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PRACTICAL EXERCISES.

SECTION I.

Exchange of Currencies.

299. In 13 how many dollars, cents and mills? Now as the pound has different values in different places, the amount in Federal Money will vary according to those values. In England 81-4s. 6d. 4.59.-20

20

=

In

0.225, and there £13-13 0.225-$57.777. Canada $158.0.25, and there 13-13-0.25 -852. In New-England $1-6s.-1.-0.30l, and there 13-13 0.3-843.333. In New-York $1-8s== £0.4, and there 13-13-0.4-32.50. In Pennsylvanja 81=7s. 6d. -7.5s.-£20%£0.375, and there £13 130.375 $34.666. And in Georgia $1=4s. 8d.—4.6 +S.₤4.6+ £0.2333+ and there 13-13÷÷÷0.2333

20.0

855.722.

300. In £16 78. 8d. 2qr. how many dollars, cents and mills? Before dividing the pounds, as above. 7s. 8d. 2qr. must be reduced to a decimal of a pound, and annexed to £16. This may be done by Art. 143, or by inspection, thus, shillings being 20ths of a pound, every 2s. will be 1 tenth of a pound: therefore write half the even number of shillings for the tenths £0. 3. One shilling being one 20th-£0.05; hence for the odd shilling we write £0.05. Farthings are 960ths of a pound, and if 960ths be increased by their 24th part, they are 1000ths. Hence 8d. 2qr. (=34qr.+1=) £0.035; and 16+0.3+0.05+ 0.035 £16.385, which divided as in the preceding example, give for English currency, $72.822, Can. $65.54, N. Y. $40. 962, &c. Hence,

301. To change pounds, shillings, pence and farthings tɔ Federal Money, and the reverse.

RULE. Reduce the shillings, &c. to the decimal of a pound; then if it is English currency, divide by 0.225, if Canada, by 0.25, if N. E. by 0.3, if N. Y. by 0.4, if Penn. by 0.375, and if Georgia, by 0.23-the quotient will be their value in dollars, cents and mills. And to change Federal Money into the above currencies, multiply it by the preceding decimals, and the product will be the answer in pounds and decimal parts.

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302. The following rules, founded on the relative valuc of the several currencies, may sometimes be of use:To change Eng. currency to N. E. add 3, N. E. to N. Y. add 3, N. Y. to N. E. subtract 4, N. E. to Penn. add Penn. to N. E. subtract, N. Y. to Penn. subtract Penn. to N. Y. add, N. E. to Can. subtract &, Can. to N. E. add, &c. ·

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NOTE. The current values of several of the above coins differ come-. what from their intrinsic value, as expressed in the table.

SECTION II.

MENSURATION.

Mensuration of Superficies.

304. The area of a figure is the space contained within the bounds of itssurface, without any regard to thickness, and is estimated by the number of squares contained in the same; the side of those squares being either an inch, a foot, a yard, a rod, &c. . Hence the area is said to be so many square inches, square feet, square yards, or square rods, &c.

305. To find the area of a parallelogram, whether it be a quare, a rectangle, a rhombus, or a rhomboid.

ROLE.-Multiply the length by the breadth, or perpendicular height, and the product will be the area.

1. What is the area of a square whose side is 5 feet?

5

Aas. 25 ft.

5

2. What is the area of a

3. What is the area of a rhombus, whose length is 13 rods, and perpendicular height 4? Aus. 48 rods.

4. What is the area of a rhomboid 24 inches long, and 8 wide? Ans. 192 inches.

5. How many acres in a rectangular piece of ground, 56 rods long, and 26 wide?

rectangle whose length is 9, 56x26÷160-9 and breadth 4 feet? Ans. 36ft.

306. To find the area of a triangle.

Ans.

RULE 1.-Multiply the base by half the perpendicular height, and the product will be the area.

RULE 2.-If the three sides only are given, add these together, and take half the sum: from the half sum subtract each side separately; multiply the half sum and the three remain-ders continually together, and the square root of the last pro duct will be the area of the triangle.

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600 feet, Ans.

2. The base of a triangle is

3. What is the area of a triangle whose three sides are 13, 14 and 15 feet?

13+14+15=42

and 42 221-half sum. 21 21 21

13 14 15 and 21×6×7×8 [=7056.

rem.8 7 6

2

Then 705684 feet, Ans.

4. The three sides of a tri

6.25 chains, and its height 5.20 angle are 16, 11 and 10 rods;

chains; what is its area?

Ans. 16.25 square chains.

what is the area?

Ans. 54.299 rods.

307. To find the area of a trapezoid.

RULE.-Multiply half the sum of the two parallel sides by the perpendicular distance between them, and the product will be

the area.

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308. To find the area of a trapezium, or an irregular polygon.

RULE.-Divide it into triangles, and then find the area of these triangles by Art. 306, and add them together.

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