3. The areas of a hexagon and of the equilateral triangle formed by joining alternate angles of the hexagon are together equal to 3888 feet; find a side of the hexagon.

4. A quadrilateral is formed by two isosceles triangles on opposite sides of a common base; show that the area of the parallelogram formed by joining the bisections of the sides of the quadrilateral taken in order is invariable, if the distance between the vertices of the triangles are invariable.

EUCLID.

Two hours and a HALF allowed for this paper.

Candidates are not allowed to answer more than eight questions.

Capital letters, not numbers, must be used in the diagrams.

The square on The only signs allowed are + and =. AB may be written "sq. on AB," and the rectangle contained by AB and CD, "rect. AB. CD."; other abbreviations, if employed, must not be ambiguous.

1. Show that part of Euclid's definition of a square is not required.

Write out the postulates.

Write out all the cases of equality of triangles which are given in the First Book of Euclid.

2. If two triangles have two sides of the one equal to two sides of the other, each to each, and have also the angles contained by these sides equal to one another, they shall also have their bases or third sides equal.

Two triangles ABC and DCB, equal in all respects, are on the same side of the base BC; if AD be joined, the triangle ABD is equal to the triangle DCA in all respects.

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

If one of the angles of a triangle be a right angle, the three exterior angles of the triangle will be together greater than three right angles.

4. If two triangles have two angles of the one equal to two angles of the other, each to each, and the sides opposite to one of the equal angles in each equal, the third angle of the one shall be equal to the third angle of the other.

Draw a figure showing that two triangles that have two sides and an angle equal in each, may have no other parts equal.

5. Every parallelogram is bisected by its diameter. Construct a parallelogram of given area with diagonals of given length.

6. Triangles on equal bases and between equal parallels are equal to one another.

If two equal triangles stand upon equal bases and have also another side of each equal, the triangles will have all, or none, of their other parts equal.

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

On the diameter of a square construct a parallelogram equal to the square, and having one of its angles equal to one fourth of a right angle.

8. If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by those sides is a right angle.

If one of the angles of a rhombus be double of the other, show that the square on the longer diameter is three times as great as the square on a side.

9. Which of the propositions of the Second Book of Euclid may be represented algebraically by the a2 + 2ax + x2?

formula a x

2

=

Draw the figure required for the proposition.

10. To describe a square that shall be equal to a given rectilineal figure.

If one of the sides of a rectangle be four times as great as the other, find the side of the square equal to the given rectangle.

11. Show that the lines bisecting the angles of a triangle meet in a point.

12. The figure formed by joining the points of bisection of the sides of a quadrilateral, taken in order, is equal to one half of the whole figure.

GRAMMAR AND COMPOSITION.

COMPOSITION.

Every Candidate must perform the exercise in Composition.

Candidates are recommended not to take more than half an hour for this exercise.

Subjects for Composition.

(1) Mountain scenery.

Or (2) English sonnet writers.

Or (3) One of the incidents of the French Revolution

commemorated in Wordsworth's Sonnets.

Or (4) The Lake Poets.

GRAMMAR.

Every Candidate must do the parsing and analysis. Part of a question well answered will obtain marks.

SECTION I.

Parse the words italicised in the following passages:(a) There are who ask not if thine eye be on them, (b) O joy! that in our embers is something that doth live

That nature yet remembers what was so fugitive. (c) But it will not be long, ere this be thrown aside.

(d)

Yet despair

Touches me not, though pensive as a bird
Whose vernal coverts winter hath laid bare.

SECTION II.

Make a table for analysis of the following sentences—

(a) They a blissful course may hold

Even now, who, not unwisely bold,
Live in the spirit of this creed,

Yet seek Thy firm support according to their need.

(b) The homely nurse doth all she can

To make her foster child, her inmate man,
Forget the glories he hath known,

And that imperial palace whence he came.

(e) What though the radiance which was once so bright
Be now for ever taken from my sight,
Though nothing can bring back the hour

Of splendour in the grass, of glory in the flower,
We will grieve not, rather find

Strength in what remains behind.

(d) We shall exult, if they who rule the land
Be men, who hold its many blessings dear,
Wise, upright, valiant; not a servile band,
Who are to judge of dangers which they fear,
And honour which they do not understand.

SECTION III.

(Not more than four of these questions to be answered.) 1. Write a brief analysis of the Ode to Duty. 2. Illustrate Wordsworth's love of Nature from his poems.

3. Give a short explanation, suitable for children, of the following passages:

This public way streamed with the pomp of a too
credulous day.

Vanguard of liberty, ye men of Kent!
She must espouse the everlasting sea.

England is a fen of stagnant water.

Plain living and high thinking are no more.

4. To what events is allusion made in the following passages?

Once did she hold the gorgeous East in fee.
Toussaint, the most unhappy man of men.
Thou, Liberty, from thine Alpine holds at length
art driven.

Another mighty Empire overthrown.

Who, like Montrose, make loyalty your pride. 5. Derive paramount, ledger, phrensy, tyrant, worldling.

6. Give the force of the prefix in apparel, dialogue, sympathy, forget, cataract, adverse, misgiving.

SCHOOL MANAGEMENT.

Question 1A must be answered, and Question 1B must be omitted, by Students who leave the Training College to take charge of Schools after this Examination, and by Acting Teachers.

Question 1A must be omitted, and Question 1B must be answered by all Students who are remaining in the Training College.

Not more than nine other questions may be answered.

Answer briefly the following questions:

1A. (a) What are the advantages of a separate classification in Arithmetic?

(b) Why should caning on the hand be absolutely prohibited in schools?

(e) Why do younger boys require shorter lessons than older boys?

(d) In what respects is long standing in class prejudicial?

(e) What data are required for calculating the average yearly attendance?

(f) The number of failures in Reading, is 17; in Writing, 19; in Arithmetic, 23; the percentage of passes is 86; find the number of children presented for Examination.