Page:The Whetstone of Witte.djvu/40

 ber: to bee suche a number, as beeyng diuided by his roote, shall haue for the quotiente the square of the same roote.

Scholar. Hereby I perceiue, that one multiplication, of any number by it selfe, doeth make a square number. And twoo multiplications in that sorte, doe make a Cubike number.

What if I doe multiplie any number thrise, or fower tymes, or oftener in that sorte, are there proper names for suche numbers?

Master. Yes in deede: as I will declare anon.

But firste before we attempt to the other sounde nōbers, it shall bee mete, that we doe declare those twoo sortes of flatte numbers, whiche I named before: that is diametralle numbers, and like flattes.

A Diametralle nomber, is suche a number as hath twoo partes of that nature: that if thei bee multiplied together, thei will make the saied diametralle nomber: And the squares of those twoo partes, beeyng added together, will make a square nōber also:

whose roote is the diameter of that diametralle nomber.

As 12 is named a diametralle nomber, for that he hath twoo partes, that is. 3. and. 4, whiche beeynd multiplied together, doe make 12. that is the firste number. And if their squares be added together, thei wil make a thirde square: and the roote of that number will bee the diameter to that platte forme of 12. As in this example you see.

The one side is. 4. and the other side is 3 whiche bothe multiplied together, doe make 12. Then take the square of fower whiche is 15 and the square of. 3, whiche is. 9. and put them