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.

    314/350 (page 294)
    294 1. 2. 14. There are two numbers , fUch , that their fumm is equal to the Produft of their multi¬ plication ; and if the Produit or fumm of the faid numbers be added to the frimm of their Squares, it makes 1 : what are the numbers ? Let a and e be put for the two numbers fought, then the Queftion may be ftated thus, viz. If.— a And.. . • 'aa-peep^ae ■= I What are the numbers 4 and e ? ■— ------—■ RESOLVTIO N. The fumm of the firft and fecond Equations is .J> aa<\-‘€e~\~2ae — a^\ And from the third Equation, by tranfpofition 7 \ ^ ^ aa>-\-^ee‘A-2ae'—-‘a — e =115^ of a - j- €, there arifcth ^ * Suppofe.— Then by fquaring each part of the fifth Equation, J> 7. And by fubcrafting the fifth Equation from the 7 fixth, there remains .5 8. And from the fourth and feventh Equations, by^ exchange of equal Quantities , there will arife . ^ 9. Which lafl Equation being refolved by the Canon' in SeB. 8. Chaf. 15. Boo!^ i, the number 7, to wit,^ a^l-e will be made known, viz. I o. Therefore from the firft and ninth Equations, . 9 11. From the ninth Equation, by tranfpolition of a, >- 12. The eleventh Equation multiplied by a, pro-? duceth.S 13. And from/the tenth and twelfth Equations, by ? exchange of equal Quantities, . . • o 14. Wherefore the laft Equation beingrefolved by the Canon in SeB. 10. Chaf. 1 5. Book^ i. the two^ numbers fought will be difeovered , viz. . . So the numbers fought are found 3 and 17, which will folve the Queftion ; for their fumm is equal to the Produd of their multiplication, and if their fumm 4^ be added to 1 the fumm of their Squares, it makes i j J, as the Queftion requires. . , jy =: aa'^ee 2 ae yy — y — 4-ie yy — y — • ; 2:= d e me — e zzi ac =: 4* 4t 1 42 a 4i a — ad 42<i — aa 5^=3 'le — i\ XpEsr. 15. There are two numbers, fuch , that the Square of their difference is equal to the Produi^ of their multiplication ; and the fumm of their Squares makes 20 ; what are the numbers ? ' Let a and e be put for the two numbers fought, and let a be the greater j then the Que¬ ftion may be ftated thus, viz. 1. If.. . aa — lae'^ee -=: ae 2. And.aa-~\-ee z=z zo What are the numbers a and e t ] | - RESO LVTIO N. 3. From the firft Equation by tranfpofition of — 2<?<r, this? _ 4. Therefore from the fecond and third Equations . . . }> . . = 20 5. And the third Equation divided by 3, gives . . . 6. And by adding the double of the filth Equation to the? . , fecond , k make,.. . . . «-I- 7. Therefore by extrading the fquare Root of each part of^ the fixth Equation, the fumm of the two numbers fought S . ap-e = will be made known, viz. . . .j 8. From the feventh Equation , by tranfpofition of 4, this? arifeth,.^ ^ The eighth Equation multiplied by d?, produceth , . ae — 10. And