Volume 1

The elements of that mathematical art commonly called algebra, expounded in four books / By John Kersey.

  • John Kersey the elder
Date:
1673
Catalogue details

Licence: Public Domain Mark

Credit: The elements of that mathematical art commonly called algebra, expounded in four books / By John Kersey. Source: Wellcome Collection.

    265/350 (page 245)
    ^Chap, 9. ExtraBiori of \/ (i) out of BimmiMs. cc -y 7. Which fumm muft be equal to h, the given fumrti of the Squares / • j hence this Equation ..^ aa^-^ -—~ 8. From which Equation, after due Redaction, there will arife S. , - . \ ^ baa—>aaaa ~ 9. And from the lafl: Equation ( Canon in 10. Chaf. 15-. Boo]^ i. ) there will arife this following Canon, to find out the two numbers fought, CANON I* V : H- -v/* iyy —' : the greater number ’ V‘ —4^^’ • = . the lefter number. That is, in words, * r From a quarter of the Square of the given fumni of the Squares, fubtra£f a quarter of the Square of the double Produft given . then add and fubiraft the fquare Root of that Remainder to and from half the given fumm of the Squares; fo (hall the fquare Roots of the Summ and Remainder of that Addition and Subtraction be the two numbers fought. h -|- i\/bb — cc = —ice I y* 4^^ — 4^^ • • a y \/yb- :cc: 10. Moreover, becaufe 11. Therefore, . * 12. Likewife bccauTe ' 15. Therefore, iq. Therefore from the eleventh and thirteenth Reps another Canon arifeth to folve the Queftion, -viz, CANON 2: . V: — V: : \/i ^ 47. -— : =: the ^reiter nnmber 2 * 'j: ^ _y-^— - : rr: the lefcr number. 2 That is, in words, . : ^ From the Square of- the given fumm of the Squares fiibtraCl the Square of the tfbuble Product given j then add and fubtraft the fquare Root of the Remainder to and from the. given fumm of the Squares: fo ftiall the fquare Root of half the Summ and Remainder of that Addition and Subtraction be the two numbers fought. By the help of either of thofc Canons we may extraft the fquare Root of a Binomial or Rcfidual, but 1 (hall nfe the latter Only, whence arifeth A General Rule for the ExtraUion of the Square Root out of Binomials and Ref duals, ^ Ff om the Square of the greater part of a given' Binonrslal or Rcfidual, fubtraft the Square of the lefler; then add the fquare Root of the Remainder to the greater part ' and fubtrad^ it alfo from the fame; laftly, connetS the fquare Roots of the half of that Summ and Re¬ mainder by the fign -j-^ if a Binomial be propofed, but'by —■ if a Rcfidual: fo you have the defired fquare Root of the given Binomial or Refidual. The practice of this Rule will be IheWn at large in the following Examples. Example i. Let it be required to exifaCf the (quare Root of this firfl: Binomial, ^ ^ 7 y 7^4 The O per Atm, 1. From the Square of the greater part 27, • r • • *1^ 7^5^ 2. Subtract the Square of the lefler part v'704, to wit, •••.!> 7^4 5. The Remainder is , , . • • • • v * ' * * * *