and diuided by. 4. doe make. 4. and. 25. as their quotiente, and thei be like flattes.
Scholar. And in these I see an other straunge worke: that if those twoo like flattes bee multiplied together: thei will make the greater square, of whiche thei came.
For. 3. tymes. 12. maketh. 36: and. 7. tymes. 28. giueth. 196: And so. 4. tymes. 25. bryngeth forthe. 100.
Master. It doeth so happen often times: but it is not alwaies so.
For if you diuide. 16. and. 100. by. 2. the quotientes will be. 8. and. 50. whiche twoo nombers multiplied together, doe make. 400. farre differyng from. 100. So. 36. and. 196. beyng bothe square nombers, and diuided by. 2. doe make. 18. and. 98. whiche be like flattes: and those like flattes multiplied together, doe yelde 1764. whiche is a square nomber, but it is. 9. tymes so greate as is. 196.
Scholar. Yet one doubte I haue: whether all square nombers be like flattes, and so bee not distincte from them?
For although in the giuision of figuralle nombers you did distincte them, yet in the examples of like flattes, you put certain square nombers emongest other.
Master. All square nombers are like flattes, eyng compared together: and els not. For as any. 2. square nombers maie be compared together: so maie thei be referred to their rootes, without comparison together. Or els thei maie be compared to other nombers that bee not square.
Therfore marke these two rules well. that no one nomber can bee called a like flatte: but in comparison to some other. For. 2. by hymself is not called a like flatte, excepte he bee compared to. 8. or to. 18. other to 32. or. 50. or some other soche.
So likewaies. 4. whiche by nature is a square nō-ber,
