multiplied by the same nomber again, whiche thei do containe (other els twise by their rootes) will make the whole greater squares.
And by this figuryng of theim, there doeth appere no inconuenience nor absurditie, in their vulgar names: but rather a iuste expressyng of their naturalle formes.
For in the first figure. 2. standyng as the side of the lesser square, and multiplied by it self, doeth make. 4. whiche is the quantitie of the lesser square. Then if I multiply that lesser square. 4: by his owne nomber, it maketh 16. whiche is the greate and whole square: and is a Square of squares.
So in the seconde figure. 3. standeth for the roote of the lesser square, contained within the pricked lines, and if it bee multiplied by it self, it maketh. 9. whiche is the quantitie of the same lesser square. Then if I multiplie that. 9. by it self, it will make. 81. whiche is the quantitie of the great Square, and is a Square of squares.
Master. I commende you well: not onely for so diligente excusyng of theim, whiche for their honeste trauell, deserue moche thankes, but also for that you seke to bryng manifest reason, and some shewe, at the least, of linearie demonstration for your purpose. So that you will not seme to speake, without some good grounde.
But as in deede, your figure doeth truely xpresse a square of squares, so it doeth suppose the other nomber, whiche by order of multiplication, doeth go next before it, to be a flatte nomber also. For it is not possible that a sounde nomber (as a Cube is alwaies) beyng multiplied by any other nomber, maie lose the nature of a sounde nomber: But shall continue a sounde nomber still. And therfore seeyng the nexte nomber, before a Square of squares was a Cube, it is notpossible
