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 AR ITHMETICK. 4^3till you have three roots; the lalt of thefe is the root fought. Or, firft extra# the cube root, and continually the root fought. then extra# the fquare root of that root. Thus, let 1785793904896 be the eighth power; by Examp. Required the root of 191102976, being extra#ing the fquare root you get the biquadrate or the fixth power. fourth power, viz. 1336336; and by extra#ing the fquare root of the biquadrate, you get the fquare or 191102976 (13824(24 root. fecond power, viz. 1156, whofe fquare root is 34, the 1 8 root fought. 23) .91 1200)5824 refolv. 69 240 VIII. Extration of the root of the ninth power. 16 268)22x0 Rule. Extra# the cube root of the given number,, 2144 1456 X 4 = 5824 and you have the cube or third power, whofe cube root is the'root fought. 2762) 6629 (o) Thus, let 5159780352 by the ninth power; by ex5524 tra#ing the cube root you get the cube or third power, viz. 1728, whofe cube root 12 is the root fought. 27644)1x0576 Univerfally, whatever the given power be, put a + y 110576 for the root, and by involution raife a -j-y to the power of the given number; then, with this^ as your guide or extra# the root in the manner prefcribed and VI. Ext ration of the root of the feventh power. canon, exemplified in the extra#ion of the root of the fifth and powers. Rule. Put a-y for the root, and the feventh power feventh if the index of the given power be a multiple of will be aaaaaaa + ^aaaaaay + 21 aaaaayy + 35 aaaayyy 4- 2, But work may be rendered eafier: For, by extra#ing 3 ^aaayyyy + ixaayyyyy + Jayyyyyy -Yyyyyyyy, by the aid the the root of the given number, you obtain a power of which proceed as in extra#ing the root of the fifth ’whofefquare index is one half of the index of the given power. power. by extra#ing the fquare root of the tenth power, Examp. Required the root of 3404825447, being Thus, you have the fifth power ; and the fquare root of the the feventh power. twelth power is the fixth power, &c. Again, if the index of the given power be a multiple 3404825447(23 root. of 3, by extra#ing the cube root you obtain a power 128 whofe index is one third of the index of the power given. Thus the cube root of the ninth power is the cube or )2124825447 refolv.. third power ; and the cube root of the twelfth power is the biquadrate or fourth power, ire. paaaaaa 448000000 Involution is dtre#ly contrary to extra#ion or evo201600000 2 1 aaa aay lution ; and therefore, if a fquare number be fquared, 50400000 3 t;aaaayy it will give the biquadrate or fourth power; and if a ISaaayyy 7560000 biquadrate be fquared, it will give the eighth power. A680400 21 aayyyy. gain, if a cube number be cubed, it will give the ninth jayyyyy 34020 power ; and if the biquadrate.be cubed, it will give the 729 yyyyyy twelfth powerj See Algebra, Chap. IX. and X. Bivif. 7082.75149X3=2124825447 prod. For the application of Arithmetic to various branches • of bufinefs, eirc. fee Alligation, Annuities, Bar(°) Brokage, Bankruptcy, Exchange, InsuVII. Extraftion of the root of the eighth power. ter, rance, Interest, Mensuration, &e.. Rule. Extra# the fquare root of the given number. ARK ARITHMOMANCY, a fpecies of divination performed by means of numbers. ARK, or Noah's Ark, a floating veflel built by Noah, for the prefervation of his family, and the feveral fpecies of animals, during the deluge. See Plate XXXVIIL fig. 1.

A K K The ark has aflbrded feveral points of curious inquiry among, the critics and haturalifts, relating to its form, capacity, materials, ic. The wood whereof the ark was built, is called in the Hebrew Gopher-wood, and in the Septuagint fqxare timbers. Some tranflate Ahe original cedar, others pine, others'*