Indian Science and Technology in the Eighteenth Century: Some Contemporary European Accounts c12.16

c12.16

The demonstration is evident to mathematicians; for as the second term’s coefficient in a general equation shows the sum of the roots, therefore in the *n* power of 1+1 where every root is unity the coefficient shows the different *ones* that can be taken in *n* things: also because the third term’s coefficient is the sum of the products of all the different twos of the roots, therefore when each root is unity the product of each two roots will be unity, and therefore the number of units or the coefficient itself shows the number of different *twos* that can be taken in *n* things. Again because the fourth term is the sum of the products of the different threes that can be taken among the roots, therefore when each root is unity, the product of each three will be unity and therefore every unit in the fourth, will show a product of three different roots, and consequently the coefficient itself shows all the different *threes* that can be taken in *n* things; and so for the rest. I should not have added this, but that I do not know well where to refer to it.