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.

    297/350 (page 277)
    277 If That is, if SPEST. I. K pa4 ~l—264 — 24 7 ^ aaa — paa -'r 2 5^ -24 = o 5 number a 1 RESOLVTiO N. Firft ( by the Method in SeB. 5. Chaf. 8. of this Sooi^ I fcarch out all the nnmheK that will feveraHydmde the laftTeffp za without a Remainder, and find them to be thefe, of *e '-a’ k “aniintng in order whether the total futnm ot the Equation propos d may be divided by a _ i, or 0 + i • bv <1 - j or «-1- 2 d-i' 1 find.t may be exaaiy divMed by . Without a RemaindTr, and the oiote i <*4 — 74-1-12, as you fee by this following DiVifion. , ^ a 2^ aaa — paa-^-^zSa — 24 ^44-1744-12 444-244 I' 1 t. ' 'rS — 744 -|- i <?4 — 744 *-j— 144 H-124 — 24 Vi. * --J- 124-^ 24 ■ > » «» o p V ■ nf ^ ^Joivn number in the Oivifor 4 — 2 is one Real or Affirmaitive Root of the Equation propofed; for as well the Divifor as the Eiividend was fuppofed equal 0 not ng, vt-z. a 2 o, whence a — 2 . the Quotient alfo is confequently. equal = hence (by the Canon in i>eit to. Chapt, I ^.Boo^ i. ) two other Affirmative values of the Root 4 will be difco- vered, to wit, 4 and 3. bo that three Real values of 4, to wit, 2, 3 and 4 are found out, by every one of which the Equation propos’d may be expounded, as the Proof will eafily ffievvi ^BST. 2. 444-2 2 44*-(-IJ74 If That is, if ' = 1^0 . 1 1—360 r= 65 What is 4 =: ? i i aaa — 2244-}-1574 BESOLVTld jsr. FirR, the Divifors of the laft Term 360 will be found thefe, viz. i,‘2,3,4, 6, 9; 10, 12, iSi 18, 20, 24, 30^ 3^j4oi 4^>^o>72,po; i2o, 180 and 366;’then W examining in order whether the furam of the Equation propos’d may be divided by 4_i ^ or 44-15 by a—2, or 4^- 2 • by 4 — 3, or 4-1-3'^ &c. 1 find that 4— 5 will precifely divide the faid fumm without a Fradion, and therefore 5 is one Affirmative Root or value of 4; then the Quotient 44 —174+72 = o, that is, 174 —44 = 72 affords two other Affirmative values of 4, to wit, 8 and 9. Thus you fee three Real values of 4; to wit, 5, 8 and 9 are found out, by every one of which the Equation propofed, towi/ aaa — 2244 15 74 —: 3 60 may be expounded, as will appear by the PrOof. SljjRST. 3. If . . ii 914'—444 = 330 7 tVtf. - • -i That is, if . . . = o'S Whnis4z=? RES 0 Lvrib N. Firff, the DiviTors 6f the laft Term 3 3 o will lie found i, 5, lO, i r, i ^,’22, 30^ y 5-, 66,11 o, 155- and 33 o • then by examiningin order whether the fiiram of the Equation propos’d, to wit, aaa—914-]- 330 may be divided by a — i, -or 4-]- i . by 4 — 2,^ or4-l-2 • &t. I find it may be divided by a—.5 and leave no Remainder • therefore 4 — y = 0 gives 4 = y, which is one Affirmative Root of the Equation propos’d , and the Quotient 44-j- 54 — 66 — o', that is-, 44 y4:~ 66 affords another Affirmative value oi 4, to wir, 6. So that tvvo Real values of a are found out, by each of which the Equation propos’d may be expounded- for if a — f,ot a 6 , from‘either fu'ppofitiW kloiiowsthat 914 — aaa =330. • • ... ^^EST. 4; • To find two numbers whofe fumm fliall be 5, and that if the fumm'of their Squares be mnkiplied by the fumm of their Cubes, the ProdUtft may Be 45 y; RE SO-