The first diuision
of nombers.
Master. Nomber is diuided into diuerse kindes, for some are whole nombers, and thei onely of Euclide, Boetius, and other good writers are called nombers. Other are broken nombers, and are commonly called fractions. Of these bothe I haue written in the firste and seconde partes of Arithmetike: So that I mighte seme to curiouse, to repete any parte of it again.
The second diuision
of nombers.
But now in eche kinde of these, there are certaine nombers named Abstracte: and other called nombers Contracte.
Abstracte. Abstracte nombers are those, whiche haue no denomination annexed vnto them. Contracte. And those that haue any denomination ioyned to theim, are called Contracte nombers.
Scholar. This I see to be a reasonable distinctiō, and agreable to the signification of the names.
For as that nomber is cōtracte, from his generall libertie of signification, which is boūde to one denomination, as in saiying .10. grotes (where .10. is restrained frō the libertie of valowyng any other thing but grotes) so if it had no denomination adioined, it might then signifie the nomber of daies, or of miles, or any like thyng, as well as of grotes. For when I saie .10. and doe not limitte any denominatiō, then is that. 10. abstracte and seuered frō all specialities, and standeth free to any name of thing.
whether broken nombers
be contracte, or not.
But this (me thinketh vnder your correction) can not extend to broken nombers: whiche euermore carry with them their denominacion: seyng thei consiste of a numerator and a denominator.
Master. You seme to saie well. And the like iudgemēte doeth appere to be in some writers of this arte. But yet seyng that fractions maie haue all other artificiall denominations, that whole nombers maie receiue: and maie also bee without them: therefore must wee either make a more curiouse distinction ofthat
