(7)
In this manner, whether the squares be many or few, (i. e. multiplied or divided by any number), they are reduced to a single square; and the same is done with the roots, which are their equivalents; that is to say, they are reduced in the same proportion as the squares. . As to the case in which squares are equal fo numbers; for instance, you say, “a square is equal to nine ;”* then this is a square, and its rootis three. Or “ five squares are equal to cighty ;”+ then one square is cqual to one-fifth of eighty, which is sixteen. Or “the half of the square is equal to eighteen ;”} then the square is thirty-six, and its root is six,
Thus, all squares, multiples, and sub-multiples of them, are reduced to a single square. Ifthere be only part of a square, you add thereto, until there is a whole square; you do the same with the equivalent in numbers.
As to the case in which roots are equal to numbers ; for instance, * one root equals three in number ;§ then the root is three, and iis square nine. Or “ four roots are equal to twenty ;”|| then one root is equal te five, and the square to be formed of it is twenty-five. Or ‘thalf the root is equal to ten; then the
- go 23
F 5e?=80., Paha 16 c= 185, 22=96 », #—6 § t=3 i 4r=20 “. £5 q Z=10 “. @=20
(5)
