HINTS ON THE MANNER OF USING DRAWING INSTRUMENTS. 1. Pencils. For drawing purposes, two of these at least are necessary, viz., the H pencil, and the HHH; one (HHH) for drawing lines of construction, the other (H) for the result lines. These should not have a needle point, but flattened like a chisel. Great care should be taken in sharpening a pencil, and when it gets short, it should be placed in a crayon-holder. 2. Compasses. These should be always held by the head, otherwise should your fingers touch the sides, the radius might be altered. Great care should also be taken to keep the joints of the compasses tight. The extremities of the compasses should also be sharp-pointed, but the paper should be pierced as little as possible by the point which constitutes the centre of the circle. For the bow-pencil compasses, "engineers' pencils" are used. 3. T Square.—In making use of this instrument, keep to the same edge of the drawing-board, over the same drawing; otherwise the drawing will probably be inaccurate. Those T squares which have the hilt passing over the blade are in practice the most convenient. A T square should also be tested from time to time. 4. Set-Squares.—These are useful instruments for setting off angles of 45°, 60°, or 30° as required. 5. Parallel Ruler.-In using this instrument, it should be held tight, with two or more fingers of the left hand. As its action is imperfect, for drawings where great exactness is required, it would be better to make se of a set-square and a straight-edge. GENERAL HINTS ON DRAWING. The figures should be first drawn with a black lead pencil. The lines should be as fine as possible, the india-rubber being used sparingly, before the drawing is inked in. The drawing paper should of course be clean and smooth or hot pressed. Should it be greasy, add a little ox-gall to the ink. Figures should be drawn on as large a scale as convenient, as the larger the scale, the more correct, generally speaking, is the solution. Straight lines and arcs should always be drawn sufficiently long at first, as you cannot produce a line, or continue an arc, with such accuracy, if the pencil is taken off the paper, or the point of the compasses is removed from the centre. Both kinds of lines should be smooth, and of uniform thickness. Lines should be drawn on the surface of the paper, and not indented into it. When a line is to be drawn parallel to a short line, it is better first of all to produce the short line indefinitely both ways, and then proceed. When several lines pass through one point, it is better to commence each line at the point which is common to them all. In inking-in, it is better to take the curve lines before those which are straight. Intersecting points are best determined when the lines or circles cut one another pependicularly. The point is not so well determined, when the lines or circles cut one another at very acute or very obtuse angles. A COURSE OF PROBLEMS IN PRACTICAL PLANE GEOMETRY. SECTION 1.-LINES AND ANGLES. DEFINITIONS. 1. A point denotes position only. It has no magnitude, hence the true mathematical point is merely the centre of the dot. Ex, A 2. A line has length only, and no breadth, so that it merely indi cates direction. Ex. AB The ends of lines are points, and when lines cut each other they are said to intersect, and the point where they cross each other is called the point of intersection. Ex. A NOTE.—Lines are of two kinds—viz., straight or right lines, and curved lines. А 3. A straight line is the shortest distance between two points. A line is said to be produced when it is lengthened at either ex- с B 4. A curved line is nowhere straight. Ex. AB Note.—The direction of a straight line may be horizontal, vertical, or oblique. 5. A horizontal line, as its name implies, is perfectly level, like the natural horizon when seen from the midst of the ocean. Ex. AB 6. A vertical line is perfectly upright, like a plumb-line. Ex. AB B 7. An oblique line is neither horizontal nor vertical. B B B B Ex. AB A A A A NOTE.—It follows that, while there can be but one horizontal line and one vertical, the number of oblique lines may be infinite. 8. Parallel lines are those which are throughout equally distant from each other, and which, therefore, if produced, can never meet. Ex. AB and CD 9. An angle is the opening between two straight lines which meet in one point. Its magnitude depends on the mutual inclination of the two lines, and not on their lengths. Er. ABC L B B с NOTE.--Angles are of three kinds-viz., the right angle, the obtuse angle, and the acute angle. 10. A perpendicular. A straight line is said to be perpendicular to another straight line when it stands on it in such a manner that the adjacent angles are equal to each other. Ex. A B NOTE.—It follows that a perpendicular line is not necessarily a vertical line. 11. A right angle is the opening between two lines which are perpendicular to each other. Ex. ABC A с B с is made the standard with which all other angles are compared. 12. An obtuse angle is greater than a right angle. Ex. ABC B |