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ENGLAND.

PRELIMINARY GENERAL EXAMINATION.- Christmas, 1864.

WEDNESDAY, December 21st.-Morning, 12 to 2.

GEOMETRY.
Examiner-W. J. REYNOLDS, Esq., M.A.

1. Define the terms—superficies (or surface), plane surface, figure, acute-angled triangle, parallelogram, rectangle.

2. The angles which one straight line makes with another, on one side of it, are either two right angles, or are together equal to two right angles.

Having proved this proposition, state (without proving) its converse.

If the two portions ABC, DBC of a rectangle ABDC be turned about the point B till the sides now coinciding with the diagonal BC are at right angles to each other, then the sides AB, BC shall

lie in one straight line. 3. If two triangles have two angles of the one equal to two angles of the other, each to each; and one side equal to one side, viz., the sides adjacent to the equal angles in each triangle; then shall the other sides be equal, each to each, and also the remaining angle of the one shall be equal to the remaining angle of the other.

4. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to each other; and the exterior angle equal to the interior and opposite on the same side of the line; and the two interior angles on the same side together equal to two right angles.

5. The opposite sides and angles of a parallelogram are equal; and the diameter bisects it.

Prove that if two straight lines be equal to each other, the squares described upon those straight lines shall be equal to each

other. 6. In any right-angled triangle, the squares described upon the sides containing the right angle are together equal to the square described upon the side opposite to the right angle.

7. If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, shall be equal to the square of the straight line made up of the half and the part produced.

8. Divide a given straight line into two parts, such that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part.

In the diagram for the construction of this proposition, prove that the right-angled triangle is one-fourth of the larger square,

ENGLAND

PRELIMINARY GENERAL EXAMINATION.

-Christmas, 1864.

WEDNESDAY, December 21st.-Afternoon, 3 to 4}.

FRENCH.
Examiner-Rev. DR. BRETTE.

I. Translate into English : Un jour, au mois de novembre, la même année de la mort de son père, il venait de faire la revue de plusieurs régiments; le conseiller d'Etat Piper était auprès de lui; le roi paraissait abîmé dans une rêverie profonde.Puis-je prendre la liberté, lui dit Piper, de demander à Votre Majesté à quoi elle songe si sérieusement ?”—“Je songe, répondit le prince, que je me sens digne de commander à ces braves gens ; et je voudrais que ni eux ni moi ne reçussions l'ordre d'une femme.” Piper saisit dans le moment l'occasion de faire une grande fortune. Il n'avait pas assez de crédit pour oser se charger lui-même de l'entreprise dangereuse d'ôter la régence à la reine, et d'avancer la majorité du roi; il proposa cette négociation au comte Axel Sparre, homme ardent, et qui cherchait à se donner de la considération : il le flatta de la confiance du roi. Sparre le crut, se chargea de tout, et ne travailla que pour Piper. Les conseillers de la régence furent bientôt persuadés : c'était à qui précipiterait l'exécution de ce dessein, pour s'en faire un mérite auprès du roi.- VOLTAIRE, Charles XII.

II. Grammatical Questions. 1. Parse and give the primitive tenses of the verbs in italics.

2. State, and illustrate by examples, the difference between un jour, une journée; un dessin, un dessein.

3. Give in French the names of all the months and seasons of the year,

and write in full “1864." 4. What are the meanings of the following words :-la mort, le mort, le mors, il mord.

5. Account for all the circumflex accents you find in the above passage; and give the reason why, in the following sentence, the past participle is in the plural :-“ Les conseillers de la régence furent bientôt persuadés."

6. Translate into English :-(i.) Montez ma malle dans ma chambre à coucher. (ii.) Nous allons monter à cheval. (iii.) Le rouge lui monta au visage. (iv.) Mon père monte un cheval superbe. (v.) Montez l'escalier, et montez la pendule. (vi.) Il n'est pas agréable de monter la garde en hiver.

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ENGLAND.

PRELIMINARY GENERAL EXAMINATION.—Christmas, 1864.

WEDNESDAY, December 21st.-Afternoon, 41 to 6.

ALGEBRA.

Examiner-J. M'DOWELL, Esq., M.A.

1. Multiply 2-2y + y2 + x +y+1 by x+y-1.

2 + 307 +4-1
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H2+3x+2

2. Multiply together 2a—«, 2a +x, and 4a+22.

3. Divide 203—7—6 by — -3.

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4. Divide the product of a2 + ax + x2 and a3 + x3 by a* +a?x2 +æ4.

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5. Find the Greatest Common Measure of the numerator and

204 + 2x2 +9 denominator of the fraction

and reduce it to

24 -4.3 + 402-9' its lowest terms.

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7. Extract the Square Root of 4x4 - 4.08 +5.x2–2x+1.

8. If a : 6:: c:d, then a+b: 0–6::c+d:c

- d.

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9. How much money is there in a purse, when the fourth part and the fifth part together amount to £42. 15s. ?

10. A certain number of two digits contains the sum of its digits four times, and their product three times. What is the number?

24

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