PART III. Dec. 1858. III. 1. Practical Geometry*. I. [One hour allowed for this Paper. N.B. The whole of the work by which these problems are solved must appear. Candidates are required to affix the number of the problem to each solution.] 1. CONSTRUCT a square having sides of 14 inches each. 2. Construct an equilateral triangle whose height shall be 2 inches. 3. Describe an ellipse whose longest diameter shall be 4 inches, the shortest 3 inches. 4. Within a circle 3 inches in diameter inscribe a regular heptagon. 5. Find a mean proportion between two right lines which are respectively 2 inches and 37 inches long. 6. Construct a parallelogram having an area equal to that of a triangle of which the sides are respectively 1 inch, 14 inches, and 2 inches. a Dec. 1858. III. I. Practical Geometry. [One hour allowed for this Paper. N.B. The whole of the work by which these problems are solved must appear. Candidates are required to affix the number of the problem to each solution.] 7. CONSTRUCT a square whose diagonal shall be 2 inches. 8. Construct an isosceles triangle of which the base is 2 inches and the opposite angle 30°. * The Examiners were furnished with several papers in some departments of drawing in case they should find it impossible to examine all the Candidates at the same time, 9. Within a rectangular parallelogram 4 inches and 27 inches inscribe an ellipse. 10. Within a triangle having sides of 2 inches, 3 inches, and 34 inches respectively, inscribe a square. 11. Within a circle of 24 inches diameter inscribe three circles equal to each other, and touching one another and the circumference of the containing circle. 12. Construct a rhombus of which the sides are 2 inches and the altitude 14 inches, and a triangle of the same area and altitude. a Dec. 1858. а III. 1. Practical Geometry. [One hour allowed for this paper. N.B. The whole of the work by which these problems are solved must appear. Candidates are required to affix the number of the problem to each solution.] 13. DIVIDE a right line 24 inches long into seven equal parts. 14. Draw a right line of any length, at one end draw a line perpendicular to it, and trisect the right angle thus formed. 15. Construct an equilateral triangle whose height is 2 inches. 16. Within a circle 3 inches in diameter inscribe five circles equal to each other, and touching one another and the circumference of the containing circle. 17. Within a circle 24 inches in diameter place three equal semicircles, touching the circumference of the circle and having their diameters adjacent. 18. Describe an ellipse, of which the longest diameter is 44 inches and the shortest 3} inches, and shew the method of finding its centre if it were not known. Dec. 1858. III. 1. Mechanical Drawing. [One hour allowed for this paper.] 1. A LONG piece of rectangular timber, 4 inches by 3 inches on the cross section, lies on the ground on one of its edges, and is penetrated in the direction of its length by a hole 2 inches in diameter, the axes of the timber and of the hole corresponding. Project the true section of the two made by cutting through the timber at right angles with the axis and at an angle of 45° with the ground plane. 2. Draw the plan of a square of 3 inch sides when two sides are inclined to the horizon at 20° and 30°. 3. An hexagonal prism of 3 inch sides is penetrated through the centre of two opposite sides at an angle of 30' with its axis by a cylindrical pipe of 2 inches external and 13 inches internal diameter. Project the true form of the section made by cutting through the intersection of the axes of the prism and the pipe at an angle of 120° with the axis of the pipe. 4. Draw the plan of a circular plane of 3 inches diameter inclined at an angle of 30° to the horizon. DEC. 1858. III. 2. freehand Drawing from the flat. [One hour allowed.] An outline drawing of a flower was given with the following directions: The Student is required to copy in pencil on this paper the above flower, increasing the scale so that AB is enlarged to CD opposite. Precise imitation and clearness of outline is necessary. No instruments or means of measurement of any kind will be allowed. Dec. 1858. III. 2. Drawing from Models. [One hour allowed.] THE Examiner was instructed to select a chair, framed square and with square legs, and to place it on a table, sufficiently advanced in front of the Candidates, and so that all should more or less see it at an angle, with the seat above or below the level of the eye. Dec. 1858. III. 2. Drawing from Memory. [One hour allowed for this Study. The Candidates may add any amount of shadow that they think necessary to the full expression of the subject.] THE Candidate is required to make a careful drawing, from memory, of a small square table with four straight legs, supporting on its top a glass fish globe. The eye of the draughtsman is to be supposed above the rim of the globe. Dec. 1858. III. 2. Drawing from Memory. [One hour allowed for this Study. The Candidates may add any amount of shadow that they think necessary to the full expression of the subject.] a The Candidate is required to make a careful drawing, from memory, of a wheelbarrow turned upside down, with its wheel and legs in the air. Dec. 1858. III. 2. Drawing from Memory. [One hour allowed for this Study. The Candidate is required to make a careful drawing, from memory, of a gantry supporting a beer-cask, the end of the barrel and of the gantry to be seen as well as the sides. |