| XXX | (91) | XXX |
BRA. pi A L G E 640. Rule V. If that fide of the equation that contains the If their produft muft be 1640, then , unknown quantity be a compleat fquare, cube, or other power; then ext raft the fquare root, cube root, or the If tlieir quotient mufl: be 6, then . , JL~6. root of that power, from both fides of the equation, If their proportion is as 3 to 2, then x: jr: ; 3 : 2 or and thus the equation ft all be reduced to one of a 2x=3j; becaufe the produft of the extremes is equal lowfer degree. to the produft of the mean terms. If x*+6x-H9=20 Direct. II. “ After an equation is formed, if yon. “ have one unknown quantity only, then, by the rules then x+3~'l~:v/20 “ of the preceding chapter, bring it to ftand alone on and x—rt:^/20—3. one fide, fo as to have only known quantities on the Rule VI. A proportion may be converted into an u“ other you ftail difcover its value. equation afferting the produft of the extreme terms Examp.fide “ Athus being alked what was his age, equal to the produft of the mean terms; or,any one of “ anfwered that ^ perfon his age multiplied by TV of his age the extremes equal to the produft of the means divi- “ gives a produft ofequal to his age. J%u. What was ded by the other extreme. “ his age ?” If x 2—x 5 —-:: 4 • 1 It appears from the queftion, that if you call his age 2 then 12—x—2x ... 3x=i2 . . . and x=4. x, then ftall ... — * —= x Or if 20—x : x : : 7 : 3 then 60—3x2=7x .... iox=6o . . . and x=6. Rule VII. If any quantity be found on both fides of and by Rule 3. . . . 3xz=48x the equation with the fame fign prefixed, it may be ta- and by R. 7. . . . 3.y:=48 ken away from both : Alfo, if all the quantities in the whence byR. 2. . , . x=i6. equation are multiplied or divided by the fame quanDirect. III. “ If there are two unknown quantitity, it may be ftruck out of them all. Thus, “ ties, then there muft be two equations arifing from the “ conditions of the queftion : Suppofe the quantities x If 3x+fc=a+i . . . 3x=dr . . . and x= —. ,
- w‘ and y; find a value of x or ^ from each of the equations, and then, by putting thefe two values equal to
Rule VIII. Inftead of any quantity in an equation, you “ each other, there will arife a new equation involving may fubllitute another equal to it. “ one unknown quantity ; which muft be reduced by the Thus if 3 x+/=2 4 “ rules of the former chapter.” and ^—9 Ex amp. I “ Let the fum of two quantities be then 3x+9=24 ... x= —$• “ and their difference rf. Let s and d be given, and let “ it be required to find the quantities themfelves.” The further improvements of this rule ftall be taught Suppofe them to be x and j’, then, by the fuppofition. in the following chapter. x+y-t Chap. X. Solution c/'Quest ions that produce S imple Equat i ons. whence Simple equations are thofe “ wherein the unknown quantity is only of one dimenfion.” In the| folution of which, we are to obferve the following direftions. Direct. I. “ After forming a diftinft idea of the “ queftion propofed, the unknown quantities are to be “ expreffed by letters, and the particulars to be tranfla- Examp. II. “ A privateer running at t!ie rate of icr “ ted from the common language into the algebraic “ miles an hour, difcovers a flxip 18 miles off making “ manner of expreffing them, that is, into fuch equations “ way at the rate of 8 miles an hour: It is demanded “ as ftall exprefs the relations or properties that are “ how many miles the ftip can run before fte be over“ given of fueh quantities. “ taken ?” Let the number of miles the ftip can run before fte be Thus, if the fum of two quantities mull be 60, that con- overtaken x, and the number of miles the pridition is expreffed thus, . . . • x+ji=66. vateer muftberuncalled before fte come up with the ftip bey ; If their difference muft be 24, that condition then ftall (by fupp.) . . y=x+i8 . . . and x: 8 : xogives . . . . . . x——2 4. ' ~ s whence
