59

A.—2

32. It is to be distinctly understood that the period of training, including the time spent in the training cruiser, is a time of probation, and the parent or guardian of every cadet is required to sign a declaration on the admission of a cadet to the effect that he shall be immediately withdrawn on the receipt of an official request for his withdrawal. 33. When a cadet is found to be making insufficient progress a letter is sent to his parent or guardian warning him of the possibility of having to withdraw the cadet unless a marked improvement takes place. This warning is generally issued a term in advance, to enable the parent provisionally to make other arrangements for continuing the boy's education in case his withdrawal should become necessary. By command of their Lordships, Admiralty, August, 1913. W. Graham Greene. Schedules of Geometry in the Qualifying Examination. a. practical geometry. 1. Bisection of angles and of straight lines. 2. Construction of perpendiculars to straight lines. 3. Construction of an angle equal to a given angle. 4. Construction of parallels to a given straight line. 5. Simple cases of the construction from sufficient data of triangles and quadrilaterals. 6. Division of straight lines into a given number of equal parts or into parts in any given proportion. 7. Construction of a triangle equal in area to a given polygon. B. THEORETICAL GEOMETRY. Angles at a point. 1. If a straight line stands on another straight line, the sum of the two angles so formed is equal to two right angles ; and the converse. 2. If two straight lines intersect, the vertically opposite angles are equal. Parallel Straight Lines. 3. When a straight line cuts two other straight lines, if—(i) A pair of alternate angles are equal, or (ii) a pair of corresponding angles are equal, or (iii) a pair of interior angles on the same side of the cutting line are together equal to two right angles, then the two straight lines are parallel; and the converse. 4. Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. 5. The sum of the angles of a triangle is equal to two right angles. 6. If the sides of a convex polygon are produced in order, the sum of the angles so formed is equal to four right angles. 7. If two triangles have two sides of the one equal to two sides of the other, each to each, and also the angles contained by those side's equal, the triangles are congruent. 8. If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. 9. If two sides of a triangle are equal, the angles opposite to these sides are equal; and the converse. 10. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 11. If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent. 14. The opposite sides and angles of a parallelogram are equal, each diagonal bisects the parallelogram, and the diagonals bisect one another. 15. If there are three or more parallel straight lines, and the intercepts made by them on any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal. Areas. 16. Parallelograms on the same or equal bases and of the same altitude are equal in area. 17. Triangles on the same or equal bases and of the same altitude are equal in area. 18. Equal triangles on the same or equal bases are of the same altitude. 19. Illustrations and explanations of the geometrical theorems corresponding to the following algebraical identities : — k (a + b + c + ) = ka + kb + kc + ...., (a + b) 2 =a 2 +'2ab + b 2 , (a - b) 2 =a 2 - 2ab +b\ a 2 —b 2 =(a+b) (a — b). Loci. 21. The locus of a point which is equidistant from two fixed points is the perpendicular bisector of the straight line joining the two fixed points. 22. The locus of a point which is equidistant from two intersecting straight lines consists of a pair of straight lines which bisect the angles between the two given lines.