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ELEMENTS OF GEOMETRY.--LESSON 3. Note. 1. Geometry is that branch of mathematics which treats of the proportions of magnitudes, &c.

Geometrical Definitions. The teacher is requested to illustrate cach definition by furnishing examples on a black board.

i. A point is a small dot, which, mathematically considered, has no parts; being of itself indivisible. As, .A

2. A line has length, but neither breadth nor thickness, and its extremes are called points. As

-B. 3. A superfices, or surface, or area, as it is termed, has length and breadth, but no thickness. As,

4. A solid has length, breadth, and A thickness; that is, it has six sides. As, for example, a block of wood one foot every way.

5. A right line, is the shortest that can be made between two points. As,

A

-B 6. If the line is not the shortest, it is

A

B called indirect or a curved line. Às, 7. The inclination, or opening of two

B lines meeting each other at a point, is called an angle. As,

C

A Note, 2. In this example the lines arc A, B, and A, C, and the angie is at A.

8. A right line, let fall upon another right line, so as to incline neither way, forms two right angles, As, A, B, D,

с B Note. 3. The right line A, B, is called the base, and the other, C, D the perpendicular. The right angles are A, C, D, and B, C, D. 9. An obtuse angle is greater than

D a right angle, and an acute angle is less than a right angle. As,

А с B Note. 4. A, C, D, is the obtuse angle, and B, C, D, the acute angle. When three letters are used to express an angle, the middle letter should always denote the angular point.

10. A circle is a round figure, bounded by a line which is continually changing its direction, and which, in all its parts, is equally distant from a point called the centre.

Аа

Note. 5. The boundary line, A, B, D, is called the circumference, or periphery.

A

B

11. The radius of a circle is a right line drawn from the centre to the circumference. As, C, A.

A

Note. 6. All radii of the same circle are manifestly equal.

12. The diameter of a circle, is a right line drawn from one side of the circumference to the other through the А centre, dividing the circle into two equal parts, called semicircles, As, A, D, or E, B.

B Note. 7. The right lines, A, C, D, and B, C, E, divide the circle inte four equal parts called quadrants.

The circumference of every circle, is supposed to be divided into 360 equal parts, called degrees; each degree into 60 equal parts called minutes; and each minute into 60 equal parts, called seconds; and these into thirds, &c.

Now, as all circles are not of the same magnitude, and as they are all divided into the same number of degrees, it follows, that a degree is not a quantity of any determinate length, as feet, inches, &c. but merely the 360 part of a circle. A degree of any of the great circles of the earth or heavens, however, is computed at 69.5 statute miles.

REMARKS, &c.--LESSON 4. Note. Practical exercises in faulty composition, in which the pupil's at. tention will be directed to the introduction of capitals, the rules of pointing, etymology and syntax; to the exercises in faulty language, the precepts for writing composition, the properties of style, and the use of the figures of speech. It is respectfully suggested that it will be proper for the pupil to transcribe each exercise upon a slate, and add the necessary corrections, &c. and then on paper to be preserved for future compari

1. The hours of the wise man is doubled to him in reason of the mode in which he appropriates them which to the fool. ish more than half is lost by consequence of his unpreparedness his indolentness or his irresolution he

son.

that would do much and mark his path with some bright spots upon which he may look with good liking and the approvement of his own conscience must take the stream of moments as they pass or he loses his tide and if he ever sails it is without a chart a compass or a pilot what can they expect but the shoals of trouble the quick sands of disappointment and the rocks of ruin which will make ship wreck of all their hopes

2. When we first set forward in life unknowing to the world and its troublesomeness and every thing around us shines with the gloss of newness how little we think or regard the dangers we are liable to how we hesitate to examine and observe the lessons of admonition which others who has trod the path before us has left behind for advantage and warning

will it not be wiseness in us to pause a while and consider the objects around us and before us and estimate their value and use and manæuvre our conduct and actions so as to avoid the pit which others have fell into and the evilness that come upon them should close our eyes in sleepiness and rush to ruination with so many warning tokens before us who is him that will pity us or bring us help in the day of our need

3. A boy who was charmed with the gloss and gaiety of a butterfly's wings dogged the animal from shrub to flower with unwearisome pains hoping to become master of it he first thought to surround it among the folds of the rose leaves and then to entrap it under his bat as it wantoned on a head of white clover at one time he tried to secure it as it waved its plumes on the petals of a georgeous poppy where it seemed to nap awhile and at another he was sure of his game as it sat musing in the sunbeam upon the boughs of an orange plant hut all his efforts was vain the speckled creature flew away in safety

SPELLING, -LESSON 5. con-vert kón' věrt, one who des-cant des-kănt',to harangue changes opinion.

des-ert dězsért, a wilderness. con-vert kon-věrt', to change. de-sert dē-zērt', to forsake. con-voy kón'vòē, an escort. dif-fuse dif-fūse', scattered. <on-voy kön-vòē', to accom-dif-fuse dif-füze', to spread. pany.

di-gest di'jěst, collection of cour-te-sy kür'tē-sē, civility. laws.

