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COPYRIGHT, 1913, 1916, BY






In Part I the instructions and the problems worked out have been designed to teach the student the elementary operations of Mechanical Drawing, giving him a knowledge of the instruments, an ability to draw a straight and true line, and to make up simple figures. A fair degree of drawing ability is now assumed and we can pass on to more complicated problems. Wherever we turn for subjects, however, we find a knowledge of geometrical figures and their properties is absolutely essential to a clear understanding of the problems chosen and we will therefore turn to a discussion of these geometrical figures and the problems which involve them.


A point is used for marking position; it has neither length, breadth, nor thickness.


A line has length only; it is produced by the motion of a point.

A straight line or right line is one that has the same direction throughout. It is the shortest distance between two points.

A curved line is one that is constantly changing in direction. It is sometimes called a curve.

A broken line is one made up of several straight lines.

Parallel lines are lines which lie in the same plane and are equally distant from each other at all points.

A horizontal line is one having the direction of a line drawn upon the surface of water that is at rest. It is a line parallel to the horizon.

A vertical line is one that lies in the direction of a thread suspended from its upper end and having a weight at the lower end. It is a line that is perpendicular to a horizontal plane.

An oblique line is one that is neither vertical nor horizontal. In Mechanical Drawing; lines drawn along the edge of the T-square, when the head of the T-square is resting against the lefthand edge of the board, are called horizontal lines. Those drawn at right angles or perpendicular to the edge of the T-square are called vertical lines.

If two lines cut each other, they are called intersecting lines, and the point at which they cross is called the point of intersection.


An angle is the measure of the difference in direction of two lines. The lines are called sides, and the point of meeting, the

Fig. 40. Right Angle

Fig. 41.

Acute Angle

Fig. 42. Obtuse Angle

vertex. The size of an angle is independent of the length of the lines.

If one straight line meets another (extended if necessary), Fig. 40, so that the two angles thus formed are equal, the lines are said to be perpendicular to each other and the angles formed are called right angles.

An acute angle is less than a right angle, Fig. 41.
An obtuse angle is greater than a right angle, Fig. 42.


A surface is produced by the motion of a line; it has two dimensions-length and breadth.

A plane figure is a plane bounded on all sides by lines; the space included within these lines (if they are straight lines) is called a polygon or a rectilinear figure.


A polygon is a plane figure bounded by straight lines. The boundary lines are called the sides and the sum of the sides is called the perimeter.

Polygons are classified according to the number of sides.
A triangle is a polygon of three sides.

A quadrilateral is a polygon of four sides.
A pentagon is a polygon of five sides, Fig. 43.
A hexagon is a polygon of six sides, Fig. 44.
A heptagon is a polygon of seven sides.
An octagon is a polygon of eight sides, Fig. 45.

Fig. 43. Pentagon

Fig. 44. Hexagon

Fig. 45. Octagon

A decagon is a polygon of ten sides.
A dodecagon is a polygon of twelve sides.
An equilateral polygon is one all of whose sides are equal.
An equiangular polygon is one all of whose angles are equal.

A regular polygon is one all of whose angles and all of whose sides are equal.

Triangles. A triangle is a polygon enclosed by three straight lines called sides. The angles of a triangle are the angles formed by the sides.

A right-angled triangle, often called a right triangle, Fig. 46, is one that has a right angle. The longest side (the one opposite

Fig. 46. Right-
Angled Triangle

Tig. 47.

Acute Angled

Fig. 48. Obtuse-Angled


the right angle) is called the hypotenuse, and the other sides are sometimes called legs.

An acute-angled triangle is one that has all of its angles acute, Fig. 47.

An obtuse-angled triangle is one that has an obtuse angle, Fig. 48.
An equilateral triangle is one having all of its sides equal, Fig. 49.
An equiangular triangle is one having all of its angles equal.

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