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.

    272/350 (page 252)
    --1--i-~4-^___ ' ^52 ExtraBwn of y/(^2) OHt of Binomials, Book It, The Operation. 4 t 1. From the Square of the greater part, from . .'p aaah^iaahh^aHh 2. Subtraft the Square of the Icfl’cr part, to wit, , ^^aahh 3* The Remainder is..«.<.«.«»,^ aaab — 2aabb‘‘\~‘abbb 4. The fquare Root of that Remainder is . . . . ^ , a — 5”. To which fquare Root add the greater part, to wit, . . ^ ^ H- 6. The Siimni ^ ' 7. The half of that Sumra is.;> . . ay/ab 8. The fquare Root of thefaid half Summ is the greater? ,—7-77- . , part of the Root fought, to wit,.^ V:a^aPi or yf\a^aaah Again, from the gfeatet part of the given Binomial, ? —r—r r viz, from ..... ^ I o. SubtraiR the fquare Root before found in the fourth ? 'i^bJab ftep, towit, ..*. .> ^ ^ 11. The Remainder is . . • • • . • . • \h«jah 12. The half of which Remainder is . . . ^ • b^ab 12. The fquare Root of the faid half Remainder is the lelTer } ■ >■x ,,, part of ]he Root fought, to wit.? or 14. I fay!, the two parts in the eighth and thirteenth fteps,7 _ _ being connefted by 4-, lliall be the fquare Root fought, > ^la^Jab ; j^:by/ab : to wit,.. * • • 'j ly. Which Binomial Root may be alfo expreR thus, . . ^(^^)aaab ^(^^')abbh The Proof may be made by multiplying the Root found out into it fclf. Example 4. Again, if the fquare Root of this Refidual bedefired, . lefs ‘The Root being extradfed by the precedent method, will? ,-7- ;‘~r r . be found ..^ ^-.d^bc Which Root may be alfo expreft thus, . . . . . <4j{^a^aahc — But if it happen that when the Square of the lefl'er part of the given Binomial or Refidual is fubtradled from the Square of the greater part, the fquare Root of the Remainder and the greater part are not commcnfurable, ( according to the Definition before given in SeU.'], of this Chapt. ) there is no more to be done in filch cafe, but to prefix before the giveri Binomial or Refidual the fign y/, with a line drawn over both its parts, to denote the univerfal fquare Root of the given Binomial or Refidual. As, to extradt the fquare Root out of this Refidaal y/: \aa J^bb: — , I write ^; .^fad-f-bb — -a: which kind of Roots are commonly called Univerfal. i_-.. r .i II .1- till. ■■ fl.. I, ij. ^f... ..... ... ..I I , „ Seft. 17. ^eUions to exercife the foregoing Rules of this Chaptet, » .1 • flVEST. I. Td divide too into two fuch parts', that if dach patt be divided by the oihet part, thfi fumiii df the Quotients may make 3. RESOLVTIO N. 1. For one of the parts fought put , . . . . . a 2. Then confequently the other part is . . . . . 100 — a 3. Therefore, according to the import of the Queftion, ^ a j *00 —^ this Equation arifeih, viz. . .i 100—-4 a ^ 4. Which Equation duly reduced gives . . . . 1004 —=: 2000 5. Wherefore by refolving thefaid Equation by theT Canon in Sed?. i o. Chap.i%. Book^ i. the two values^ ^ 5 5”° 4*' * of 4, which are the defired parts of 100, will be^ ^ jq —- loy^j found ihefe, to wit, . . , , * . .