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MENSURATION OF SURFACES.
LINEAL MEASURES. 12 inches
i foot. 3 feet
i pole, rood, or perch,
SQUARE MEASURES. 144 Square inches
I pole or rood.
1 furlong. 64 furlongs
The English chain is divided into 100 links, each link being. 7:92 inches. And 80 chain-lengths, is 1 English mile.
The Scots chain is divided in 100 links, each link being 8.8& inches, and so chains is one Scots mile.
To measure surfaces and solids by duodecimals, or cross multiplication.
RULE. Multiply each denomination of the length by the feet of breadth, beginning at the lower place, and setting each product under that denomination of the multiplicand from which it arises, carrying by 12, when necessary, to the higher place. Then multiply by the inches of breadth (if any) setting each product one place to the right hand, carrying by 12 as above. Lastly, Multiply by the parts, fetting down each product, another place to the right, and so on.
EXAMPLE. A pavement 16 feet 4 inches long, 7 feet 6 inches broad, How
many square feet?
First, say, 7 times 4 is 28, which is 2 to carry, and 4 over. Write down 4, the excess in the column of inches; then say, 7 times 16 is 112, and the 2 you carry is 114, which set down in the column of feet. Again, 6 times 4 is 24, which is 2 to carry and o over; then say, 6 times 16 is 96, and 2 is 98, which is 8 feet 2 inches; which, when you'll have placed in their proper columns, add, and the sum will be 122 feet 6 inches.
Note, The superficial content of masons, joiners, plasterers, painters, &c. work, is frequently caft up by the preceding rule; for the better understanding of which observe, that
The fuperficies of any redangle is found by multiplying the length by the breadth; and the content of any triangle is four.d by multiplying half the base by the perpendicular altitude, as shall be explained afterwards.
Any lincal measure, multiplied by the same lineal measure, produces Squares of the same. Thus, lineal feet, multiplied by lineal feet, produce square feet; lineal inches into lineal inches produce square inches; and so on.
Lincal feet into lineal-inches, produce rectangles 1 foot long, and i inch broad, which, divided by 12 quats feet; and the remainder multiplied by 12, produces square inches.
Lineal feet into lineal lines produce rectangles i foot long and 1 line broad; which, divided by 144 quots square feet, and each unit in the remainder are rect. angles, equal to square inches.