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two sides of a room does not make the corner in which

they meet greater or less.

legs of the one six Lay one on the other,

Let there be two rules, the inches, of the other a foot long. joint upon joint, and open them together. There is one and the same opening-one corner, or angle. Remove the one ruler from the other as it is: there are two equal angles with sides of different lengths.

Take a long stick, and pin another to the middle of it, so that it can move round like the hand of a clock, and first let the moveable stick lie upon the other. Then move it slowly round from left to right. There will be an angle between the two sticks on either side of the moveable stick. As you move the stick, one of these angles increases and the other diminishes. When the two angles are exactly equal, the one stick is said to be perpendicular to the other, and the angles on either side are called right angles.

An angle greater than a right angle is called an obtuse angle; an angle less than a right angle is called an acute angle.




THE area of a figure is the extent of its surface. A triangle is a figure which has three sides, and therefore three angles.

The side upon which a triangle stands is called the base of the triangle.

Equilateral means having “equal sides.”

An equilateral triangle is a triangle whose three sides are all equal.

A parallelogram is a four-sided figure, whose opposite sides are parallel.

The diagonal of a parallelogram is a line drawn through it from one angle to the angle opposite.

A square is a parallelogram, all whose sides are equal, and all the angles right angles.

An oblong is a parallelogram whose angles are right angles, but its side are not all equal.

A pentagon is a five-sided figure, and a hexagon a six-sided figure; an octagon is an eight-sided figure

A circle is a figure contained by a line which is such

that any point in it is at the same distance from one point inside the circle. This point is called the centre. The line which bounds the circle is called the circumference, or periphery. Every straight line drawn from the circumference to the centre is called a radius of the circle. A straight line drawn from any point in the circumference, through the centre to meet the circumference again, is called a diameter.

A diameter cuts a circle into two halves. Each half is called a semicircle.

A part of the circumference is called an arc; a part of the circle cut off by a straight line is a segment of a circle.

The circumference is concave to one who stands within it, and convex to one who stands outside of it. A tangent is a straight line which touches a circle.


A NIGHTINGALE, that all day long
Had cheer'd the village with his song,
Nor yet at eve his note suspended,
Nor yet when eventide was ended,
Began to feel, as well he might,
The keen demands of appetite;
When, looking eagerly around,
He spied far off, upon the ground,
A something shining in the dark,
And knew the glow-worm by his spark;
So, stooping down from hawthorn top,
He thought to put him in his crop.
The worm, aware of his intent,
Harangued him thus, right eloquent—
Did you admire my lamp, quoth he,

As much as I your minstrelsy,
You would abhor to do me wrong,
As much as I to spoil your song;
For 'twas the self-same power divine
Taught you to sing, and me to shine;
That you with music, I with light,
Might beautify and cheer the night.
The songster heard his short oration,
And, warbling out his approbation,
Released him, as my story tells,
And found a supper somewhere else.
Hence jarring disputants may learn
Their real int'rest to discern;

That brother should not war with brother,
And worry and devour each other:
But sing and shine by sweet consent,
Till life's poor transient night is spent,
* Harangued him.] Made a speech to him.

Respecting in each other's case

The gifts of nature and of grace.

Those Christians best deserve the name,
Who studiously make peace their aim;
Peace both the duty and the prize
Of him that creeps and him that flies.





GOD has given to many animals marvellous skill. Birds can with their bills frame nests, which no human art can imitate. Beavers with their teeth and paws can cut down trees, build dams, and construct houses to dwell in.

But God has given to man a wisdom, which is more serviceable than the skill of all other animals. With his hand alone he can do much; but by his wisdom he can contrive means of doing infinitely more than one of the most sagacious and most skilful of the brute creation.

Man can construct tools and instruments, with which to work; and this is one great difference between man and brute, that man can make tools.

The art by which we work with tools or instruments is called mechanical, which means the contriving art.

A machine is a contrivance by which any force is made serviceable for a particular work; and so any tool might be properly called a machine. But the word machine is generally used of those contrivances

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