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Q. How, then, does Compound differ from Simple Fellowship ?
A. Compound regards time, Simple does not.
Q. From the preceding example, what appears to be the

RULE? A. Multiply each man's stock by the time it is continued in trade. · Then, As the sum of the products : each man's product :: the whole gain or loss : each man's gain or loss.

Afore Exercises for the Slate. 2. Three merchants, A, B, and C, enter into partnership; A puts in $60 for 4 mo., B $50 for 10 mo., and C $80 for 19 mo.; but by misfortune they lose $50 : how much loss inust mach man sustain ?

(A's, $7,0587. Ans. B's, $14,705+.

(C's, $28.2357. 3. Three butchers hire a pasture for $48; À puts in 80 sheep for 4 mo., B 60 sheep for 2 mo., and C 72 sheep for 5 mo.; what share of the rent must each man pay? (A's, $19,20.

Ans. B's, & 7,2).

4. Two merchants entered into partnership for 16 mo.; A at first put in stock to the annount of $600, and, at the end of 9 months, put in $100 more ; B. put in at first $750, and, at the expiration of 6 months, took out $250; with this stock they gained $386; what was each man's part? An SA's, $200,797.

ns. B's. $185,202. 5. On the first of January, A began trade with $700, and, on the first of February following, he took in B with $340; on the first of June following, he took in C with $800 ; at the end of the year, they found they had gained $872: what was each man's share of the gain ?

Ans. A's share, $334,929; B's, $20,71; C's, $236,36.

MENSURATION.

I LXXIX. SQUARE MEASURE.

Q. What are your ideas of a Square ? A

A. It is any thing which is as long as it is wide.

What kind of a figure does this on ne rabe appear to be ?

A. A square figure.
Q. Why?

A. Because the time and ati i long as the side I..

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å. How many sides vas this figure, an what is their ler, th?
Q. How many equal corners has it?
A. Four.
Q. What are these come to yere al silei
A. Angles.
Q. Ilow, then, would you describe a nu are figure ?
A. It has four equal res, and four equal

angles.

Q. In the above figure, if each side ve I foot in length, what ougla to he called? d. I square foot.

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Q. If the sides of a square be each I yard in A 3 feet = 1 yard. B length, as in the figure on the right, what ought is to be called ?

A. 1 square yard.

Q. In this square, 1 perceive there are several maller squares coutained in the arger. If you count all the smaller squares, allowing each one to be 1 foot, bow many square feet or square wards will they make 1

Q. Why?'

A. Because there are 9 small squares, each containing 1 sq. ft., which make 9 sq. ft., i.e., 1 sq. yd.

Q. How many square feet, then, make 1 square yard ?
A. 9.

Q. If we multiply 3 feet (the length of 1 side) by the width, 3 feet, making 9, the same result is produced as before. What, then, will multiplying the length of any square by the breadth, or the length into itself, give?

Ä. The square feet, square inches, &c., contained in the figure.

Q. How many square inches in a figure 2 inches long and 2 inches wide ?

A. 2x2=4.

Q. Ilow many in a figure 4 inches long and 4 inches wide ? 12 mches square, that is, 12 inches long, and 12 inches wide ? 8 inches aquare ? '6 inches square? 20 inches square ? 30 inches square ?

Q. How many square feet in a figure'l fool, or 12 inches, square !
4. I square foot.
Q. Blow inany square inches in 1 square foot ? and why?
A. 144 sq. in. ; because 12 in. x 12 in. = 144.
Q. Ilow many square feet in 1 square yard ? and why?
A. 9 sq. ft. ; because 3 ft. X 3 ft. = 9.
Q. How many square yards in 1 square rod ? and why?

A. 304 sq. yds.; because 54 yds. X 51 yds. = 304. How many square feet in 1 square rod ? and why?

A. 272. sq. ft. ; because 164 ft. (the number of feet in 1 rod in length) x 164 ft. = 2721.

Q. This figure on the rigl: A is called a Parallelogram: what,then, are your ideas of a Parallelogram?

A. That it is a figure which is long- 7 D er than it is wide

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Q. We see by this figure, that there are two kinds of Parallelo gtams, viz. ABCD) and ABÉF. By inspecting these they will be found to be equal : how, then, may a Parallelograin be defined ?

A. It is a figure which has its opposite sides of equal length, and its opposite angles equal. ,

Q. If this figure bad been square, and each side 2 feet in length, $ is plain that it would have contained 4 square feet; but, allowing tin longest side to be 2 feet, and the shortest side only I fout, it will, or course, contain but as many square feet: bow many, then, docs contain ?

A. 2 ft. (length) x 1 ft. (breadth) = 2 sq. ft.

Q. If a figure 1 inch in breadth and 1 inch in length contains ! square inch, how many square inches will a figure 1 inch wide and % inches long contain ? '3 inches long? 4 inches long? 8 inches long? 12 inches long? 20 inches long?

Q. If a ligure 1 foot wide and 1 foot long convains 1 sqnare foot, how inany square feet will a figure 1 foot wide and ? feet long contain i S feet long ?' 4 feet long? 8 feet long? 10 feet long?

Q. How, then, do you proceed to find the square feet, inches, &c. of a square or parallelograin ?

A. Multiply the length by the breadth.

1. How many square feet- in a room 10 feet long and 2 feet wide? (10 X 2=20 sq. ft., Ans.) In a room 8 feet wide and 12'feet long? 20 feet long?

2. How many square rods in a piece of land 4 rods wide and 8 rods long? 10 rods long? '11 rods long ? 12 rode long? 10 rods long and 4 rods wide ?

Q. When a piece of land, in any shape, contains 40 square rods, what is it called '?

A. 1 rood. 3. Ilow many square rods in a piece of land 40 rods long and 2 rods wide? 4 rods wide ?

Q: When a piece of land, in any shape, contains 160 square rods, what is it called?

A. 1 acre.

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4. How many square rods in a picce of land 20 rods long and 2 rods wide ? How many such picces will make an acrc, or 160 square rods?

5. How wide inust a piece of land be, which is 80 rods long, to make an acre ? 40 rods long? 20 rods long?

6. How many square fcet of boards are contained in the floor of a room 10 feet square ? 20 feet square? 10 feet wide and 20 feet long? 20 feet wide and 30 feet long?

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Containing 25 square milos.

Q. How, then, must square feel, square inches, &c. be divided I . A. Square inches by square inches, square feet by square feet, &c.

5 square miles. Q. We are now prepared to an swer that interesting qnęstion which occurs in Geography, viz, the difference between miles square and square

5 miles square. miles. The figures on the righi are introduced for the purpose of its illustration. Examine them attentively; then tell me, for instance, What is the difference between 5 square miles and 6 iniles square ?

A. 5 square miles
means 5 miles in length and
only 1 in breadth ; but 5
miles square means 5 miles
in length and 5 miles in
breadth, making 5 times as many miles as only 1
in breadth; that is, 25 square miles.
From these illustrations we derive the following general

RULE.
Q. How do you proceed to find the contents of a Square ar
Parallelogram?
A. Multiply the length by the breadth.

Exercises for the Slate.
1. In a room 16 feet long and 11 feet wide, how many square
feet? 4. 176.

2. How many acres in a piece of land 560 rods long and 39 rods wide ? 560 X 32 =112 square acres, Ans.

The pupil must recollect that square inches must be divided by square inches, square yards by square vards, &c.

3. How many acres in a piece of land 370 rods wide and 426rods long? A. 385 acres, 20 rour.

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