Chapter 10
I call those principles in each genus, the existence of which it is impossible to demonstrate. What then first things, and such as result from these signify, is assumed, but as to principles, we must assume that they are, but demonstrate the rest, as what unity is, or what the straight and a triangle are; it is necessary however to assume that unity and magnitude exist, but to demonstrate the other things.
Of those which are employed in demonstrative sciences, some are peculiar to each science, but others are common, and common according to analogy, since each is useful, so far as it is in the genus under science. The peculiar indeed are such as, that a line is a thing of this kind, and that the straight is, but the common are, as that if equals be taken from equals the remainders are equal. Now each of these is sufficient, so far as it is in the genus, for (a geometrician) will effect the same, though he should not assume of all, but in magnitudes alone, and the arithmetician in respect of numbers (alone).
Proper principles, again, are those which are assumed to be, and about which science considers whatever are inherent per se, as arithmetic assumes unities, and geometry points and lines, for they assume that these are, and that they are this particular thing. But the essential properties of these, what each signifies, they assume, as arithmetic, what the odd is, or the even, or a square, or a cube; and geometry,
