Page:The Whetstone of Witte.djvu/45

 it: whiche you should vse in this case.

Scholar. Will not any twoo soche partes serue, whiche by multiplication will make the whole nomber?

Master. You maie by the former examples, easily se the contrary. For 12 is a diametrall nomber: and hath these partes (as it is sone perciued). 2. 3. 4. 6. Yet if you take. 2. and. 6. for the sides of it, thei will not make a diameter in knowen nomber.

Scholar. That I vnderstande: for the square of 2. beyng. 4. added to. 26. whiche is the square of 6. doeth make. 40. whose roote must bee greater then. 6. and lesse then. 7. And therfore. 40. can haue no roote in whole nomber.

Master. Neither yet in broken nombers: for that is a generalle rule: that if any whole nomber haue a roote, that roote shall be a whole nomber. So that if the roote can not bee founde in whole nomber: you shall neuer finde it in broken nombers.

And for more certaintie of that I saied before, that all partes be not apte for the sides of a diametralle nomber, to finde out the diameter: merke well the seconde example, whiche is. 60. and hath these partes.

2. 3. 4. 5. 6. 10. 12. 15. 20. 30.

So that beginnyng with the two extremeste, that is. 2. and. 30. thei will by multiplication make. 60.

And likewaies any two nombers, equally distant from those extremes: As. 3. and 20. Likewaies. 4. and 15: other. 5. and. 12. And in like maner. 6. and. 10. All those couples by multiplication doe make. 60. Yet none of them are apte sides to finde the diameter by, but onely 5 and. 12. For of the other sides beyng multiplied squarely (that is by thē selfes) and those squares beyng added together, there wil not rise a square nomber. As you shall better vnderstande, when you