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ENGINEERING

DRAWING AND DESIGN.

PART I.

PRACTICAL, PLANE, AND SOLID GEOMETRY.

SECTION I.

INTRODUCTION.

THE following Exercises are intended for students using drawing instruments for the first time. All lines should be drawn with the T-square and set squares, and all divisions made with the dividers. Lines parallel to the long edges of the board should be drawn with the T-square, and lines at right angles with the set squares:—

EX. 1.—Draw a square of 31′′ side, and divide it into small squares each of "side.

(Two adjacent sides of the square should be divided into seven equal parts, and lines drawn through the points parallel to the sides of the square.)

EX. 2.—Draw an oblong, sides 4" and 22", and bisect each of the sides. Join the middle points of the sides to form a rhombus. Bisect the sides of this figure, and join the middle points, to form a second oblong. Again, bisect the sides of this oblong, and join the middle points to form a second rhombus. Try if the similar sides of the oblongs are parallel to each other, and also the sides of the rhombuses.

(A rhombus is a four-sided figure, having all its sides equal, but its angles not right angles.)

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EX. 3.-Draw a circle of 31⁄2" diameter. With the radius of the circle as distance, start from any point on the circumference, and step off distances round the circumference. The radius should just step round the circumference six times. Join the points together forming an equal six-sided polygon, known as a hexagon.

EX. 4.-Draw a line, A B, 34" long. With A and B as centre, and the length of A B as radius, draw arcs cutting in C. Join C to A and B, then A B C will be an equilateral triangle. Find the middle point of each of the sides, and join to the opposite corner. These three lines will meet in a point. Show, by drawing the circles, that this point is the centre of the inscribed and circumscribed circles of the triangle.*

(The inscribed circle is the circle touching the three sides, the circumscribed circle passes through the three corners.)

EX. 5.-Draw a circle 31" diameter, and divide the circumference into eight equal parts. Join the points, forming a polygon having eight equal sides, known as an octagon.

(This is best done by drawing two diameters at right angles, and then two other diameters with the 45° set square, sloping right and left.)

EX. 6.-Draw a square of 21′′ side. On each side of the square and outside it, construct an equilateral triangle. Draw the inscribed circle of each triangle, and also the inscribed circle of the square (find its centre by drawing the diagonals). Test your work by seeing if a circle drawn from the centre of the square passes through the centres of the triangles.

EX. 7.-Construct a square when the length of its diagonal is 4".

(Draw a circle of this diameter and inscribe the square within it.)

EX. 8.-Draw a hexagon inside a circle of 21" diameter. With each corner of the hexagon as centre, draw a circle of radius equal to half the side of the hexagon. Test your work by seeing if a circle drawn from the centre of the hexagon can be made to touch and include the six small circles.

(Find the centre of the hexagon by drawing two of its longest diagonals.) EX. 9.-Using the 45° and 60° set squares, draw (a) a triangle, base 3", base angles 45° and 60°; (b) an isosceles triangle, base 31", base angles 45°; (c) a rhombus, sides 31", acute angles 60°; (d) a parallelogram, sides 4" and 21", acute angles 45°.

* This point is only the centre of both circles when the triangle is equilateral.

SECTION II.

GEOMETRICAL CONSTRUCTIONS FOR LINES
AND ANGLES.

THERE are a large number of simple problems which constantly occur in all kinds of mechanical drawing, such as the division of lines, arcs, and angles, the drawing of parallels and perpendiculars, which can generally be worked with the usual instruments, and without adopting any geometrical construction. But it often happens that such methods are not as convenient, or likely to be as accurate, as certain constructive methods based upon Euclid's Elements, of which the following are the most useful and important. They should, therefore, be remembered by the student, and adopted whenever special accuracy is desired:

PROBLEM I. (Figs. 1, 2).—To bisect a line, arc, or angle. Fig. 1.-Let A B be the given line or arc. With one end, A, as centre, and radius greater than half, A B, draw arcs on opposite

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sides of A B. With the other end, B, as centre, and the same radius, draw arcs cutting the first arcs in C and D. Then the line joining C D will cut A B in its middle point, E, and will therefore bisect it.

(Note that only small arcs need be drawn, and that it is enough to simply mark the line or arc in the point, E, and not draw the whole line joining C D. It is evident that the radius of the arcs must exceed half A B, or the arcs will not cut.)

If the line or arc is to be divided into four, eight, or a greater number of equal parts, the same construction has simply to be repeated, treating the equal parts A E, E B, each in the same way as AB

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