Page:The Whetstone of Witte.djvu/59

 And then examine those partes, whiche seme to haue any likelihood: accordyng to the former doctrine.

As for example: if. 72. be proponed to be examined in that sorte, I sette his partes in order thus.

Nowbeit I neded not to set doune. 2. nother. 4. for leser partes, nother those other greater partes, that aunswere to them: For, as I said before, thei can not bee the lesser side in any diametralle nomber. Wherefore thei nede no examination.

Fathermore, for them that you shall nede to examine, if the lesser nomber bee an odde nomber, the square of it must contain double to that greater nomber (that is coupled with it) and one more.

And if the lesser be an euen nomber (of them twoo that you would examine) then must the square of it containe the greater nomber (that standeth by it). 4. tymes, and. 4. ore. And this is not onely a shorter waie, then I see to be taughte by other artes menne: but it is also more certaine, for all nombers not compounded of other diametralle nombers.

Scholar. By this doctrine it appeareth quickely, that. 72. is no diametrall nomber.

For although it doeth ende in. 2. and maie bee diuided by. 12. yet no couple of nombers here haue those properties that is required.

For vnder. 3. is. 24. whiche is to greate: and vnder 6. there is. 12. whiche is to greate also.

But vnder. 8. standeth. 9: whiche is to litle, by a greate deale.

Master. Then proue in this other nomber. 132.

Scholar. His partes will stande thus.