Note 602 — Chapter XXV

Few books of arithmetic, or even algebra, as far as I know, draw the reader’s attention at the outset to this essential distinction between discrete and continuous quantity, which is sure to be overlooked in all their subsequent reasonings. Wallis has done it very well; after stating very clearly that there are no proper numbers but integers he meets the objection, that fractions are called intermediate numbers. Concedo quidem sic responderi posse; concedo etiam numeros quos fractos vocant, sive fractiones, esse quidam uni et nulli quasi intermedios. Sed addo, quod jam transitur εις αλλο γενος. Respondetur enim non de quot, sed de quanto. Pertinet igitur hæc responsio propriè loquendo, non tam ad quantitatem discretam, seu numerum, quam ad continuam; prout hora supponitur esse quid continuum in partes divisibile, quamvis quidem harum partium ad totum ratio numeris exprimatur. Mathesis Universalis, c. 1.