2. I demand the cube root of 74088? 3. Anf. 42. What is the cube root of 1092727? Anf. 103. 4. Required the cube root of 5735339? Anf. 179. 5. Extract the cube root of 27054036008. Anf. 3002. 6. Find the cabe root of 673373097125. Anf..8765. 7. What 7. What is the cube root of 36155°027576? 8. I demand the cube root of 121861281 33:07: To extract the cube root of vulgar fractions or mixed numbers. R U L E. The fraction being reduced to its lowest terms, extract the cube root of the numerator, for a new numerator, and of the denominator, for a new denominator. Mixed numbers may be reduced either to improper fractions or decimals, and then extracted. If the given fraction, or mixed number, be an imperfect power, it must be reduced to a decimal and then be extracted. 7. Find the cube root of 405. 8. What is the cube root of 54}? 9. Extract the cube root of 84. 10. I demand the cube root of 7? 11. Find the cube root of 33. CASE Anf. 7. Anf. 2:057+. Anf. 1.966+. Anf. 14735+ III. To find the fide of a cube that fhall be equal in folidity to any given folid. R U L E. Extract the cube root of the folid content of the given body, which root will be the fide of the cube required. EXAMPLES. 1. The folid content of a given cylinder is 1092727 inches; required the fide of a cube that is equal in area thereto ? 2. There is a ftone of a cubic form, which contains 135795744 cubic inches; I demand the fuperficial con tent of one of its fides? Anf. 264196 ins. CASE CAS E IV. To find two mean proportionals between two given numbers. R U L E. 1 Divide the greater extreme by the lefs, and the cube root of the quotient, multiplied by the lefs extreme, gives the lefs mean. Multiply the faid cube root by the lefs mean, and the product is the greater mean proportional. F. Find two mean proportionals between 7 and 189.. 27(3X7 21 the leffer mean 7)189 27 2.7 3 63 the greater mean : : As 7 21 63 189 Proof. 2. Find the two geometric means between 8 and 1728. Anf. 48 and 288. 3. Find the two geometric means between 5 and 1715. Anf. 35 and 245. RE M A R K. ift. The two laft cafes relate. to the use of the cube root. It has alfo many other ufes, which will occur to the learner in his going through a course of mathemati cal ftudies. 2d. There are other roots, befides the fquare, and cube root, that may be extracted; as the biquadrate, or fourth root; the furfolid, or fifth root; the fquared cube, or fixth root, &c. for extracting which feveral rules are given by different authors; but, as they are of no use in business, they are omitted here. DUODECIMALS DUODECIMALS, or CROSS MULTIPLICATION. DUODECIMALS or trofs multiplication, is a rule much used by workmen and artificers in cafting up the contents of their works. It is called duodecimals, because the parts decrease by twelves, from the place of feet towards the right hand. And, it is called cross multiplication, because the factors are fometimes multiplied crofs ways. R U L E. Under the multiplicand write the fame names of the multiplier; that is, feet under feet, inches under inches, parts under parts, &c. Then, multiply every term in the multiplicand, beginning at the loweft, by the feet in the multiplier, and write each product under its refpective term, carrying one for every 12, from each lower denomination to its next higher. This done, multiply every term in the multiplicand by the inches in the mul tiplier, and fet the product of each term one place removed towards the right hand. Proceed in like manner with the feconds, and all the reft of the denominations, if there be any more; and the fum of the lines will be the answer. a 2d. If the feet in the multiplicand are expreffed by a large number; inftead of multiplying by the inches, parts, &c. proceed as in the rules of practice, by takin gfuch aliquot parts as are equal to the inches, feconds, &c. of the multiplier. 3d. If the feet in both the multiplicand and multiplier are expreffed by a large number; multiply the feet by |