The Philosophy of Roger Bacon

...can be described as joined, because none of them implies the greatest distance; therefore it is clear concerning the arc, namely that when two are joined to one another, all things which are separated by a measure of distance are determined by a single straight path between them—a reasoning which considers distance solely according to a straight path. If, however, in one quantity, one thing is continued so that there is no distance except by reason of these terms The author is distinguishing between the "distance" measured as a straight line and the "path" traveled along a curve., then it is distance. Therefore, in the motion of an arc, two terms can be bounded in this way: as one that is at the end. For instance, the motion from e to f by reason of the arc is equal to the motion from f to e. All such arcs—or at least the motion along the semicircle a-b-e-f—is equal to the motion along the joined semicircle a-b-f-b. And if there were another semicircle a-b-f-b, it would be different than it was before; yet one arc is nevertheless equal to the motion along the same [path], just as the motion or the arc is equal

to the motion of the other, and so with the others. And thus always one is equal to the other, because in distance the whole is considered by reason of these equalities; and therefore, since it is so for every arc of the same kind, if motion along one arc from one term to another is given, it is equal to the motion or arc from the term from which this would be made along the same arc. Furthermore, the reasoning of the distances of these [points] will suffice for the quantity of motion or the arc. Then, indeed, the distance and the quantity of motions are the same according to the arc or diameter containing them, according to these distances and those universally placed between them. Furthermore, as it is said in the Metaphysics original: "metaph^ice"; referring to Aristotle's "Metaphysics.", Book 10 The text says "vi" (6), but the margin and the content suggest Book 10 (X), where Aristotle discusses "The One" and opposites., that

a plurality of the one is distinguished by the same distance, which is also in time.

Contrariety In medieval logic, "contraries" are the most extreme opposites within a single genus, like hot and cold in the genus of temperature. Bacon is using this to determine if circular motions can be "opposite" to each other. is a certain division, and of one division there are two primary extremes. Therefore, it is said that contraries are two primary extremes; thus, when they are at the [limit], they are the two extremes. Indeed, it is said that one quantity according to one division—if indeed this is a gradual division—can represent distance only, or it can represent an arc. But it is not according to the arc, because there are many of them. Therefore, it represents distance, since that one [distance] is the only one between these two extremes. Furthermore, let two equidistant lines parallel lines be drawn from the diameter; and so it proceeds as is necessary to demonstrate in geometry and in natural things: that the space between equidistant lines is such that only distance is there, which is neither bent nor curved. Therefore, the distance between two internal terms ought not to be quantified by the same.

A simple geometric sketch appears in the right margin, consisting of a horizontal line with three vertical tick marks and a diagonal line forming a shallow angle at the right-hand end.