IND 
IND , 
stag the salvation of those who differ from 
them in most of their articles of belief. A 
spirit which seems to be a natural effect of 
the creed of the Geneva Reformer. See 
Bkownists and Presbyterians. 
INDETERMINATE, in general, an ap- 
pellation given to whatever is not certain, 
fixed, and limited ; in which sense it is the 
same with indefinite. 
Indeterminate problem, is that which 
admits of many different solutions and an- 
swers, called also an unlimited problem. In 
questions of this kind the number of un- 
known quantities concerned is greater than 
the number of the conditions and equations 
by which they are .to be found ; from which 
it happens that generally some other con- 
ditions or quantities are assumed to supply 
the defect, which being taken at pleasure, 
give the same number of answers as varie- 
ties in those assumptions. If, for instance, 
it were required to find the value of two 
square numbers, whose difference is equal 
to a, a given quantity. Here if x 2 and y 1 
denote the squares then a: 2 — y 2 = a:, which 
is only one equation for finding two quan- 
tities. Now by assuming some other un- 
known quantity as z so that zri + V = 
the sum of the roots ; then is x- — ~^ g f or 
2 z 
x 1 — y 2 — a 
x 2 -J- 2 x y -f- y 2 — z 2 
2 X 1 2 x y — a 
x = z 2 -f- a z 2 -J- a 
2x-j-2i / ~ 2 s. 
And by the same mode y t?, which 
Z 
are the two roots having the difference 
of their squares equal to a given quantity 
o, and are expressed by means of an as- 
sumed quantity z; so that there will be 
as many answers to the question, as there 
can be taken values of the indeterminate 
quantity z. 
Mr. Leslie, in the transactions of the 
Royal Society of Edinburgh, has given a 
paper on this subject, the object of which 
is to resolve the complicated expressions 
which we obtain in the solution of indeter- 
minate problems, into simple equations, and 
this is done by means of a principle', which, 
though extremely simple, admits of a very 
extensive application. Let A x B be any 
compound quantity equal to another, 
C x D, and let m be any rational number 
assumed at pleasure ; it is manifest that, 
taking equimultiples, A x m B = C x m D.’ 
If, therefore, we suppose that A = m D, it 
must follow that m B = C, or B z= — • 
T’! m 
■Thus two equations of a lower dimension 
are obtained. If these be capable of fur- 
ther decomposition, we may assume the 
multiples n and p, and form four equations 
still more simple. By the repeated appli- 
cation ot this principle, an higher equation 
admitting of divisors, will be resolved into 
those of the first order, the number of 
which will be one greater than that of the 
multiples assumed. For example, resum- 
ing the problem at first given, viz. to find 
two rational numbers, the difference of 
the squares of which shall be a given num- 
ber. Let the given number be the product 
of a and b ; then by hypothesis, x 2 — if 
= ab-, but these compound quantities ad- 
roit °f an easy resolution, for x -|_ y x 
x — y = a X b. If therefore we suppose 
x + V = ™ «, we shall obtain x — v = ~ 
m 
where m is arbitrary, and if rational, x and 
y must also be rational. Hence the reso- 
lution of these two equations gives the 
values ot x and y, the numbers sought, in 
terms of m, viz. x = — ? ~H ~, and y ~ 
2 in J 
m 2 a — b 
2 m 
INDEX, in anatomy, the same with the 
fore finger. See Fingers. 
Index, in arithmetic and algebra,, shows 
to what power any quantity is involved, and 
is otherwise called exponent. See Expo- 
nent. 
Index of a logarithm, that which shows 
of how many places the absolute number, 
belonging to a logarithm, doth consist ; and 
of what nature it is, whether an integer or 
fraction. Thus, in this logarithm 2.523421, 
the number 2 standing on the left hand of 
the point is called the index; because it 
shows that the absolute number, answering 
to the above logarithm, consists of three 
places : for the number is always one more 
than the index. If the absolute number be 
a fi action, then the index of the logarithm 
hath a negative sign, marked thus 2 . 523421 . 
See Logarithm. 
Index of a globe, the little style or gno- 
mon, which being fixed on the pole of the 
globe, and turning round with it, points 
out the hours upon the hour circle. See 
Globe. 
INDIA rubber. See Coutchouc. 
INDICATIVE, in grammar, the first 
mood, or manner, of conjugating a verb, by 
