any thing by demonstration simply, but by hypothesis.
Logically then from these things a person may believe about what has been said, but analytically it is more concisely manifest thus, that there cannot be infinite predicates in demonstrative sciences, the subject of the present treatise, either in an ascending or descending series. For demonstration is of such things as are essentially present with things, essentially in two ways, both such as are in them in respect of what a thing is, and those in which the things themselves are inherent in respect of what a thing is, thus the odd in number which indeed is inherent in number, but number itself is inherent in the definition of it, again also, multitude or the divisible is inherent in the definition of number. Still neither of these can be infinites, nor as the odd is predicated of number, for again there will be something else in the odd, in which being inherent, (the odd) would be inherent, and if this be so, number will be first inherent in those things which are inherent in it. If then such infinites cannot be inherent in the one, neither will there be infinites in ascending series. Still it is necessary that all should be inherent in the first, for example, in number, and number in them, so that they will reciprocate, but not be more widely extensive. Neither are those infinite which are inherent in the definition of a thing, for if they were, we could not define, so that if all predicates are predicated per se, and these are not infinite, things in an upward progression will stop, wherefore also those which descend.
