Warner and Swasey.

MECHANICAL DRAWING.

PART II.

GEOMETRICAL DEFINITIONS.

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 any two of its points.

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

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

Lines are perpendicular to each other, if when they cross, the four angles formed are equal. If they meet and form two equal angles they are perpendicular.

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 left-hand 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.

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

ANGLES.

An angle is formed when two straight lines meet.

An angle is often defined as being the difference in direction of two straight lines. The lines are called the sides and the point of meeting is called the vertex. The size of an angle depends upon the amount of divergence of the sides and is independent of the length of these lines.

RIGHT ANGLE.

ACUTE ANGLE.

OBTUSE ANGLE.

If one straight line meet another and the angles thus formed are equal they are right angles. When two lines are perpendicular to each other the angles formed are right angles.

An acute angle is less than a right angle.

An obtuse angle is greater than a right angle.

SURFACES.

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.

TRIANGLES.

A triangle is a figure enclosed by three straight lines. It is a polygon of three sides. The bounding lines are the sides, and the points of intersection of the sides are the vertices. The angles of a triangle are the angles formed by the sides.

A right-angled triangle, often called a right triangle, is one that has a right angle.

An acute-angled triangle is one that has all of its angles acute.
An obtuse-angled triangle is one that has an obtuse angle.
In an equilateral triangle all of the sides are equal.

If all of the angles of a triangle are equal, the figure is called an equiangular triangle.

A triangle is called scalene, when no two of its sides are equal.

In an isosceles triangle two of the sides are equal.

RIGHT ANGLED TRIANGLE.

ACUTE ANGLED TRIANGLE.

OBTUSE ANGLED TRIANGLE.

The base of a triangle is the lowest side; however, any side may be taken as the base. In an isosceles triangle the side which is not one of the equal sides is usually considered the base.

The altitude of a triangle is the perpendicular drawn from the vertex to the base.

EQUILATERAL TRIANGLE.

ISOSCELES TRIANGLE.

SCALENE TRIANGLE.

QUADRILATERALS.

A quadrilateral is a plane figure bounded by four straight lines.

The diagonal of a quadrilateral is a straight line joining two opposite vertices.

QUADRILATERAL.

TRAPEZOID.

PARALLELOGRAM.

A trapezium is a quadrilateral, no two of whose sides are parallel.

A trapezoid is a quadrilateral having two sides parallel.

The bases of a trapezoid are its parallel sides. The altitude is the perpendicular distance between the bases.

A parallelogram is a quadrilateral whose opposite sides are parallel.

The altitude of a parallelogram is the perpendicular distance between the bases which are the parallel sides.

There are four kinds of parallelograms:

RECTANGLE.

SQUARE.

RHOMBUS.

A rectangle is a parallelogram, all of whose angles are right angles. The opposite sides are equal.

A square is a rectangle, all of whose sides are equal.

A rhombus is a parallelogram which has four equal sides;

but the angles are not right angles.

A rhomboid is a parallelogram whose adjacent sides are unequal; the angles are not right angles.

POLYGONS.

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 fire sides.
A hexagon is a polygon of six sides.
A heptagon is a polygon of seven sides.
An octagon is a polygon of eight sides.
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. ▲ regular polygon is one all of whose angles are equal and all of whose sides are equal.