirit, up on those shining heights yonder, hears the choirs of angels sing, and revels in the full rich harmonies that are wafted through all the world.

UHLAND (Abstract).

10. Translate :

Mich wundert nicht, wenn du dich von mir wendest,
Und müde nun die lange Marter endest.
Nur wie ein Leh'n empfieng ich dieses Glück.
Die Zeit ist um—so nimm es nun zurück!
Nach Leben dürstest du mit allen Sinnen-
Ich steh' abseits und seh' den Tag verrinnen.
Ein Siegerlächeln spielt um deinen Mund-
Ich bin zertreten, müd’und fieberwund
Und wenn du staunend stehst in lauter Licht-
Mir fallen Schatten übers Angesicht.
Was soll ich dir ? Dem Weg führt steil empor,
Wenn meiner längst im Dunkel sich verlor.
Noch zögerst du, das letzte Wort zu sagen.
Ich weiss was deine Augen scheu mich fragen
O dass du tief in meine Seele sähst !
Mich wundert nicht, wenn du nun von mir gehst.

MAILY Koch.

11. Translate into English :

Reiner Genuss und wahrer Nutzen kann nur wechselseitig sein, und ich freue mich da es nun scheint, als wenn wir mit einander fortwandern müssten. Ich habe den redlichen und so seltenen Ernst, der in Allem erscheint was Sie geschrieben und gethan haben, inmer zu schätzen gewusst ; und ich darf nun Anspruch machen, durch Sie selbst mit dem Gange Ihres Geistes, besonders in den letzten Jahren, bekannt zu werden. Haben wir uns wechselseitig die Punkte klar gemacht, wohin wir gegenwärtig gelangt sind, so werden wir desto ununterbrochener gemeinschaftlich arbeiten können. Alles, was an und in mir ist, werde ich mit Freuden mitteilen. Denn da ich sehr lebbaft fühle, dass mein Unternehmen das Mass der menschlichen Kräfte und ihre irdische Dauer weit übersteigt, so möchte ich Manches bei Ihnen niederlegen, und dadurch nicht allein erhalten, sondern auch beleben.

GOETHE An Schiller, 1794.

PURE MATHEMATICS, I.

(Geometry and Trigonometry)

Time: three hourş. 1. Show how to find the lengths of two lines, when their difference and the rectangle contained by them are given.

2. Show that the three perpendiculars from the vertices of a triangle upon the opposite sides meet in a point.

ABC D is a quadrilateral inscribed in a circle. AC and BD meet at right angles at 0. DA and CB meet at E. Show that EO is at right angles to the straight line joining the middle points of AD and BC.

3. Show that if two triangles have one angle of the one equal to one angle of the other, and the sides about another angle of each proportional, the sides opposite the equal angles being homologous, the third angles of the triangle are either equal or supplementary

ACB is a right angled triangle inscribed in a semicircle, C being the right angle. A straight line DEFG meets BC produced in G, the semicircle in F, CA in E, and AB at right angles in D. Show that DE, DG = DF".

4. Show that the rectangle contained by any two sides of a triangle is equal to the rectangle contained by the perpendicular on the third side, and the diameter of the circumscribing circle.

AD is the perpendicular from the vertex A on the base BC. DE and DF are perpendiculars from D on the sides AB and AC.

Show that the rectangle contained by the diameter and EF is twice the area of the triangle ABC.

5. Given the base BC of a triangle and the length of the straight line joining B to the middle point of the opposite side, show that the vertex must lie on a certain circle.

6. Show that if two parallel planes be cut by another plane their common sections with it are parallel.

7. Find the numerical value of the ratio between a side and a diagonal of a regular pentagon.

8. In the triangle ABC, the angles B and C differ by 90°, and the sides opposite these angles are in the ratio of 23 to 7. Find the values of the angles, given

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9. If D is the middle point of the base of a triangle ABC, show that twice the area of the triangle is equal to (AD? - BD?) tan A. How do you interpret this result when A D is equal to BD?

10. The base of a circular tower subtends an angle A at a point in the same horizontal plane. At another point in the same plane, whose distance from the tower is greater by l feet, the tower subtends an angle B. Find the distance of each point from the tower.

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3. Find the value of x that satisfies the equation

tan-?x + tan-'(1 – x) 2 tan-'(x – 2°).

4. If ax* + 4bx} + 6cx2 + 4dx + e is exactly divisible by ar+ 36.x? + 3cx + d, prove that the latter expression is a perfect cube and that the former expression = (akx + eb).

5. Solve the equations

i. ala + x) + b(b + y) = c(a + x) (6+y)

a(a + ) + b (b + y) = c'(a +)(+ y))
ii. x(x – a) =Yz

yly b)=zx
z(z - c) = zy

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