Book 13
4
And just as it is true to say generally of the other sciences that they deal with a particular subject—not with that which is accidental to it (e.g. not with white if the healthy is white, and the subject of the science is the healthy), but with that which is the subject of the particular science; with the healthy if it treats of things qua healthy, and with man if qua man—so this is also true of geometry. If the things of which it treats are accidentally sensible although it does not treat of them qua sensible, it does not follow that the mathematical sciences treat of sensible things—nor, on the other hand, that they treat of other things which exist independently apart from these.
5
Many attributes are essential properties of things as possessing a particular characteristic; e.g., there are attributes peculiar to an animal qua female or qua male, although there is no such thing as female or male in separation from animals. Hence there are also attributes which are peculiar to things merely qua lines or planes.
6
And in proportion as the things which we are considering are prior in formula and simpler, they admit of greater exactness; for simplicity implies exactness. Hence we find greater exactness where there is no magnitude, and the greatest exactness where there is no motion; or if motion is involved, where it is primary, because this is the simplest kind; and the simplest kind of primary motion is uniform motion.Aristot. Met. 12.7.6.
7
The same principle applies to both harmonics and optics, for neither of these sciences studies objects qua sight or qua sound, but qua lines and numbersOptics studies lines and harmonics numbers because these sciences are subordinate to geometry and arithmetic (Aristot. An. Post. 75b 15).; yet the latter are affections peculiar to the former. The same is also true of mechanics.
