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side is not a ratio according to the habitat/custom of number to number. I prove this assumption
thus […] This example is famous in philosophy, and therefore I pursue its exposition further. 405
Bradwardine does not turn to this geometric example to teach a concept or to prove a theorem.
No, he uses this example because it is clearly exemplary—because it has a tradition “in
philosophia” ‘in philosophy’ based upon a “habitudinem numeri ad numerum” ‘the habit of
number to number.’ Bradwardine’s proof does not further his own arguments or help him clarify
a point; rather, it strictly is a way to situate his own thinking in a wider Latinate tradition of
Aristotelian refutation and thought.
Like Bradwardine, Trevisa devotes so much time in proving something that at first sight
may seem counterintuitive and tangential simply because he is following a traditional repetition
of this example. Therefore, just as Bradwardine ends his proof as “hoc probo quoniam proportio
lateris quadrati ad dyametrum non est sicut proportio numeri ad numerum” ‘therefore here I
prove that the proportion of the side of a square to its diameter as such is not a proportion of
number to number,’ Trevisa ends his gloss as “and it may not be knowe in nombrarie in what
proporcioun þe dyameter is longere þan costa.” Both mathematician and translator explain a
seemingly tangential discussion because they seek to situate the habitat of their language in
Latinate tradition and not because they wish to express a concept.
Further, despite having a broader vocabulary to speak about proportions and numbers in
terms of integers, whole numbers, rational numbers, etc. and despite addressing a learned
audience, Bradwardine concludes his geometric proof with the ambiguous Latin term
“numerum” ‘number.’ He does so not because his audience would not know that “numerum”
could also refer to irrational “numeri” but because this proof was traditionally referred to in this
manner. Similarly, Trevisa does not translate “incomensurabile” as “imeete” because he finds it
405 Thomas Bradwardine, Geometria Speculativa, Trans. George Molland (Stuttgart: Franz Steiner,
1989) 100-103. My translation.
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