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the thing measured ; land is measured by superficial measure, and its dimensions are generally taken in acres, rods and links : boards are also measured by su. perficial measure, and the dimensions are taken in feet and inches, &c.
Artificers' work is calculated by different dimensions.
Masons' flat work, such as plastering by the square foot or yard.
Painting, paving, &c. by the yard.
Partitioning, flooring, roofing, tiling, &c. are calculated by the square of 100 feet.
Brick work is generally calculated by the solid foot.
Multiply the length by the breadth, the product is the superficial content, or area, in the same measure, or dimension, as that which the dimensions were taken
if yards, then the area is yards, if feet then the area is feet, &c.
To measure, or find the area of a board, or any other plane surface whose width is equal ; such a fig
ure is called a parallelogram. Rule.-Multiply the length by the breadth, and such dimension as the length and breadth are taken in, such will be the dimension of the area ; if feet, the area will be square feet, &c.
Note. It is obvious that if the length of any plane sur-
It is evident from the preceding figure, that if the length-B C 27, be multiplied by the width A B; or DC 5, the product will be 135, and will be the number of squares contained in the figure ; and it need not be argued that if these dimensions were taken in feet, that the area would be square feet, if taken in rods, or yards, that the area would be rods, or yards, &c.
Examples. 1. What is the area of a floor that is 22 feet 6 in. by 14.ft. 9 in. ?
Area 331 10 6 Ans. 2. How many feet of boards will cover a floor of a hall, that is 41 ft. 9 in.; by 30 ft. 6 in. allowing the floor to be % boards thick ?
Ans. 2546 ft. 9 in. 3. How many square feet are in a board that is 21 feet long, and 11 in. wide?
Ans. 19 3'19 ft. 4. How many square feet of boards will it take to lay' a single floor, that is 28 ft. 6 in. long, and 14 ft. 6 in. wide ?
Ans. 413 ft. 3'.
CASE II. To measure a board or any other plane, when it is wide.
at one end than the other, and of a true taper. RULE.Add together the width of the two ends, and half the sun is the mean widths of take the width in the middle (which is the same as the half of the sum of the width of the two ends,) then multiply the length by the mean width, the product is the answer, or area required.
ft. in. in. ft. in.
1 ft. 10 x 23 ft. 11'>25 ft. 10 11" Ans. 2. What is the area of a piece of land that is 30 rds. long ; 20 rds. wide at one end, and 18 rds. at the other?
Ans. 570 rds. 3. What is the area of a hall that is 32 ft. longi 22 ft. wide at one end, and 20 at the other?
Ans. 672 ft. 4. A man has a farm lying 300 rds. on the road, and the width of it at one end is 80 rds, and at the other 60: I demand the content of the farm.
Ans. 21000 rds. or 131 acres, 40 rds.
To measure the surface of a rightangled triangle. Note.--A right angled triangle is formed by a right line fajn ling, perpendicularly on another line, as the line A B falling upon the line C B, makes a right angle at B.
Rule Multiply the base C B, by half the perpendicular A B, and the product will be the area ; or muta
tiply the base and perpendicular together, and half the product will be the area : also, the perpendicular multiplied by half the base, the product is the area.
Note. All triangles, not having one right angle, are in general terms called oblique angled triangles, &c. Figure second represents an oblique apgled triangle; and the same rules that apply in measuring a right angled triangle will apply in measuring an oblique angled triangle.
EXPLANATION.It is evident that the area of angle may be found by multiplying the base by half the perpendicular; or by multiplying the base and perpendicular together, and taking half the product; or by multiplying the perpendicular by half the base. By multiplying half of À B (fig. 1) by C B, the parallelo. gram DFC B is measured; EF A is in the triangle, and is not measured; C D E is not in the triangle and is measured in the parallelogram; CD E being equal to E FA there can be no loss sustained : în figure 2, multiplying half the perpendicular D C, by the base A B, reduces the triangle A D B 'to the parallelogram HPB A; T2 D is equal to T H A, and D 20 is equal to OPB. Therefore it is evident that the parallelogram HP B A is equal in area to the triangle A D B.
1. What is the content of a piece of land 13 rods on the base, and 8•8 rods on the perpendicular, in form of figure first?
Half perp.44x13955914 rds. Aas.
2. What is the area of a piece of ground in form figure 2d, base 2704 rds.; perpendicular 8.2 rds.?
Ans. 112.34 rods. 3. What is the area of the gable end of a house, beam 40 feet, and height 12 feet 6 inches ?
Ans. 250 sq. ft. 4. What is the superficial content of a piece of board, in form of figure first: the length of which is 16 ft. 9 in. and the wide end 1 ft. 10 in. and the narrow end coming to a point ?
in. ft. in. ft. in." 10 + 511X16 9=15, 43 Ans. 5. What is the content of the second figure, A B 20 ft. and CD'6 ft. 4 in.? Ans. 63 ft. 4 in.
Note. The method of measuring every board with the pen would be too tedious for common práctice; I therefore shall show the method of making a board rule, and measuring boards with the same.
To make a board rule, and measure baards with it,
RULE.-Prepare a hard piece of wood two feet long and about 3 inches wide, and about half an inch thick ; divide the sides of the rule into lines about half an inch apart ; number these lines beginning with 10 and so on till all are numbered; it is more convenient to make the rule two feet and one inch long, fixing a steel point one incħ from the end of the rule, and numbering the divisions of the rule on the odd inch, and when measuring the length of a board with a rồle the steel point will scratch every i
two feet) divide a foot on cach line on the rule into was inany equal parts as is expressed by the figures on the end of the rule ; thus 1 foot on the line numbered 10 at the end must be divided into 10 equal. parts, and the line numbered 11, into eleven equal parts, &c. number each of these parts beginning with 1 and so on till all are numbered. See the following figure