capable of Innumerable Answers.
3*3
ariseth enCe ^ ^anfposition of 3 u, this Equation? _
. Tl ’ ... ' * ' ' ’ * *•>
thJ^- en ^ the latter part of the Equation in.
t L. n,n eteenth step in the place of y in the thirteenth,)
j, ^ ar iseth,.'
ii[ p ^nce, after due Reduction, this Equation arifcth, >’ torn the latter part of the nineteenth Equation, it ?
^Vbeinferr’dthat.. . . .s
tion^ ^ r ° m tke latter parr of the twenry-first Equa-^_
10-
e 1 o -
e = 2«-
__ „ 1
» ^3 j—
ft C~ 1
Z«
■3»
is foce by the twenty-second and twenty-third steps, u ( or the number of Girls)n « to fall between t and 3-3, let 2 be taken for the value of u , •viz..
Sur
’• Tt
Ppose
u — 1
from the nineteenth and twenty-fourth steps, J* y = 4 ( —-jo—3 #)
^ n d from the twenty-first and twenty-fourth steps, ^ - — 2 ( — 2«— 2)
b y the eleventh, twenty-sixth , twenty-fifth and twenty-fourth steps , four wholej\ g f Sare discovered, to wit, 12, 2,4 and 2, for the values of a, e,y and ».
^ntn b y taking 3 for the value of m , (which is within the limits before discovered)1 1 Eteenth and twenty-first steps will discover r and 4 for the values of y and e, ( a being“esore. Wherefore two Answers to the Question are found out, for the number% n n being put 12, the number of Women will be 2,
%,!) ^ber of Boys 4, and the number of Girls 2 . or thety* °f Men being 12 as before, there will be fourl o„ j!') 1 Boy and 3 Girls. Again, if 11 be put equall 0r the number of Men,) and the process be repeated
--- r V ,- r -
Vj[| 1eleventh step to the end of the Resolution, therelil( e found two Answers more in whole numbers. Innncr » if 9 > 10 a °d 13 be severally put equal to <r,s C y fwers more will be discovered; But if L and 14'^its • ^ put equal to <*, although they be within thethe eighth and tenth steps, yet the work being
OhL _ y 3C KfisA** nrSIl *iAt> tA Cn/I « <v ond m art tutinl
a
e
y
H
9
9
1
I
10
6
3
I
n
5
2
2
11
3
5
I
12
2
4
2
12
4
1
3
13
1
3
3
Juiyr® as before will not succeed to find e> y and h in whole numbers. so that there areHr e t p Vei n Answers, to wit, those inserted in the Table } but that every one of them will• If a ^Question may easily be proved.
X? th e of this nature be desired that hath but one Answer in whole numbers,r^ 4ri s D ni,rn ber of persons be 60 , and 100 the number of ihillings spent ; also let everyQr| r shillings, every Woman f of a shilling, every Boy j- of a shilling, and every
"in £ of a shilling - then by forming the Resolution as before, the number of MenGhj s , un d 46 , the number of Women 3 , the number of Boys 5.
6 .
and the number
., 1-0 .. . £VEST. n .
y IfconpL e 200 ,nt0 ^ ve sech whole numbers, that if the first be multiplied by ir<by the third by 1, the fourth by and the fifth by z, the summ of the Pro-
j Thi S y alsomakc 2 °°-
j%(| j Question may be resolved like the foregoing twentyeth and twemy-second, butpjj ns avc * c as an exercise to the industrious Analyst , who, (if he thinks it to be worth^tty 0 ’) may find out 6639 Answers to it in whole numbers, (as Monsieur Backet, inh JfiicJhj f* a 8 es of his little Book before cited in Sett. 1. of this Chapter, doth affirm.
0 ^ of *h ’^' arta glia handling this very Question, ( which is the last of the seventeenthJ3 e seigf a * >art of Arithmetick,) thought it a great matter that he had found outAnswer to it in these five whole numbers, to wit, <5, 12, 34, yr, y6, andj ^, 0 ’ hat Questions of this fort could not be perfectly solved, either by the AlgebraicalTersely Cert a«n Rule; but the contents of this Chapter do manifestly shew, that theon Was in the Artist, and not in the Art.
The End of the Second BOOK.