A Treatise os Algebra. 165

20/ + fg 1S X 20; + a sgt +

thus 2°/ r ^Py'p|' +

3X20/+/^

+ ✓»/+

12, and ^Z/ 2 + £ 2 +

c/£ 2 + * ;

+&+/'+*' *

f'~g x *s/s‘

+/ 2 -^

1 /x—Ft

which Equations, if f be assumed — 5, and F = 4, will

be reduced to 5.6462+ .0104.5 x 361 + 40/+ 6.3245+ .63241= 12, and 6.4031 + .7811 + .625/ +

20 + 5, + 4, x .3333 — .18521 + .1482/ = 13 ;whence 1.0081 + .4181= .0293, and 1.591 — 5.255 1= .0698: Therefore, in this Cafe, A = 1.008, B =

0.4x8, Q_= .0293, a =1.59, b — — 5.255 Snd q

.0698 ; consequently 1 ^

A q — aQ\

= —.0040; therefore * = 5.0305 and

SECT. XIII.

Os indeterminate or unlimited Problems.Problem is said to be indeterminate, or unlimited,

s~\_ when the Number of Equations, expressing theConditions thereof, is less than that of the unknownQuantities ; such Kind of Problems, strictly speaking,being capable of innumerable Answers : But the Answersin whole Numbers, to which the Question is commonlyrestrained, are, for the general Part, limited to a deter-minate Number ; for the more ready discovering ofwhich, I shall subjoin the following

M 3

LEMMA.