lesselesser nomber diametralle, and. 15. and. 26. for the sides of the greater nomber: As the lesser nomber shall bee 12. so the greater must be. 540. that is. 45. tymes. 12.
For. 15. vnto. 3. is in a quintuple proportion, and is written thus. 5⁄1: and. 36. vnto 4 is a noncuple proportion, and is written thus 9⁄1. Now if you multiplie these nombers together, thei will make 45: whiche declareth the proportions of the twoo diametralle nombers. And so of all the reste, as you maie easily consider.
Scholar. I praie you, let me examine one or twoo of thē, in comparison to that firste diametrall nomber. 12.
I see that 15 beyng the lesser side, and 20. the greater side, doe make. 300. as their diametralle nomber: and that. 300. is. 25. tymes so moche as. 12. is. Therfore by your saiyng the proportion of 15. to. 3. and of. 20. to 4. must make. 25. And so it doeth. For eche of them is a quintuple proportion. And it is quickely gessed, that 5. multiplied by. 5. doeth make. 25.
For father proofe, I take the diametralle nomber 1680. whose sides are. 15. and. 112. First I see, that. 15. to. 3. beareth a quintuple proportion: and. 112. to. 4. is as. 28. to. 1. Therfore I multiplie. 28. by. 5. and it maketh. 140. Then if I multiplie that nomber by. 12. it will make. 1680.
This is a sufficiente trialle for these nombers.
Of euen sides. But of soche diametralle nombers, as haue euen nombers for their lesser side, you haue giuen no rule, nother examples, saue onely of. 8. wherfore I praie you tell me, how shall I finde out the diametralle nomber, with his other side, and the diameter in soche euen nombers.
Master. You shall make it square, as you did in the other nombers, that wer odde: And of that square you shall take twoo quarters, whiche you shall alter in soche sorte, that you shall abate. 1. frō the one quarter, and put it to the other quarter. And so haue youtwoo
