Then a 18±√ 324 — 243 by Canon 3; that is a 18+ This 3d Form is call'd Ambiguous, because it hath two Affirmative Values of the unknown Quantity (a), either of which Values being had, the other may be found by Subftraction or Divifion, in like manner, as in Example 1. Notwithstanding all Quadratick Æquations of this 3d Form have two Affirmative, (or Imaginary) Roots; yet but one of those Roots will give a true Answer to the Queftion, and that is to be chofen according to the Nature and Limits of the Queftion, as fhall be fhew'd further on. From the foregoing Canons, by the help of Subftitution, other Canons may be Deduc'd, which will folve all Adfected Quadrarick Equations. Thus Suppose 4—e, and the foregoing Equations will become a There is another Method of resolving Adtected Quadratick Æ quations, and that is by cafting off the 2d or low eft Term of the unknown Quantity, which is done by Substitution, thus; take always half the known Coefficient, and in Cafes ft and 4 add it to, but in Cafes 2d and 3d Subtract it from, its fellow Factor, and for their Sum or Difference Subftitüte another Letter. As other in these From 2 and 67+ ÷ p (= 0) = √ ÷ pp +b Hence it is evident that whatsoever Method is ufed in folving thefe (or indeed any other) Equations, the Refult will still be the fame, if the Work be true. PART XI. Of Numerical Questions. CHA P. I. Questions producing Simple Æquations. a Question 1. s (200) Pounds is fo to be Divided between two Men, that the one is to have d (73) Pounds more than the other. What is the Share of each Man? Suppose the Shares fought to be a the Greater, ande the Leffer. 4+25 Sa = + 4 (20073 Pounds=f136:10:00) 2= greater Share. a Or thus, d leffer Share (= 63 l. 10 s. oo d.) A Gentleman finding divers Poor People at his Door, gave each of them b(3) Pence, and had c(6) Pence remaining but, if he wou'd have given them d(4) Pence each, he wou'd want (2) Pence. How many Poor People were there? One being ask’d how old he was, answer'd, if() of my Age in Years, were Multiplyed by () of my Age, the Pro duct wou'd be my Age. I demand his Age? |
