The Philosophy of Roger Bacon

...concerning potentiality and pure act, which are truly in God. For anything that exists according to potentiality Latin: potentia; the capacity for something to happen or be divided, as opposed to actus, the state of it actually being so is truly no actual proposition; and they say the same who claim that a body is absolutely divided according to all its points. For every single division is possible, and what is more, one is prepared before another.
possible

And because it is possible—since potentiality can exist where lines are raised—and because any other division is possible in the same way, a man can see from this that every contingent thing is true. It is impossible [to say the body is already divided] because, although each single division is possible, yet in the manner described, one is not possible simultaneously with another. Since it is not truly "nothing," it occurs to contingent things that a division at point a does not contradict a division at point b, nor at point c, and so on for any given point. But to grant that all these divisions exist simultaneously is daily proven false. Therefore, it seems that such a [simultaneous] state is not possible. And even if this is a subtle sophism A "sophism" in scholastic logic is a clever but potentially misleading argument used to test the limits of a definition, it can be solved: although the division at point a does not contradict the division at point b, nor the division at a specifically designated point a, yet a division at point a is repugnant to a division at every point indistinctly. These points, if taken together, would destroy infinite quantity... until those points existing at a distance in actuality cannot be taken or designated simultaneously.

Furthermore, another position seems to build up proofs which they commonly use regarding the incommensurability and equality
potentiality of

of the side and the diagonal The "side and diagonal" of a square were a standard medieval proof against the idea that lines are made of finite points; if they were, the diagonal and the side would have a common measure, which geometry proves they do not. For they do not indicate equality in their words because they claim there are degrees [of magnitude], and that these do not belong to the lines in the whole space
to this

nor do they have their parts from any other source but from themselves. And because the demonstration depends on the induction of the supposition that the lines occupy the whole space in which the diagonals stood... it would follow that the act would be equal in the number of lines... and through the indifference and density of these parts of the diagonal, there is no impediment... so that a full account might be required. Nevertheless, so that the natural philosopher might see more purely what

The Utility
of Mathematics
Truly
namely

can be deduced by mathematics itself, as much in the result as in the process, I shall touch upon these things at least to show them. For from the corollary of the proposition which is called the 6th of the [First] Element referring to Euclid’s Elements, the foundational textbook of geometry in the Middle Ages, it is clear that a line drawn from a right angle to the base of a triangle is a mean proportional between the segments of the base...