Page:The Whetstone of Witte.djvu/23

 halues, that is into 15. And that. 14. into. 7. whiche is the halfe of. 14. but is an odde nomber.

Scholar. This I perceiue well. And, as I iudge, the distinction into those. 3. kindes, is not onely reasonable, but also nedefull. And yet you seme to speake doubtfully, of this laste membre. Bicause I remember not that you vse this worde commōly, but where you giue place rather to custome, then to reason.

Master. Or els to custome of the common sorte of writers, rather then to the iudgemente of the moste aunciente writers.

And so in this case Euclide doeth not seme to admitte this thirde member. But accompteth it vnder the seconde kinde. As maie well appeare in his. 9. boke, and 34. proposition, where he calleth suche a nomber, euenly euen, and euenly odde also, whiche place cōferred with the definitions in the same booke, doeth approue in many wise mennes opinions, that Euclide minded but 2. onely kindes of those nōbers. And yet in this thing (I thinke) he did rather approue. 3. varieties by his propositiōs, then establishe onely. 2. sortes by his first definitions.

But herein I will spende no more tyme. But saie briefly that the distinciō of. 3. kindes, serueth to good vse, and ease in teachyng.

And now for farther knowledge of nombers, some are called nombers perfecte, & some are nombers imperfect.

Perfecte nombers are suche ones, whose partes ioyned together, will make exactly the whole nomber.

And therfore are. 6. and. 28. accompted perfect nōbers: bicause the partes of eche of theim added together, doe make the ful and intere nomber, whose partes thei bee. As of. 6. the halfe is. 3. the thirde parte is 2. the sixte parte is. 1. As for a quarter, and fifte parte it hath not in whole nomber. Now put together. 1. 2. and. 3. and thei make iuste. 6. whose partes thei bee.