Page:The Whetstone of Witte.djvu/67

 proportion betwene other twoo nombers, those twoo are like flattes.

That is to saie: if any twoo nombers, beyng mulpliedmultiplied [sic] together, doe make a square nomber (for none but soche can haue a middle nomber betwene theim) then are thei like flattes.

As. 3. and. 12. multiplied together doe make. 36. whiche is a square nomber: and. 6. therby appeareth to bee the middell nomber betwene theim. And therfore are. 3. and. 12. like flattes.

Likewaies. 3. and. 27. for thei make. 81. whiche is a square: and their middle nomber is. 9.

And so are. 2. and. 8: 2. and. 18: 2. and. 50. 2. & .72 3. and. 48: 3. and. 75: 4. and. 9. 4. and. 16: 4. and 25. 5. and. 20. 5. and 45: 6. and. 24: 6. and. 54.

And so of infinite other.

This exposition is confirmed by the firste and seconde proposition of the nineth boke of Euclide, where he saieth thus.

If twoo nombers beyng like flattes, bee multiplied together, the nomber that thei make, shall be a square nomber.

And if. 2. nombers beyng multiplied together, do make a square nōber, then are thei like flattes.

By whiche rules it doeth appere, that you cā hanehaue [sic] no progressiō Geometricalle, but it must be made either of square nombers, or els of like flattes, wherby there appeareth a greate agreablenes, betwene like flattes and square nombers. And therfore saieth Euclide also in the. 26. proposition of the eight booke.

Nombers that bee like flattes, haue soche proportion together, as one square nomber bea-