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an APPENDIX of ALG EBRA. A*.*. (or the great Art) is a Method of manag
ing arithmetical and geometrical Computations by letters, by means whereof any Question may be clearly solved, and curious Theorems deduced for solving all Questions wherein Numbers or lines are concerned, which would be in vain to attempt either by Arithmetic or Geometry. I have here subjoined the principles of Algebra, with sundry examples to exercise the young Algebraist.—Having made every thing short and plain, that the Rules may not be burthensome to Youth. The Characters or Signs which are used in the follow-ing Appendix are in the Preceding Book, except the following; x* signify that x is squared x3=the Cube of x, and x any Power of x, &c. yT= any Square Root w/*TEhe Cube Root, and x ––– y = any Root at Pleasure, Quantities that are not known are represented by x, y, z, and v, those that are known by a, b, c, d, &c. Abortion may be comprehended in one Case, provided the following Directions be well understood. 1. When Quantities are of the same Kind, whether they have co-efficients or not, add them together, and their Sum will be the Sum required ; but if unlike, subtract the co-efficients (if any) and set down the Difference with the Sign of the greater,--or—as the Question may require.
subtradion may be performed by changing all the terms
that are to be subtracted,—in + or +into—and then adding them together, and the Sum will be the Difference.
Multiplication is performed by one general Rule; ob. serving that like Signs produce-F,and unlike—in the Produćt. N. B. If the quantities have co-efficients multiply them, if not, join the Letters like the Letters of a Word, obsery. ing to place the sign-Hor—(as above) before them, 6
- This last shews that the Rećangle or Product of the Sum and Difference of any two Quantities is equal to the IDifference of their Squares, * is very useful.
Involution of Quantities is nothing but multiplying them continually together as the Power they are to be raised toThus xxx-x* x x=x3 &c. Sir Isaac Newton has given the following rule for rais. ing any Binominal to any Power, which is this, Fulc
Reduáion of Equations, Has sundry Rules, according as the Problem is proposed; therefore when a Problem is proposed, having but one unknown Quantity, it is called a single Equation, though before the Quantity can be cleared we must examine it whether it requires Addition, Subtraćtion, Multiplication, or Division, &c, And then having cleared the unknown Quantity, and brought it to one fide of the Equation, and all the known Quantities o .. other, the Problem will be done by some of the above - €S. Here follow a few Examples to illustrate the Rule, Note. Any Quantity may be transposed to either fide of the Equation, by changing its Sign. Thus x+6=14... x–14— 6-8 And if x–9–3.’. X=12. Let 5 x–9=4 x+8. | Then it is plain 5x must be-4x-i-17 and by taking 4x out of both sides of the Equation we have x=17. so Redućtion where two or more unknown Quantities are o concerned ; find the value of any of them, and then com: pare them together, remembering to get as many Values of each unknown Quantity as you have Equations, other. wise it will be in vain to attempt the Solution of any Pro- blegn s