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• A GENERAL RULE
FOR EXTRACTING THE ROOTS OF ALL POWERS.
PREPARE the number given for extraction, by pointing off from the units' place, as the root required directs.
Find the first figure in the root, by the table of powers, which subtract from the given number.
3. Bring down the first figure in the next point to the remainder, and call it the dividend.
4. Involve the root into the next inferior power to that which is given ; multiply it by the given power, and call it the divisor.
5. Find a quotient figure by common division, and annex it to the root ; then involve the whole root into the given power, and call that the subtrahend.
6. Subtract that number from as many points of the given pow. er as is brought down, beginning at the lowest place, and to the remainder bring down the first figure of the next point for a new div. idend. 7. Find a new divisor, and proceed in all respects as before.
3 X 3 X 3 X 4 =108 Divisor 37% 37% 37% 37=1874161 Subtrahend
37 X 374 37X 4 =202612 Divisor 376 X 376 x 370 X 376= 19987173376 Subtrahend.
DUODECIMALS, or Cross Multiplication, is a rule made ufe of in measuring and computing the dimensions of the several parts of build. ings; it is likewile used to find ships'tonnage and the contents of bales, cales, &c.
Dimensions are taken in feet, inches, and parts. Artificers' work is computed by different measures, viz. Glazing, and masons' fiat work, by the foot ; Painting, paving, plastering, &c. by the yard ; Partitioning, flooring, roofing, tiling, &c, by the square of 100 feet; Brick-work, &c. by the rod of 16 feet, whose square is 2724. The contents of bales, cases, &c, by the ton of 49
Cubic feet. The tonnage of ships, by the ton of 95 feet.
RULE FOR MULTIPLYING DUODECIMALLY. 1. Under the multiplicand write the corresponding denominations of the multiplier.
2. Multiply each term in the multiplicand, (beginning at the lowest) by the feet in the multiplier ; write each result under its respective term, observing to carry an unit from each lower denomination to its superior.
3. In the same manner, multiply the multiplicand by the inches in the multiplier, and write the result of each term, one place more to the right hand of them, in the multiplicand.
Work in the same manner with the other parts in the multiplier, setting the result of each term two places to the right hand of thofe in the multiplicand, and fo on for thirds, fourths, &c.
5. Proceed in the like manner with all the rest of the denominations, and their sum will give the answer required.
2. Multiply 9 feet 6 inches by 4 feet 9 inches.
3. What is the price of a marble flab, whose length is 5 feet 7 inches, and breadth 1 foot 10 inches, at i dollar per
foot ? Anf. io dols. 23 cts.
4. There is a house with three tiers of windows, 3 in a tier, the height of the first tier is 7 feet 10 inches, of the second 6 feet 8 inches, and of the third
feet 11 inches; what will the glazing come to, at 14d. per foot ?
Ans. £ .13 IIS. 10(d.
5. If a house measures within the walls 52 feet 8 inches in length, and feet 6 inches in breadth, and the roof be of a true pitch, or the rafters of the breadth of the building, what will it come to, roofing at 1os. 6d. per square ? Anf. £.12 125, 11 d.
APPLICATION OF DUODECIMALS.
To find how many cubic or solid square feet (in order to ascertain
the freight) are contained in cases, bales, &c. that is, how many cubic feet ihey will take up in a ship.
2. Suppose the dimensions of a bale to be 7 feet 6 inches, 3 feet 3 inches, and a foot 10 inches ; what is the folid content ?
What is the freight of a bale containing 65 feet 9 inches, at 15 dollars per ton of 40 feet ?
3. A merchant imports from London 6 bales of the following dimensions, viz.
Length. Height. Depth.
2 4 I 9
I 9 5.
2 8 1 8 What are the solid contents, and how much will the freight amount to, at 20 dollars per ton ? The contents are viz.
To find Ships' Tonnage by Carpenters'- Measure. Rule. For single decked vessels, multiply the length, breadth at the main beam, and depth of the hold together, and divide the produet by 95.
EXAMPLE What is the tonnage of a single decked vefsel, whose length is 60 feet, breadth 20 feet, and depth 8 feet ?
60 length. 20 breadth.