In compound Quantities, the Operation 13. may proceed from Right to Left, as in com- Multiplication of mon Arithmetick; but it is more usual to compound perform Algebraical Multiplication from Left quantities. to Right. Thus, Way, as on 144*21728 1000+400+40 +200+80+8 The Total Produ. Ac+3A9E+3AE9+Ec the Side.. 1000+700+20+8 that is in fhort 1728. N. B. A thorough Infight into these two laft Examples, is of great Ufe, as tending to G 3 render 14: Of Divi fion. 15. render the Extraction of the fquare and cube Root eafy to be apprehended, and confequently performed. Of which fee more, Chap. 12. Algebraical Divifion takes the Divifor, as often as may be, out of the Dividend, and places the Remainder in the Quotient. Where it is to be noted, that Numerator is to be divided by Numerator, and Denominator by Denominator. EXAMPLE I Denominator a aa 3A) 6AA (2A or, Numerator 3) 6 (2. EXAMPLE II. Denominator c bc b. 3C) 15BC (5B or, Numerator 3) 15 (5. In like manner, A)AA(A, or A)A2(A, or A)Aq(A. Allo A)AAA(AA, or A)A' (A', or A)Ac(Aq. Alfo AA)AAA(A, or A) A' (A, or Aq)Ac(A, &c. If the Signs given be alike, then the of the Sign Quantity found by Divifion will be Affirto be affix mative; if the Signs be unlike, then the Quotient. Quantity found will be Negative. For, whereas Divifion undoes, what Multipli to the cation cation does; and the Product of this, is the Dividend of that; the Factors of this, the Divisor and Quotient of that therefore, Divi- Divi-Quoti for. dend. ent. In Divi ++ (+ because in into + Multiplica-into fion. + tion. + inro gives 5C)—5C2 (—C. 4D) 12DE (3E. EXAMPLE VII. A+E) Aq+2AE+Eq (A+E AE+Eq E X G4 EXAMPLE VIII. A+E) Ac+3 AqE+3AEq+Ec (Aq+2AE+Eq. Ac+2AqE+AEq cal Multiplication and Divi AqE+2AEq it 16. By comparing the fore-going ExamAlgebrai ples of, Divifion, with the correfpondent Examples of Multiplication; will appear, that Algebraical (as well as common) Multiplication and Divifion, do mutually prove one the other. fion, mutually prove one the other. 17. The best And alfo it will appear, that the best Way to perform Algebraical Divifion, is by confidering, what is the Quantity, which being multiplied into the Divifor, will produce the Divical Dividend. For that is always the Quotient. Way to perform Algebra fion. 18. of the Di vifion of Quanti ies, which are of De nominati ons altogether Diffe rent. Lastly, If the Divifor and Dividend be altogether of different Dénominations, then the Divifion can be no otherwise perform'd, than by fhewing, that the faid Quantities are to be divided; which is done by writing them like a Fraction Thus, A) B ( B And fo much for the four primary Operations in Algebra. CHAP. СНАР. Х. Of Reduction. Reduction is the Turning of a Quantity 1. of one Denomination, into an equi- Reductivalent Quantity of another Denominati- on, what. on. It is manifold. 2. The Reduction, which fhall be here first spoken of, is that of an Integer of Reducti on of In tegers into one external Denomination into anoIt is two-fold, Defcending and equivalent ther. Afcending. Integers, two-fold. 3. Reducti gers of a tion, into Defcending Reduction, is that, whereby an Integer of an higher or greater Deno- First, Demination, is turn'd into an Equivalent of fcending a lefs Denomination. And this is done on, or the by multiplying the Number to be reduc'd Reducti by fo many Units of the lefs Denomination of Inteon, as are Equivalent to one Unit of the greater greater Denomination. Thus, Pounds Denominaare turn'd into Shillings by multiplying an Equiby 20, Shillings into Pence by multiply-valent of a ing by 12, Pencé into Farthings by mul- mination. tiplying by 4: Because, 4 Farthings=1 Pence, and 12 Pence Shilling, and 20 Shillings = Pound. So Yards are turn'd into Feet by multiplying by 3, and Feet into Inches by multiplying by 12: Because, lefs Deno |