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livide the whole by the number of shili;uct by 9.

4. Reduce 19s. 58d. New-York, &c. currency, to Federal Money

94)0,974 decimal of 198 57d.

82,433 Ans. 5. Reduce 64. New-England currency, to Federal Money.

,3) 64000 decimal expression.

8213,331 Ans. Note.-By the foregoing rule you may carry on the decimal to any degree of exactness; but in ordinary practice, the following Contraction may be useful.

RULE II. To the shillings contained in the given sum, annex 8

en

ang's contained iv a dollar, and the quotient will be cents.

1

EXAMPLES.

1. Reduce 45s. 60. New-England currency, to Federal Money.

6x8+2 = 50 to he annexed,
6)45,50 or 6)4550

Scts.
87,58% Ans.

758 cents.=7,58 • 2. Reduce 21. 10s. 9d. New-York, &c. currency, to Federal Money.

9x8+2=74 to be annexed. Then 8)5074

Or thus, 8)50,74

8 cts. Ans. 634 cents.=6 34

$6,34 Ans N. B. When there are no pence in the given sum, you niust annex two cyphers to the shillings; then divide as before, &c.

3. Reduce 31. 55. New-England currency, to Federal money.

31. 55. se 65€. Then 6)6500

thes, 1083 cents.

SOME USEFUL RULES,

FOR FINDING THE CONTENTS OF SUPERFICIES AND

SOLIDS.

SECTION I. OF. SUPERFICIES: The superficies or area of any plane surface, is composed or made up of squares, either greater or less, according to the different measures by which the dimensions of the figure are taken or measured :-and because 12 inches in length make 1 foot of long measure, there fore, 12x12=144, the square inches in a superficial foot, &c.

ART. I. To find the area of a square having equal sides,

RULE. Multiply the side of the square into itself, and the product WITT the the area, or content.

EXAMPLES. 1. How many square feet or boards are contained in the floor of a room which is 20 feet square ?

20x20=400 feet, the Answer. 2. Suppose a square lot of land measures 26 rods on each side, how many acres doth it contain ?

Notr.---160 square rods make an acre.
Therefore, 26 x 26=676 sq. rods, and 676;-160=4a.

36r, the Answer. ART. 2. To measure a parallelogram, or long square.

RULE. Multiply the length by the breadth, and the product will be the area, or superficial content.

1. A certain garden, in forrt of a long square, is 96 ft. song, and 54 wide; how many square feet of ground are contained in it ? Ans. 96 x 5455144 square feet.

2. A lot of land, in form of a long square, is 120 rods m length, and 60 rods wide; how many acres are in it?

120X60=7200 sqr. rods, then 720=45 acres. Ans.

3. If a board or plank be 21 feet long, and 18 inches sroad; how many square feet are contained in it?

18 inches=1,5 feet, then 21x1,5=31,5 Ans,

EXAMPLES.

Or, in measuring boards, you may multiply the length in feet by the breadth in inches, and divide by 12, the quotient will give the answer in square feet, &c.

Thus, in the foregoing example, 21x18+12=31,5 as before.

4. If a board be 8 inches wide, how much in length will make a square foot ? RULE.--Divide 144 by the breadth, thus, 8)144

Ans. 18 in. 5. If a piece of land be 5 rods wide, how many rods in Pength will make an acre ?

RULE.-Divide 160 by the breadth, and the quotient will be the length required, thus, 5)160

Ans. 32 rods in length. Art. 3. To measure a Triangle. Definition.-A Triangle is any three cornered figure which is bounded by three right lines.*

RULE. Multiply the base of the given triangle into half its perpendicular height, or half

the base into the whole per .. pendicular, and the product will be the area.

EXAMPLES.

1. Required the area of a triangle whose base or longest side is 32 inches, and the perpendicular height 14 inches.

32x7=224 square inches, the Answer. 2. There is a triangular or three cornered lot of land whose base or longest side is 51f rods; the perpendicular from the corner opposite the base measures 44 rods; how many acres doth it contain ?

51,5X22=1133 square rods,=7 acres, 13 rods.

A Triangle may be either right angled or oblique : in either case the teacher can easily give the scholar a right idea of the base and perpendicular, by marking it down on a slate, paper, &c.

TO MEASURE A CIRCLE. ART. 4. The diameter of a Circle being given, to find the Circumference.

RULE. As 7 : is to 22 : : so is the given diameter : to the circumference. Or, more exactly, As 113 : is to 355 :: &c. the diameter is found inversely:

Note.—The diameter is a right line drawn across the ctrele through its centre.

EXAMPLES.

1. What is the circumference of a wheel whose diameter is 4 feet As 7 : 22 : : 4 : 12,57 the circumference.

2. What is the circumference of a circle wiose diame. ter is 35 P--As 7 : 22 : : 35 : 110 Ans.mand inversely as 22 : 7 :: 110 : 35, the diameter, &c. ART.5. To find the area of a Circle.

RULE. Multiply half the diameter by half the circumference, and the product is the area ; or if the diameter is given without the circumference, multiply the square of the diameter by ,7854 and the product will be the area.

EXAMPLES.

1. Required the area of a circle whose diameter is 12 inches, and circumference 37,7 inches.

18,55=half the circumference.

6=half thé diameter.

113,10 área in square inches. 2. Required the area of a circular garden whose diame ter is 11 rods ?

,7854 By the second method, 11x11 = 121

Ans. 95,0334 rods. SECTION 2. OF SOLIDS. Solids are estimated by the solid inch, solid foot, &c. :728 of these inches, that is 12x12x12 make 1 cubic ør solid foot.

Art. 6. To measure a Cube. Definition.- cube is a solid of six equal sides, each of which is an exact square.

RULE. Multiply the side by itself, and that product by the same side, and this last product will be the solid content of the cube.

EXAMPLES.

1. The side of a cubic block being 18 inches, or 1 fogt and 6 inches, how many solid inches doth it contain ? ft. in. ft.

1 6-1,5 and 1,5X1,5X1,5=3,375 solid feet. Ans. Or, 18x18x18-5832 solid inches, and 1=3,375

2. Suppose a cellar to be dug that shall contain 12 feet every way, in length, breadth and depth ; how many solid feet of earth must be taken out to complete the same ?

12x12x12=1728 solid feet, the Ans. Art. 7. To find the content of any regular solid of three

dimensions, length, breadth and thickness, as a piece of timber squared, whose length is more than the breadtha and depth.

RULE. Multiply the breadth by the depth, or thickness, and that product by the length, which gives the solid content.

EXAMPLES.

1. A square piece of timber, being one foot 6 inches, or 18 inches broad, 9 inches thick, and 9 feet or 108 inches long; how

many

solid feet doth it contain ? 1 ft. 6 in=1,5 foot. 9 inches

,75 foot.

Prod. 1,125x9=10,125 solid feet, the Ans.

in. in. in. solid in.
Or, 18X9x108=17496_1728=10,125 feet.

But, in measuring timber, you may multiply the breaulth in inches, and the depth in inches, and that product by the length in feet, and divide the last product by 144, which will give the solid content in feet, &a

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