The Philosophy of Roger Bacon (c. 1270) - Page 11

finished

They have posited atoms original: "atthomum"; referring to the smallest indivisible units of matter according to Democritus, Leucippus, and Epicurus, and many others, but these would be the bodies of the world and [yet] divisible. For otherwise it would follow that the diagonal original: "diameter" would be commensurable with the side original: "coste", and not only commensurable but equal, which is found and demonstrated through the seventh [proposition] of the tenth The Latin "noni decimi" suggests nineteenth, but Euclid’s Elements contains only thirteen or fifteen books; this likely refers to Book 10, which deals with incommensurability [book] of the eloquence of Euclid. However, many foolishly say that this is not possible. Because I wish, by the grace of the letter, for many things to be plain:
it is

it is the case, however, that the knowledge of geometry excels, and therefore one who is ignorant of these things recurs to [arguments of] power or to endurance as he tries [to explain nature]. For the natural philosopher should know that he is almost everywhere ignorant or wavering [without geometry].
If a difficulty stands, it stands as a response.

note.

Compendium of Nature

Geometry

On the nature of the heavens

The Utility of Mathematics

one in another and it will penetrate the other, because a body can be in the same place.

In many mathematical matters, the whole [truth] is found in the aforementioned discovery, but it cannot be that all things are [mathematically] proven. It is proven that quantity and what they render [are continuous]. In all things, bodies are continuous unless they are [actually] non-continuous, or as much as we can place these diagonals in three or other [directions], and they require continuity or [the nature] of things; but the distances of two do not have many [parts], which are neither the smallest nor entirely [indivisible]. For if it were said that the whole is as the whole, then they would be in the same place, and the substance of one would be mixed with and would penetrate the substance of another. This is the root of the argument concerning indivisibles and utilities, and in all things, all atoms are similar, and neither [can a body be reduced] into an atom; and therefore no body
remains?? is made from an atom, because it is another thing, but if a body were to be, then it would truly be one of the six parts The "six parts" likely refers to the directions of physical extension: up, down, left, right, front, and back... only by the reason of continuity to hold one... as it was first said that Metaphysics original: "mathaphysica" [is necessary] because we cannot take away the power of unity from things, which is true, whose motion is in one and the same time. However, to say that Metaphysics and the side [of a square] through experience... and many such things exist. Likewise, then, no motion would endure
Before

unless it were motion. For a movable thing is always that which passes through an equal [space], and the measure of an atom [is such] that where they do not touch, they do not join in a parallel manner.
first

And I wish [to show] where the line of the atom fails if the world is continuous; for it is the hand which holds itself in act just as points hold themselves. Time produces in the movement of the soul original: "muiuio animae" infinite things; it produces in the movement of space where there will be infinite atoms in act. Likewise, when atoms are where they are good, they are not [indivisible] but divide themselves... for the sake of all, while the diversity is changed through them and added and widened, then with much order it happens thus.