and to perform many useful problems upon true scientific principles. The problems for setting out work upon the ground, and those for reducing drawings to any scale or proportion, even without knowing the scale of the original drawing, will be found interesting, and very useful in practice.

This work, which treats of the first rudiments of practice, will be found particularly interesting and useful to gentlemen who practise, or are fond of the mechanical exercises, and to young men or apprentices in any of the professions, though, on some occasions, the older workmen may be benefitted by a perusal. The terms introduced are those in general use amongst workmen in London: and on this account it will be of essential service to young An art cannot be

men coming to the metropolis.

taught but by its proper terms.

Other branches of

art might have been introduced into this work, but those here treated of are intimately connected with each other, and have a natural affinity, and will, it is presumed, form upon the whole, a very interesting work to young mechanics; those who wish for further information in the building art, and particularly

B

on what relates to Geometrical Construction, may consult my other publications on Practical Carpentry.

Every art is improved by the emulation of its competitors: it is therefore the ardent hope of the author that the reader may not be disappointed of meeting with abundance of that information which his mind may be desirous to obtain.

PETER NICHOLSON.

PRACTICAL GEOMETRY.

GEOMETRY is the science of extension and magnitude: by Geometry the various angles of a building and the position of its sides are determined, as a square, a cube, a triangle, &c.: Boards and all Tools used by the Carpenter and Joiner are geometrical constructions: by Geometry all kinds of roofs and various other things laying in oblique angles are determined: the proper construction of all sorts of arches and groins depend entirely upon the principles of Geometry. I have, therefore, prefaced this work with an explanation and definition of such geometrical figures as will frequently occur in carrying on of works, and which are therefore necessary to be well known by all artizans and workmen, as well as by those who may superintend them: this slight in. troduction to Geometry will also be useful to all persons who wish to understand the practice and descriptions of the handy. works herein explained.

Geometry is the science of extension, and magnitude, and consists of theory and practice.

The theoretical part is founded upon the reasoning of selfevident principles; it demonstrates the construction, and shows the properties of regularly defined figures. The theory is the foundation of the practical part; and without a knowledge of it, no invention to any degree certain can be made. The use of Geometry is not confined only to speculative truths in Mathematics,

but the operations of mechanical arts owe their perfection to it; drawing and setting out every description of work, are entirely dependent upon it.

DEFINITIONS.

1. A point is that which has position, but not magnitude.

2. A line is the trace of a point, or that which would be described by the progressive motion of a point, and consequently has length only.

3. A superfices has length and breadth.

4. A solid is a figure of three dimensions, having length, breadth, and thickness. Hence surfaces are extremities of solids, and lines the extremities of surfaces, and points the extremities of lines.

If two lines will always coincide, however applied, when any two points in the one coincides with the two points in the other, the two lines are called straight lines, or otherwise right lines.

A curve continually changes its direction between its extreme points, or has no part straight.

Parallel lines are always at the same distance, and will never meet, though ever so far produced. Oblique right lines change their distance, and would meet if produced.

One line is perpendicular to another, when it inclines no more to one side than another.

A straight line is a tangent to a circle, when it touches the circle without cutting when both are produced.

An angle is the inclination of two lines towards one another in the same plane, meeting in a point.

Angles are either right, acute, or oblique.

A right angle is that which is made by one line perpendicular to another, or when the angles on each side are equal.

An acute angle is less than a right angle.

An obtuse angle is greater than a right angle.

A plane is a surface with which a straight line will every where coincide: and is otherwise called a straight surface.

Plane figures, bounded by right lines, have names according to the number of their sides, or of their angles, for they have as many sides as angles: the least number is three.

An equilateral triangle is that whose three sides are equal.
An isosceles triangle has only two sides unequal.

A scalene triangle has all sides unequal.

A right-angle triangle has only one right angle.

Other triangles are oblique-angled, and are either obtuse or acute. An acute-angled triangle has all its angles acute.

An obtuse-angled triangle has one obtuse angle.

A figure of four sides, or angles, is called a quadrilateral, or quadrangle.

A parallelogram is a quadrilateral, which has both pairs of its opposite sides parallel, and takes the following particular names: A rectangle is a parallelogram, having all its angles right ones. A square is an equilateral rectangle, having all its sides equal, and all its angles right ones.

A rhombus is an equilateral parallelogram whose angles are oblique.

A rhomboid is an oblique-angled parallelogram, and its opposite sides only are equal.

A trapezium is a quadrilateral, which has neither pair of its sides parallel.

A trapezoid hath only one pair of its opposite sides parallel. Plane figures having more than four sides, are in general called polygons, and receive other particular names according to the number of their sides or angles.

A pentagon is a polygon of five sides, a hexagon of six sides, a heptagon seven, an octagon eight, an eneagon nine, a decagon ten, an undecagon eleven, and a dodecagon twelve sides.

A regular polygon has all its sides, and its angles equal; and if they are not equal, the polygon is irregular.

An equilateral triangle is also a regular figure of three sides,