bers Abstracte.
Odde nōbers Compounde. Now to speake of odde nombers, some of thē are compounde, & some vncompoūde. Thei are compounde, whiche maie bee diuided into any other partes than vnities. As. 9. whiche is cōpounde of. 3. And. 15. that is made of. 5. and. 3. Also. 21. is compounde of. 7. and. 3. And so furthe. But. 3. 5. 7. 11. 13. 17. 19. 23. 29. and suche like, bee odde nombers vncompounde. Vncompoūe. For thei are not made of any other then of vnities.
Here must you vnderstande by composition, the multiplication of the partes of nombers together, as you remembre, before was declared.
Scholar. I consider it so. And I remembre all that you haue taught me, for the diuisiō of nōbers abstracte and absolute. Nombers Relatiue. What saie you now of nōbers relatiue?
Master. Some tymes their relation hath regarde to their partes, namely, whether these. 2. that bee so compared, haue any common parte, that will diuide them bothe. For if thei haue so, then are thei called nombers commensurable. Commensurable. As. 12. and. 21. bee nombers commensurable: for. 3. will diuide eche of theim.
Likewaies. 20. and. 36. be cōmmensurable, seyng 4. is a commoō diuisor for theim bothe. But if thei haue no suche common diuisor, then are thei called incommensurable. Incommensurable. As 18 and 25. For 25 can bee diuided by no nomber more then by. 5. And. 18. can not be diuided by it.
In like maner. 36. and. 49. are incommensurable: For 49. hath no diuisor but. 7. And 7. can not diuide. 36.
Scholar. Doe you meane then, that incommensurable nombers, haue no cōparison nor proportion together?
Master. Naie, nothyng lesse. For any. 2. nombers maie haue comparison & proportion together, although thei be incommensurable. As. 3. and. 4. are incommensurable, and yet are thei in a proportion together: as shall appeare anon.
But first I will declare vnto you, the varieties ofproportion
