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What will be C's tax ?-4940. What D's ?-5130. What E'8?8710. What F's?. 14624. What H's ?-3512. What I's ?334160. What I's? 1571. What K's?-12012.
ILXXVIII. 1. Two men hired a pasture for $9; A put in 2 oxen for 6 months, and B 3 oxen for 5 months; what ought each to pay for the pasture ?
2 oxen for 6 months is the same as (2 X 6=) 12 oxen for 1 month; and 3 oxen for 5 months is the same as (3 x 5= 15 oxen for 1 month.
The shares of A and B are the same as if A hád put in 12 oxen, and B 15, for 1 month each; hence the relation of 12 to 15 is the same as in Simple Fellowship, thus,
2 X 6=12
27 : 15 ::9
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.
More Exercises for the Slaie. 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 12 mo.; but by misfortune they lose $50 : how much "loss must each man sustain ?
A's, $7,058+: Ans. B's, $14,705+.
C's, $28,235+ 3. Three butchers hire a pasture for $43; 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, $ 7,20.
4. Two merchants entered into partnership for 16 mo.; A at first put in stock to the amount of $600, and, at the end of 9 months, put in $100 more; B. put in at first $750, and, at the gained $386 ; what was each man's part? Ans. B*S; $185,202. expiration of 6 months, took out $250; with this stock they
5. On the first of January, A began trade with $760, and, on the first of February following, he took in B with $540; 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, $384,929 ; B's, $250,71; C's, $236,36.
I LXXIX. SQUARE MEASURE.
appear to be ?
Q. What are your ideas of a Square ?
B A. It is any thing which is as long as it is wide.
Q. What kind of a figure does this on the right
A. Because the side AB is as long as the side BC.
A. It has four equal sides, and four equal angles.
Q. In the above figure, if each side be 1 foot in length, what ought it to be called ? A. 1 square foot.
3 feet = 1 yard.
Q. If the sides of a square be each 1 yard in A 3 feet =l yard. B length, as in the figure on the right, what ought it to be called ?
A. 1 square yard.
Q. In this square, I perceive there are several smaller squares contained in the larger. If you count all the smaller squares, allowing each one to be 1 foot, how many square feet or square og yards will they make ? Q. Why?
с 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, inake 1 square yard ?
Q. If we multiply 3 feet (the length of 1 side) by the width, 3 feet, making, 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 ?
A. The square feet, square inches, &c., contained in the figure.
Q. How many square inches in a figure inches long and 2 incheswide ?
A. 2x2 = 4.
Q. How many in a figure 4 inches long and 4 inches wide ? 12 inches square, that is, 12 inches long, and 12 inches wide ? 8 inches square ? " 6 inches square? 20 inches square ? 30 inches square ?
Q. How many square feet in a figure 1 foot, or 12 inches, square !
A. 304 sq. yds.; because 51 yds. X 54 yds. = 304.
How many square feet in 1 square rod ? and why?
A. 2721 sq. ft. ; because 164 ft. (the number of feet in 1 rod in length) x 16 ft. = 2724. Q. This figure on the right A
B is called a Parallelogram: what,then, are your ideas of a Parallelogram?
A. That it is a figure which is long-F D er than it is wide.
Q. We see by this figure, that there are two kinds of Parallelograms, viz. ABCD and ABÉF. By inspecting these they will be found to be equal : how, then, may a Parallelogram be defined ?
A. It is a figure which has its opposite sides of equal length, and its opposite angles equal.
Q. If this figure had been square, and each side 2 feet in length, it is plain that it would have contained 4 square feet; but, allowing the longest side to be 2 feet, and the shortest side only 1 foot, it will, of course, contain but as many square feet: how many, then, does it 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 1 square inch, how many square inches will a figure 1 inch wide and 2 inches long contain ? 3 inches long? 4 inches long? . 8 inches long? 12 inches long? 20 inches long ?
Q. If a figure 1 foot wide and 1 foot long contains 1 square foot, how many square feet will a figure 1 foot wide and 2 feet long contain ? 3 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 parallelogram?
A. Multiply the length by the breadth.
1. How many square feet in a room 10 feet long and 2 feet wide? (10 X2=20 sq. ft., Ans.). In a room 8 feet wide and 12 feet long? 20 feet lang?
2. How many square rods in a piece of land 4 rods wide and 8 rods long? '10 rods long? 11 rods long? 12 rods 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. How 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. l acre.
4. How many square rods in a piece of land 20 rods long and 2 rods wide ? How many such pieces will make an acre, or 160 square rods?
5. How wide must a piece of land be, which is 80 rods long, to make an acre ? 40 rods long? 20 rods long?
6. How many square feet 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 ?
7. How many square yards in a figure 3 feet long and 3 feet wide ? 6 feet square? 10 feet long and 9 feet wide? 6 feet long and 2 feet wide? (2 X 6=12-9=1} yds., Ans.) In a figure 10 feet long and 4 wide? A. 44 yds. 8. How
many square yards in 9 square feet? In 108 ? In 72? In 99? In 27 ? In 80 ? In 37 ?
5 miles square.
Containing 25 square miles.
Q. How, then, must square feet, square inches, &c. be divided?
A. Square inches by square inches, square feet by square feet, &c.
5 square miles. Q. We are now prepared to answer that interesting question which occurs in Geography, viz. the difference between miles square and square miles. The figures on the right 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 5 miles square ? A.
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 or 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? A. 176.
2. How many acres in a piece of land 560 rods long and 32 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 yards, &c.
3. How many acres in a piece of land 370 rods wide and 426 rods long? A. 985 acres, 20 rods.