Page:The Whetstone of Witte.djvu/55

 twoo nombers, differyng onely by. 2. and bothe beyng odde. The lesser of them twoo, is the greater side of the diametralle nomber: and the other is the diameter to it. As. 8. beyng your lesser side, the square of it is 64. whose quarter is. 16. from whiche I abate. 1. and there resteth. 15. and that is the seconde side. Also I adde 1. to 16. and it maketh. 17: whiche is the diameter.

Scholar. This is no thyng harde. As by example I will proue. IF. 12. bee the lesser side: his square is 144. and the quarter of it is. 36. Then abatyng. 1. I see there will bee. 35. for the other side of teh diametralle nomber. And addyng. 1. to. 36. it maketh. 37. to be the diameter. And if I multiplie. 35. by. 12. it bryngeth forthe. 420. whiche is the diametralle nomber.

Now for proofe of these nombers, I multiplie. 12. by it self, and it maketh. 144. Then I multiplie the other side, that is. 35. by it self, and it yeldeth. 1225. Those bothe together doe make. 1369. And seyng 37 multiplied by it selfe, doeth make the same nomber. Therfore are thei all true nombers.

An other example. 10. beyng set for the lesser side, I doe multiplie it squarely: and there riseth. 100. whose quarter is. 25. For whiche I take (as you taught me). 24. and. 26. And so the whole diametralle nomber is. 240. For proofe of the other nombers, I take. 100. whiche commeth of. 10. multiplied square, and to it I adde. 576. whiche is the square to. 24. and their bothe doe make. 676. And so muche amounteth by the multiplication of. 26. squarely.

Master. This maie suffice for this presente: if you marke that the euē nombers haue not onely one generalle forme, whiche I did expresse in the former rule, but also soche as be compounde of any other nōbers, euen or odde: Haue the like nombers in proportion, for the greater side, and for their diameter as the nombers haue, of whiche thei bee compounde. And