FOR SCIENCE SCHOOLS AND CLASSES. APRIL, MAY, AND JUNE, 1894. SUBJECT I. PRACTICAL PLANE AND SOLID GEOMETRY. EXAMINERS, MAJOR SIR G. S. CLARKE, K.C.M.G., R.E., AND PROFESSOR T. F. PIGOT, C.E., M.I.M.E. GENERAL INSTRUCTIONS. If the rules are not attended to, the paper will be cancelled. You may take the Geometrical Drawing, or the Elementary, or the Advanced, or the Honours paper, but you must confine yourself to one of them. All figures must be drawn on the single sheet of paper supplied, for no second sheet will be allowed. The constructions may be left in pencil, provided they are distinct and neat, and that the construction lines are shown. They must be strictly geometrical and not the result of calculation or trial. In the absence of those lines which are essential to a correct solution no marks will be awarded, however correct the result may appear. Lines parallel or perpendicular to others may be drawn mechanically without showing any construction. Lines may be bisected by trial. A single accent (') signifies feet; a double accent (") inches. Put the number of the question before your answer. You are to confine your answers strictly to the questions proposed. Questions marked (*) have accompanying diagrams. The value attached to each question is shown in brackets after the question. Your name is not given to the Examiners, and you are forbidden to write to them about your answers. The examination in this subject lasts for four hours. Geometrical Drawing. INSTRUCTIONS. Read the General Instructions above. Only eight questions are to be attempted. (1205) A 2 Plane Geometry. 1. Construct a scale of 3.5" to 30', to show feet, and correctly figured. Draw to the scale a triangle, its sides, respectively, 20', 15', and 12' long. (10.) *2. Divide the line AB into three consecutive parts, to each other in the proportion of 1: : 1. (8.) *3. The figure represents a continuous outline composed of portions of three circles and of their common tangents. Draw the figure to the indicated dimensions. (10.) 4. Draw a quadrilateral figure ABCD, with the following dimensions: AB = 2", BC = 1.5′′, AD = 1·5′′. The diagonal Find the length of the side of a square equal in area to the quadrilateral. (12.) 5. Draw a circle of 1" radius; and (a) draw a triangle circumscribing the circle, its angles being, respectively, 75°, 70°, and 35°; (b) join the points where these lines are tangent to the circle, and write down the values of the angles of the triangle thus formed. (12.) [NOTE.-The angle subtended by a chord at the centre of a circle is double of that subtended by the same chord at the circumference.] *6. Draw the figure from the indicated dimensions. (14.) No marks will be awarded for mere reproduction of the figure. 7. Inscribe a pentagon in a circle of 1.5" radius. Draw the diagonals, and the circle circumscribing the pentagon formed by their intersection. (12.) 8. The minor axis of an ellipse is 24" long, and the distance between the foci is 2". Find the major axis and draw the curve. (10.) Solid Geometry. *9. The figure represents the plan (ABCD) and elevation (A'A'D',D') of a truncated prism with a rectangular base. Draw an elevation of the solid in a direction perpendicular to the line ab. (14.) 10. The figure represents the plan (AEFD) and elevation (A'B'C'D') of a vertical block with a square hole (in elevation I'K'G'H') through it. Draw the section of the block made by a vertical plane represented in plan by the line ab, and shade the portions of the block cut by the plane. (16.) First Stage or Elementary Examination. Read the General Instructions on page 1, Only eight questions are to be attempted, Plane Geometry. 11. In a circle of 13" diameter, place a chord 18" long. At each extremity of this chord draw a tangent to the circle. Describe a second larger circle touching the first and also the tangents. (10.) 12. Construct a square abcd of 21" side. Bisect this square by a line drawn from a point on the side ab distant 1" from a. Reduce this square to a parallelogram of which the bisecting line is a diagonal. (10.) *13. The figure represents the section of an oval sewer, the outline of which is made up of circular arcs. The construction is indicated. Draw the section in strict accordance with the figured dimensions. Scale ğ" = 1 foot. Solid Geometry. 14. Show in plan and elevation : (12.) a. A point 2" from the ground line and 14" from the b. A line parallel to and 14" from the vertical plane *15. A line of which a'b' is the elevation passes through the given point bb', and intersects the given line cd, c'd'. Draw the plan of this line and determine its inclination to the horizontal plane. (12.) *16. Determine the distance apart of the given parallel planes. (10.) 17. An isosceles triangle (base 2", sides 2") rests with its base on the horizontal plane, and is rotated about the base till the height of the vertex is " above the horizontal plane. It is then further rotated till the height of the vertex is 2". Determine the angle contained by the planes of the triangle in these two positions. (12.) *19. a, *18. The plan a of a point lying in the plane mon is given. From this point draw, in plan and elevation, a line lying in the plane and inclined at 35° to the horizontal plane. From the same point draw a second line also in the given plane and making 45° with the first line. (12.) b and c are points on the respective traces of a given plane as shown. Determine the true form of the triangle ABC. (12.) 20. A pentagon abcde (side 14") is the plan of a right prism (height 2") standing on the horizontal plane. This prism is cut by an oblique plane which passes through the lower edge cd and the upper point a. Draw an elevation of the truncated prism on a line parallel to ab. (14.) 21. Draw the plan of a right hexagonal pyramid (side of base, 1", height 23′′) lying with one triangular face on the horizontal plane. Draw also an elevation on a plane parallel to any side of the base which is not horizontal. (12.) *22. The elevation of a semi-circular headed window is given, and also a plan at AB. Draw an elevation of the window on a ground line parallel to xy. : (16.) Graphic Arithmetic. 23. Determine a line whose length shall represent, taking 3" as the unit. (12.) *24. If the given line ab represents the fraction, determine 31. Draw a triangle ABC with the following dimensions AB=4", BC = 23", AC = 2". Inscribe in the triangle a parallelogram with four equal sides, one side lying on AC, and the adjoining sides inclined to AC at 45°. |