Page:The Whetstone of Witte.djvu/58

 This table maie you extende infinitely. And these thinges maie you se, as thinges of greate admiratiō.

1. There is no diametralle nomber, but it maie be diuided by. 12. Wherfore thei be all euen nombers euenly and oddely.

2. Again, there is no diametralle nomber, but it endeth in. 0. in. 2. or in. 8.

3. Thirdely, there is no diametralle nomber, that can haue any more diameters then one.

4. Yet maie one nomber bee the diameter to diuerse other.

As you se 25. is the diameter to. 168. and also to. 300. So. 65. is the diameter to. 1008. and also to. 1500. Likewaies. 145. is the diameter to. 2448. and to 3432.

5. Fiftely: No square nomber can bee a diametralle nomber.

Scholar. These properties be notable.

But how shall I knowe, when a nomber is proponed, whether it be a diametralle nomber, or not?

Master. In that thyng I finde a tediouse trauell, by any rules, in those that write of it. But I wil ease you of moche paine therein.

Firste remember the properties of those nombers.

And if you haue any other figure in the first place, then. 0. 2. or. 8. it is no diametralle nomber.

Secondarily, if it maie not bee diuided by. 12. although it ende in one of those. 3. figures, it is no diametrall nomber.

Wherfore if it haue bothe those twoo properties (whiche an infinite multitude of nombers doe want) and be no square nomber (as none be that ende in. 2. or. 8. or with odde cyphers) then sette out all the partes of it, in soche sorte, that the lesser parte doe stande directly ouer those greater partes, which beyng multiplied together, will make the whole nomber.