Page:The Whetstone of Witte.djvu/70

 ber, and alwaies shall bee so: yet is it not accepted as a like flatte, onles it bee referred to some other square nomber.

Scholar. What if it be compared with. 12. which you named before to be a like flatte?

Master. You remember: one of Euclide his rules (whiche I repeated before) is, that like flattes beeyng multiplied together, will make a square nōber. And sodoeth not. 12. beyng multiplied by. 4.

Scholar. Now I doe vnderstande your woordes better. So. 3. and. 8. compared together, bee not like flattes: yet echo of them compared to other nombers, maie be like flattes. As. 3. compared to. 12. or to. 27: and 8. compared to. 18. or to. 50.

Master. Now will we lette these like flattes alone for a tyme: And intreate more of rooted nōbers. And first I will tell you somewhat of the names and natures of soche nombers as haue rootes: Then secondarily I will teache you the order to extract their rootes: And afterwarde will I shewe some parte of the vse of theim.

Wherfore to begin, where we lefte a litle before, the explicatiō of rootes: I saie, that the roote of nomber, is a nomber also: and is of soche sorte, that by sondrie multiplications of it, by it self, or by the nomber resultyng thereof, it doeth produce that nōber, whose rooeroote [sic] it is. And accordyng to the nomber of times that it is multiplied, the nomber that resulteth thereof, taketh his name.

So that one multiplication maketh a square nomber And twoo multiplications doe make a Cubike nomber.

Likewaies. 3. multiplications, doe giue a square of squares. And. 4. multiplications doe yelde a sursolide.

And so infinitely.

For as multiplication hath no ende, so the nombers amountyng to them be innumerable, and their