COLLEGE OF PRECEPTORS.

(Incorporated by Royal Charter.)

PROFESSIONAL PRELIMINARY EXAMINATION.MARCH, 1883.

WEDNESDAY, March 7th-Morning, 11.30 to 1.

EUCLID.

Books I.-IV.

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

1. Define the terms-parallel straight lines, circle, sector of circle, angle of segment of circle.

2. If one side of a triangle be produced, the exterior angle shall be greater than either of the interior and opposite angles.

3. To a given straight line to apply a parallelogram that shall be equal to a given triangle and shall have one of its angles equal to a given rectilineal angle.

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

made up

After proving this, state (without proving) the other proposition in the 2nd Book of which the hypothesis is the same as that of this proposition.

5. If one circle touch another internally at any point, the straight line which joins their centres shall (when produced) pass through that point of contact.

6. If a quadrilateral figure be inscribed in a circle, its opposite angles are together equal to two right angles.

On the same base AB and on the same side of it, are two segments of circles from which respectively are cut off similar segments by straight lines BD, BF, these similar segments being situated on the sides of BD, BF, which are remote from A. Show that the points A, D, F lie in a straight line.

7. In a given circle to inscribe a triangle equiangular to a given triangle.

8. To inscribe an equiangular and equilateral quindecagon in a given circle.

State (without proving) the mode of describing such a figure about a given circle.

COLLEGE OF PRECEPTORS.

(Incorporated by Royal Charter.)

PROFESSIONAL PRELIMINARY EXAMINATION.

-MARCH, 1883.

WEDNESDAY, March 7th-Morning, 11.30 to 1.

EUCLID.

BOOK I.

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

1. Define the terms-angle, triangle, square, parallel straight lines.

2. If at a point in a straight line, two other straight lines on the opposite sides of it make the adjacent angles together equal to two right angles; then these two straight lines shall be in one and the same straight line.

Having proved this proposition, write (without their proofs) the enunciations of the subsequent propositions in the demonstration of which it is used.

3. If two triangles have two sides of the one equal to two sides of the other, each to each; and if the angle contained by the two sides of the one be greater than the angle contained by the two sides, equal to them, of the other; then shall the base of the one that has the greater angle, be greater than the base of the other.

4. If a straight line falling on two other straight lines make the exterior angle equal to the interior and opposite, on the same side of the line; then the two straight lines shall be parallel.

5. Through a given point to draw a straight line parallel to a given straight line.

Show a way of describing an isosceles triangle of which the base and one side shall lie in given straight lines, and the other side (produced if necessary) shall pass through a given point.

6. The opposite sides and angles of a parallelogram are equal to each other; and the diameter of a parallelogram bisects it.

7. Equal triangles on equal bases, in the same straight line and towards the same parts, are between the same parallels.

8. To describe a square on a given straight line.

1. Two forces, each equal to a weight of 10 lbs., act in directions making an angle of 120°; find their resultant.

2. Prove that, when three forces, not parallel, act on a solid body and keep it at rest, their directions pass through the same point.

A trap-door is kept open at an angle of 45° by a horizontal cord tied to the edge and to a point above the hinge; find the direction of the reaction of the hinge.

3. Weights of 1, 2, 3, and 4 lbs. are suspended in order, at intervals of 1 foot, on a rod 3 feet long; find the point about which the loaded rod will balance, neglecting the weight of the rod itself.

4. Define the Centre of Gravity of a body; and show how to find the Centre of Gravity of a plane four-sided figure.

5. Describe the ordinary balance, and state, as fully as you can, what are the requisites of a good balance, and how they may be tested.

6. A uniform heavy chain hangs over a smooth pulley at the top of a smooth inclined plane, so that part lies along the plane and part hangs vertical. What must be the relation between the lengths of the two parts that the chain may be at rest?

7. Define the terms-velocity, acceleration, and momentum.

If a point start with a velocity of 10 feet a second, and gain a velocity of 5 feet a second in every two seconds, what distance will it traverse in six seconds?

