+ b bclc − a) (a - b) * ca(a - b) (b − c)† ub(b − c) (c − a) 5. A certain number of persons paid a bill; if there had been 10 more each would have paid 2s. less; if there had been five less each would have paid 2s. 6d. more; find the number of persons and what each had to pay. 6. Prove that the product of any two expressions is equal to the product of their H.C.F. and L.C.M. 7. Find the factors of N.B.-Only five questions to be attempted, of which not more than three must be in Section A or in Section B. The Examiner will read only the first five answers left uncancelled. The questions in this paper are all of equal value. Euclid's proofs need not be given, but his method of reasoning and the logical order of his theorems must be preserved. Algebraic solutions will not be accepted. Mr. Ross, Senior Inspector. Mr. CHAMBERS, District Inspector. SECTION A. 1. If a straight line be bisected and produced to any point, the squares of the whole line thus produced, and of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced. C Geometry. 2. In equal circles, or in the same circle the angles which stand upon equal arcs are equal to one another, whether they are at the centres or the circumferences. 3. If a diameter of a circle cut a chord which does not pass through the centre, but not at right angles, prove that the rectangle contained by the segments of the diameter is equal to the rectangle contained by the segments of the chord. 4. To describe a square about a given circle. SECTION B. 5. Show that the line adjoining the vertex to the middle point of the base of an acute-angled triangle is greater than half the base. 6. ABC is a triangle right-angled at C. Points D and E are taken in AB and AB produced such that BD=BE=BC. Show that the rectangle contained by AD and AE = AC2. 7. If Q, R, S are the feet of the perpendiculars let fall from the vertices A, B, C respectively of a triangle ABC on the opposite sides, prove that AQ, BR, and CS are the bisectors of the angles of the triangle QRS. 8. If the perpendiculars from the angles A, B, C of a triangle ABC to the opposite sides be produced to meet the circumference of the circumscribed circle in D, E, F, respectively, then the arcs EF, FD, DE are bisected at A, B, C respectively. THEORY OF METHOD. Two hours allowed for this paper. N.B.-Only five questions to be attempted. The Examiner Mr. HEADEN, Senior Inspector. 1. Draw up a course of object lessons introductory to geo- Briefly 2. What is the educational value of story-telling in the infant school? Show how this subject may be connected with 3. Write notes for a lesson on simple long division. 4. By what means would you secure the attention of pupils at a reading lesson? 5. Show the importance of drawing, considered from an educational and a practical point of view. 6. Explain how letter-writing should be taught. 7. Give a sketch of a first lesson on the complex sentence. 8. Give a short account of the Third Kindergarten Gift. Explain how the elements of arithmetic may be taught by means of this gift. HISTORY. One hour and a half allowed for this paper. N.B.-Only five questions to be attempted. The Examiner will read only the first five answers left uncancelled. The questions in this paper are all of equal value. Mr. W. A. BROWN, Senior Inspector. Mr. MCENERY, District Inspector. 1. What were the original aims of the Holy Alliance, and what were its subsequent developments? 2. State the chief articles of the Treaty of Adrianople, 1829. ministers served under Louis 3. What noteworthy ministers Philippe? Review rapidly his reign. 4. Sketch the history of Piedmont from 1848 to 1860 inclusive. 5. What were the disputes that led to the Crimean War? Account for the part played by Sardinia in that war. 6. Give an account of the campaign of 1866 in Germany. State its causes and results. History. 7. Give a succinct account of the Luxemburg question, 1867. 8. Where are the following, and for what noted:-Chios, Navarino, Solferino, Tchernaya, Troppau? DRAWING. Two hours allowed for this paper. N.B.-Only four questions to be attempted, one of which must be No. 1, and another, either No. 2 or No. 3, but not both. The Examiner will read only the first four answers left uncancelled. India-rubber is not to be used for any of the work. Dr. ALEXANDER, Senior Inspector. Mr. BEVIS, Head Organiser. 1. Assume the design for an ornamental railing, Fig. 1, to be drawn to a scale th full size, redraw the design to a scale full size. The geometrical portion may be drawn with a compass and ruler. (Not more than one hour should be de voted to this question.) * 2. Draw to the scale of yards printed on this paper (Fig. 3) the plan of the field the dimensions of which are shown on the rough sketch, Fig. 2. (Note.-Observe that the distance from A to the first offset is 105 yards, and from A to the second offset is 215 yards, and that the total distance from A to B is 335 yards; this method has been adopted on each of the lines.) 3. Take the bottom and the left-hand edge of your drawing paper as the two co-ordinates X and Y. From these mark in the positions of the eight towns given, using the scale (Fig. 3) as a scale of miles. With Dublin as a centre, give the distance from it to each of the other towns. * The question paper should be doubled over along the line A B on the scale, and 4. Make a freehand sketch of two elevations and plan of a dog kennel, and put on all the necessary dimensions so that a class can make a correct drawing of the sketch to a scale of full size on a piece of paper 7 inches by 11 inches. 5. Give notes of a lesson on the method of teaching a class to draw the design Fig. 1. (Illustrate your notes by sketches). 6. Draw to a scale full size the elevation and plan shown in Fig. 4; also draw a side elevation looking at it from the direction shown by the arrow A. The tilted brick makes with the ground an angle of 45 degrees. |