Page:The Whetstone of Witte.djvu/46

 haue learned to knowe square nombers, by extractiō of their rootes.

Yet in the meane ceason I will set forthe certaine notes, to knowe the diameter, and the apte sides, in all diametralle nombers.

1. And firste I saie: that as thei are three nombers in all (I meane the twoo sides, and the diameter) so all waies if the firste or leaste side bee odde, then shall there be twoo of them odde nombers. And the diameter shall euer bee the other of the odde nombers: that is to saie, the greateste of them.

2. Secondarily. It is true that all diametrall nombers are euen nombers. And no odde nomber can bee a diametralle nomber.

3. Thirdly. I saie, that all odde nombers aboue one, maie be the lesser side in soche diametralle nombers.

But euen nombers doe not serue so generally: for thei onely maie stand in soche place, whiche be greater then. 4: As. 6. 8. 10. 12. 14. 16. 18. 20. &c. And none other euen nombers then soche as maie be diuided by 4. maie be the greater side in any diametralle nomber.

4. Fourthly. If the lesser side bee an odde nomber, then ordinarily, the square of it is iuste equalle with that that amounteth by the addition of the diameter, to the greater nomber. As in the firste example, 3. is the lesser nomber, and. 4. is the greater: vnto them bothe the diameter is. 5. Now. 3. hath for his square 9. and so moche is made by the addition of. 4. and. 5.

Again in the seconde example, the lesser nomber is 5. and his square is 25. The greater nomber is 12, and the diameter. 13. Put. 12. and. 13. together, and thei make. 25. whiche is equalle with the square of the lesser.

Likewaies. 7. and 24. multiplied together maketh 168. whiche is a diametralle nomber. And bicause the square of the lesser side (whiche here is. 49.) must bee