while studying one problem that is rather intricate to you, than while performing several that are easy. Dwell upon what the immortal Newton said of his own habit of study. "I keep," says he, "the subject constantly before me, and wait till the first dawnings open by little and little into a full and clear light."

INVENTIONAL GEOMETRY.

THE science of relative quantity, solid, su perficial, and linear, is called Geometry, and the practical application of it, Mensuration. Thus we have mensuration of solids, mensuration of surfaces, and mensuration of lines; and to ascertain these quantities it is requisite that we should have dimensions.

The top, bottom, and sides of a solid body, as a cube,' are called its faces or surfaces,' and the edges of these surfaces are called lines.

The distance between the top and bottom of the cube is a dimension called the height, depth, or thickness of the cube; the distance between the left face and the right face is anoth

1 The most convenient form for ilustration is that of the cubic inch, which is a solid, having equal rectangular surfaces. ? A surface is sometimes called a superficies.

er dimension, called the breadth or width; and the distance between the front face and the back face is the third dimension, called the length of the cube.

Thus a cube is called a magnitude of three dimensions.

The three terms most commonly applied to the dimensions of a cube are length, breadth, and thickness.

1. Place a cube with one face flat on a table, and with another face toward you, and say which dimension you consider to be the thickness, which the breadth, and which the length.

2. Show to what objects the word height is more appropriate, and to what objects the word depth, and to what the word thickness.

As a surface has no thickness, it has two dimensions only, length and breadth. Thus a surface is called a magnitude of two dimensions.

3. Show how many faces a cube has.'

The surfaces of a cube are considered to be plane sur faces.

When a surface is such, that a line placed anywhere upon it will rest wholly on that surface, such surface is said to be a plane surface.1

As a line has neither breadth nor thickness, it has one dimension only, that of length.

Thus a line is called a magnitude of one dimension.

4. Count how many lines are formed on a cube by the intersection of its six plane surfaces.

If that which has neither breadth, nor thickness, but length only, can be said to have any form, then a line is such, that if it were turned upon its extremities, each part of it would keep its own place in space.

We cannot with a pencil make a line on paper-we represent a line.

The boundaries or ends of a line are called points, and the intersection of two lines gives a point.

As a point has neither length, breadth, nor

1 When the word line is used in these definitions and ques tions a straight line is always meant.