Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/292

 the multiple is consequent to the most rapid proportion, and the most rapid proportion to fire in motion. Sometimes it does not happen that a conclusion is made from the assumptions, and sometimes it happens, but is not perceived: if however it were impossible to demonstrate the true from the false, it would be easy to resolve, for (the terms) would be necessarily converted. Thus let A exist, and this existing, these things also exist[,] the existence of which I know, as B, from these[,] then I will demonstrate that that exists. What pertain however to mathematics, are rather converted, because they take nothing accidental, (and in this they differ from dialectical subjects,) but definitions. Yet they are increased, not through media, but through additional assumption, as A of B, this of C, this again of D, and so on to infinity. Also transversely, as A both of C and of E, as there is a number so great or even infinite, which is A, an odd number so great B, and an odd number C. A then is (true) of C, and the even is a number so great D, the even number is E, wherefore A is (true) of E.

Chapter 13
there is a difference between knowing that a thing is, and why it is, first in the same