8. State Newton's Third Law of Motion, and apply it to the case of impulsive forces.

9. How is a Barometer made? What is the relation between the heights of a Water and a Mercury Barometer ?

10. What is the Principle of Archimedes, and how may it be demonstrated experimentally?

1. Defendi rempublicam adolescens, non deseram senex : contempsi Catilinae gladios, non pertimescam tuos.

2. Illa igitur corona contentus Thrasybulus, neque amplius requisivit, neque quemquam honore se antecessisse existimavit.

3. Oppidani, qui se locorum asperitate munitos crediderant, magna atque insolita re perculsi, nihilo segnius bellum parare : idem nobis facere.

Also the following passage:

4. Fulvia, insolentiae Curii causa cognita, tale periculum reipublicae haud occultum habuit, sed sublato auctore de Catilinae conjuratione quae quoque modo audierat compluribus narravit. Ea res in primis studia hominum accendit ad consulatum mandandum M. Tullio Ciceroni. Namque antea pleraque nobilitas invidia aestuabat, et quasi pollui consulatum credebant, si eum, quamvis egregius, homo novus adeptus foret. Sed ubi periculum advenit, invidia atque superbia post fuere.

PART II. Grammatical Questions.

1. Which word is the subject, and which the object, of the verb antecessisse? 2. Explain the use of the infinitives parare and facere. 3. In what person, number, gender, and case is qui, and why? 4. In what cases are hominum, Ciceroni, and eum, and why? 5. Explain the construction of the two words invidia-("nobilitas invidia aestuabat," and "invidia atque superbia," &c.)? 6. What part of the verb is fuere, and why is it plural? 7. Explain the term novus homo.

PART III. Translate into Latin

1. What a man sows that shall he also reap.

2. He who wishes to know what shall be, ought to observe what has been.

3. Having returned home victorious, he was elected Consul. 4. I shall speak what appears to me to be right.

5. He said that he asked of his accusers two things only, and

he feared that they would not grant even these.

[Candidates must satisfy the Examiner in at least two PARTS of this paper.]

CAESAR-DE BELLO GALLICO, LIB. I. and II.

PART I. Translate into English: :

1. Defendi rempublicam adolescens, non deseram senex : contempsi Catilinae gladios, non pertimescam tuos.

2. Illa igitur corona contentus Thrasybulus, neque amplius requisivit, neque quemquam honore antecessisse existimavit.

3. Oppidani, qui se locorum asperitate munitos crediderant, magna atque insolita re perculsi, nihilo segnius bellum parare : idem nostri facere.

Also the following passage:

4. Suessiones suos esse finitimos fines latissimos feracissimosque agros possidere. Apud eos fuisse regem nostra etiam memoria Divitiacum, totius Galliae potentissimum, qui cum magnae partis harum regionum, tum etiam Britanniae imperium obtinuerit: nunc esse regem Galbam: ad hunc, propter justitiam prudentiamque suam, totius belli summam omnium voluntate deferri; oppida habere numero duodecim, polliceri millia armata quinquaginta.

PART II. Grammatical Questions.

1. Which word is the subject, and which the object, of the verb antecessisse? 2. Explain the use of the infinitives parare and facere. 3. In what person, number, gender, and case is qui, (qui se locorum, &c.), and why? 4. In what cases are finitimos, partis, and voluntate, and why? 5. Why is potentissimum in the accusative case? 6. Explain why obtinuerit is in the subjunctive mood, and why it is singular number. 7. Distinguish between cardinal numerals and ordinal numerals. Of which kind is duodecim?

PART III. Translate into Latin :

1. What a man sows that shall he also reap.

2. He who wishes to know what shall be, ought to observe what has been.

3. Having returned home victorious, he was elected Consul. 4. I shall speak what appears to me to be right.

5. He said that he asked of his accusers two things, and he feared they would not grant even these.

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