The elements of that mathematical art commonly called algebra, expounded in two books / By John Kersey ... To which is added lectures read in the School of Geometry in Oxford, concerning the geometrical construction of algebraical equations; and the numerical resolution of the same by the compendium of logarithms. By Dr. Edmund Halley.

  • John Kersey the elder
Date:
1717
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Licence: Public Domain Mark

Credit: The elements of that mathematical art commonly called algebra, expounded in two books / By John Kersey ... To which is added lectures read in the School of Geometry in Oxford, concerning the geometrical construction of algebraical equations; and the numerical resolution of the same by the compendium of logarithms. By Dr. Edmund Halley. Source: Wellcome Collection.

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    CHAP. 12. The Vfe of Reductions in Chap. 11. 5p . - L- - — \ * 1 Likewife, If .. . 2bd-\- ica = Becaufe 2^+5c is drawn into the un-j known Root 4, I divide each part by >■ . .. a = 2b-f 3c, and there arifes . . .J T ; * v = 2 idb-^icdd ▲ ; id:./. So alfo, If. 4act = By dividing each part by 4 which is \ _ drawn into aat there arifes ... 3 * = do : IS Again, If ;.. 3aa—$a = Becaufe 3 is drawn into aa which is the-^ highefi unknown Power in the Equa-/ _T tion, I divide every Term by 3, andC * * aa * there arifes . = 24 ‘ 1 * • i .’ f ' 1 k i U = s Likewife, If ... .. 2ccaa—Adda = Becaufe 2cc is drawn into aa which is ^ the higheft unknown Power in the/ _2dd Equation, I divide every Term by 2a’,r aa ~JC a “ and there arifes .^ = sbbcc • Again, If .‘. 2bbaa-^^cdaa—dda = Becaufe 2bbJricd is drawn into aa the* higheft unknown Degree in the Equa-f _ dd _ tion, l divide each part by 2bb-\- 2bb-\-^cd * and there arifes .j -.ccdd „ ccdd 2bb-\-?,ci Alfo, If .. ^aaa\2\aa—6a - Becaufe 3 is drawn into aaa thchigheft^> unknown Power in the Equation,I di-b. aaa-\- 8aa—2a = vide each part by 3, and there arifes ^ ~— —ii' 1 . = I20Q ' ‘ • t « = 400 VI. If there be a furd Quantity in an Equation, that is, if a Radical fign as V *, or V (3) be prefixed before fome Quantity 5 firft by Tranfpofition ( according to Sett. or 6. of Chap, n.) make the furd Quantity foie poflefforof one part of an Equation, then call away the Radical fign, and exalt the other part of the Equation to the fame Degree or Power which is denoted by the Radical fign, by multiplying Quadratically or Cubically, c. io at length an Equation will be found exprefs’d al¬ together by rational Quantities: As for Example * If this Equation be propofed . . . . 4 “ Va * By fquaring each part, there will be produced ... a = * ? = 9 In like manner. If.’ Vba - By multiplying each part into it felf > , _ quadraticaly, there comes forth .. . y ] ’ * * bat ~ Then dividing each part of the laft > Equation by &, there arifes ... 3 ... a - ■ = 3 be : ybbcc = 9 bac . nob.- * Again, If ............. b-\-Vba = Firft by tranfpofition of b there arifes . . . . . /fo - Then by fquaring each part of the laft \ , Equation, there will be produced .,3 * * * * ba ” Whence, by dividing each part by £, > there arifes.3 ..a ~ = C = c—b - cc—2cb-\-bb. = C+b b