Page:The Whetstone of Witte.djvu/68

 reth to an other.

This maie you proue by any of the former examples. For. 12. to. 3. is in like proportion, as. 16. to. 4. or. 36. to. 9.

Also. 27. to. 3. hath like proportion as. 36. to. 4: or 144. to. 16. other. 81. to. 9.

And father, if you deuide the one of theim by the other, the quotiente will be a square nomber.

Scholar. That doeth appeare euidentely at the firste vewe.

For. 12. diuided by. 3. doeth make. 4. And. 75. diuided by. 3. giueth. 25.

So. 52. by. 6. maketh. 9. And. 72. by. 2. yeldeth. 36. And so I see in the reste, that all the quotientes will be square nombers.

But I desire moche to knowe, how those nombers be produced. For that I knowe not yet.

Master. Take any twoo square nombers, what so euer thei bee, and multiplie them by any one nomber, that you liste: and thei will make. 2. like flattes.

So. 4. and. 9. multiplied by. 2. doe make. 8. and. 18: whiche bee like flattes.

Again, if you multiplied them by. 5. thei make. 20. and. 45. whiche be also like flattes.

Scholar. I am perfect inough in this, if that be al.

Master. An other waie you maie make them also: If you take any twoo square nombers, that will admitte one diuisor, and diuide them bothe by it.

As for example. Seyng 9. and. 36. will be bothe diuided by. 3. I doe so diuide theim: and their quotientes are. 3. and. 12. whiche are diametralle nombers.

So in like maner, if I diuide 196 and 49 (whiche bothe are square nombers) by. 7. the quotientes will be 28. and. 7.

Again, 16. and. 100. beyng bothe square nombers