TRACT 33,

HISTORY OR ALGEBRA.

ISS

binations of that thing. Multiply this quotient by the 2dterm of the first line, and divide the product by the numberwhich is opposite to it in the second line, the- quotient willbe the number of combinations of that thing. Again, mul-tiply this quotient by the 3d term, and divide by that whichis below it, and so on. Then add together whatever is thusobtained below each term, the sum will be the amount of allthe combinations of these things.”

Such is their manner of expressing all their algebraicrules, in words at length, which sometimes, in complexcases, makes them difficult to follow, and easily mistaken.Whereas the same rule is soon comprehended at sight, when.expressed in our own convenient mode and notation ; as in

the present case, x x ~~ x Scc, denotes the

combinations of any number (w) of things, taken two bytwo, three by three, four by four, &c, the series beingcontinued to as many factors as there are things to be com-bined. The translation then continues in the following ex-ample : —

Example. “ The six-flavoured, Called in Hindu , KkutPus, contains, 1st a sweet, 2d a salt, 3d a sour, 4th a soft,5th a bitter, 6th a sharp : I would know the number of dif-ferent mixtures which may be had by adding these together.Write them thus:

{i

= is,

6 5 4 3 22 3 4 5 615 x 2

3 j ; then y = 6, = 15,

15x4

20 ,

20 x S4

6 ,

6 x 1

5 ’ 6

pf mixtures then of 6 things is 63,”

1, the sum is 63. The number

Progressions.

“ Of numbers increasing. This may be of several kinds.First, with the number 1, that is, when each term exceedsthe preceding by 1. The way to find the sum to any num-ber is ; add 1 to that number, and multiply by half thatnumber. To find the sum of the terms arising from thecontinued addition of the former terms; add 2 to the num-