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.

    334/350 (page 314)
    3‘4 fromthefifteenthftep^niallbe5,or7,orii; and ij,or8,ori. Nowinanfwer to the Queflion , 3, i S and <5, (to wit, a, c and; ) are three fuch whole numbers, that their fumm is 24; and if the firft be multiplied by 36, the fccond by 24, and the third by 8, thefummof the threeProduftsmakes 7id,.as was required. The like may be faid of each of the two other Anfwers. But if Fradions or mixt numbers were admitted, innumerable Anfwers might be given to the Queftion, as before hath been Ihewn in the fifteenth flep. * ..i * • > A^ote. When one part of an Equation confifls^of an Affirmative letter andfomeN^a- tive Abfolute number, a limit may thence be inferr’d, above which the number fignified by that letter ought to be taken. But if one'part of an Equation conlifts of a Negative letter and of an Affirmative Abfolute number, it will give a limit beneath which the number reprefented by that letter muft be chofen. Sometimes alfo two limits will be difeovered, ( as in this thirteenth Queftion for the choice of the number and fometimes but one, ( as in divers of the following Queftions.) ' - . ^EST. 14. To find three fuch whole numbers that their fumm may make 100 j and that if the firft be multiplied by 4, the fecond by 3, and the third by if, the fumm of the three Produds may make 300. - ^ - - For the three numbers fought put 4, > and ' then the Queftion may be ftated thus • , I. If-, w .. *: ’• . i' •* ~ 100 2f And • • ••• • . 4!. 4^ 3 ^ *4* ^ 3 What arc the whole numbers 4, V and ; ? (| -- ... ■ ■■■' * * * ' ^'RESOLVTlON. ' ’ * '2^ The firft Equation multiplied by 4, (which is prefixt 7 . i ’ to a in‘ the fecond Equationproduceth • -S 47 4° 4. The fecond Equation fubtraded from the third, leaves ^ .. e — - . 5 y. The fourth Equation by tranfpofiiion pf ►]—p gives ^ 6, If inftead of e in the firft Equation there be taken the latter part of the fifth, this will arife, 7. That is, after due Redudion, 2= 100 100- I the 7 U1 s 5 100 8. From the latter part of the.fifth Equation it’s ma- nifeft: that 9. And confequently by multiplying each part in the eighth ftep by 5 ... 10. And by dividing each part in the ninth ftep by it follows that. 111 s iiy 4 = ^ 100 500 Whence *tis manifeft, that if the three numbers fought were not reftrained to whole numbers, any number kfs than 4y7f might be taken for the number ;, and then the numbers 4 and <? would be difeovered from the feventh and fifth fteps. But to have the Queftion folved by whole numbers, the number y muft be fome whole number not greater than 4^, and fuch as may caufe ligand ^ to 5 S be whole numbers, for otherwife the values of e and a in the fifth and fevenih fteps will not be expreffible by whole numbers • but 11 and 6y ' j , • ’ 5 — cannot be whole numbers unlcfs y be 5-, or fome Multiple of y, and therefore ; may be y, or 10, or 15, or any of the reft of the numbers in the third Columcl of this Table. and confequently, from the fifth and feventh fteps of the Refolution, the whole numbers e and 4 will be fuch as ftand under e and 4. Thus you fee that the Queftion receives nine Anfwers in whole numbers, which are all that it’s capable of: So that if you take 6 for 4j for e-j and 5 for ;, their fumm is 100 . and if 6 be multiplied by 4} a e 7 6 8p S 12 78 10 18 ^7 n 24 56 20 30 45 1^5 36^ 34 3° 42 ^3 35 48 12 40 1 ^4 I 45