together, and thei will make. 25. whose roote, beyng 5. is the diameter of that platte forme.
Scholar. That doe I perceiue well, bicause it is confirmed by the. 33. theoreme of the pathewaie.
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Master. Yet take an other example. In this platte forme of. 60. you see the one side to bee. 5. and the other side to bee 12. Now take the square nomber of. 12. whiche is. 144. and the square of. 5. whiche is. 25. and put them together: so will it make 169. whiche is a square nomber: and hath. 13. for his roote.
Likewaies. 120. is to be accoumpted a diametralle nomber. For so muche as it hath twoo partes: that is 8. and. 15. whiche beeyng multiplied together, doe make the firste nomber. 120. And the square of those twoo partes (that is. 64. for. 8: and. 225. for. 15.) beyng bothe added together, doe make. 289. whiche is a square nōber: and hath for his roote. 17. And therfore that. 17. is the diameter to that diametralle nomber. 120.
Like examples infinite might I giue you. But these for explication of the name, maie suffice.
Scholar. I doe well vnderstande the examples: saue that I knowe not how to find the roote of the laste square nomber, whiche amounteth by the addition of the former twoo squares together.
Master. That arte will I teche you anon. But we maie not forgette first to ende all the difinitions of soche names, as I minde to write of.
Like flattes. Whereof yet there resteth like flattes: which maie bee as well taken for trianguler figures. as for quadrate figures.
So that of any of them, when the sides of one platforme, beareth like proportion together, as the sidesof