[food. courte-sy kúrt'sē, act of rev-di-gest dē-jěst', dissolution of

dis-cord dis'kòrd, disagrecdes-cant děs'kănt, a discourse.

erence.

ment,

Jis-cord dis-kord', to disagree. [fare-well fare-wěll', act of dedis-count dis’kòûnt, an abate parture. ment.

fer-ment fer' měnt, commotion, dis-count dis-kòûnt', to pay fer-ment fer-měnt', to froth, or back.

foam. dis-yse dis-ūse', out of use. fore-taste före'tāstc, anticipadis-use dis-ūze', to cease using. tion. en-trance en’tră nse, a passage fore-taste före-tāste', to antien-trance ěn-trănse', to enrap. cipate. ture.

fre-quent frë'kwěnt, often. es-cort és kört, a convoy;

fre-quent fre-kwěnť, to visit of es-cort ěs-kòrt', to guard. ten. es-say ěs'sā, trial.

fu-sil fu'zil, can be melted. es-say ěs-sa', an endeavour. fu-sil fūczē', a firelock. ex-cuse eks-kūse', an apology.gal-lant găl'lănt, brave. ex-cuse ēks-kūze', to forgive. gal·lant găl-lănt', a beau. ex-er-cise ěks'ér-size, employ-hin-der hìn'dır, to obstruct. ment.

hin-der hìn'dūr, situate behind. ex-er-cise eks'ěr-size, to em-im-port im'port, brought home. ploy.

im-port im-põrt', to bring home ex.ile ěks'ile, banishment. im-press im'prés, stamp. ex-ile égz'ile, to banish. lim-press im-prěs', to print, ex-port ēks'port, sent out in stamp. traffic.

in-cense in'sēnse, perfume of ex-port eks-port', to carry out fered. or way:

in-cense in-sēnse', to enrage. ex-tract ēks'trăkt, a quotation. in-crease in'krēse, growth. ex-tract ēks-trăkt', to quote, in-crease in-krēse', to grow. select.

in-sultin'sült, abuse. fare-well fáre'wěll, parting in-sult in-súlt', to abuse. complaint. READING EXERCISES,

&c.LESSON 6. Gen. Warren's address to his soldiers at the battle of Bunker-

hill.
1. Stand! the ground's your own, my braves!

Will ye give it up to slaves ?
Will ye look for greener graves ?

Hope ye mercy stilī?
What's the merey despots feel?
Here it in the battle's peal!
Read it on yon bristling steel !

Ask it,----ye who will!

2. Fear

ye

foes who kill for hire? Will ye to your

homes retire ?
Look behind you! they're on fire!

And before
Who have done it! From the vale
Up they come, and will you quail?
Leaden rain and iron hail,

Let their welcome be!

you, see

3. In the God of battle trust!

Die we may, and die we must ,
But, 0, where can dust to dust

Be consign'd so well
As where the heav'ns their dews shall shed
On the martyr'd patriot's bed?
Where the granate rears its head,

Of their deeds to tell! NOTE. On the 17th of June, 1825, half a century from the day or which the battle was fought, the corner stone of a lofty granate monument was laid on the spot where Gen. Warren fell. ELEMENTS OF GEOMETRY.--LESSON 7.

Definitions. 13. An arc of a circle is any part of the circumference; as, AB, or B D; and it is said to be an arc of as many degrees as it includes parts of the 360, into which the circle is supposed A to be divided.

B

D

D

14. A chord is a right line drawn from one end of an arch to the other; and it is the measure of the arc. As A B.

B

E Nore. 1 The chord of an arc of 60 degrees, is equal in length to the radius of the circle, of which it is a part; hence, A C, or BC, is equal to A B.

15. The segment of a circle, is that part of it which is cut off by the chord. As the part A, D, B, in the last figure is called a segment.

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