HADRIAN. Your answer leaves me in ignorance.
SAPIENTIA. That is not surprising, since not one number, but many, come under this definition.
HADRIAN. Explain more clearly, otherwise how can I follow you?
SAPIENTIA. Charity has now completed two olympiads, Hope two lustres, and Faith three olympiads.
HADRIAN. I am curious to know why the number "8," which is two olympiads, and the number "10," which is two lustres, are called "diminished"; also why the number "12," which is made up of three olympiads, is said to be "augmented."
SAPIENTIA, Every number is said to be "diminished" the parts of which when added together give a sum which is less than the number of which they are parts. Such a number is 8. For the half of 8 is 4, the quarter of 8 is 2, and the eighth of 8 is 1 ; and these added together give 7. It is the same with 10. Its half is 5, its fifth part 2, its tenth part 1, and these added together give 8. On the other hand, a number is said to be "augmented" when its parts added together exceed it. Such, for instance, is 12. Its half is 6, its third 4, its fourth 3, its sixth 2, its twelfth 1, and the sum of these figures 16. And in accordance with the principle which decrees that between all excesses shall rule the exquisite proportion of the mean, that number is called "perfect" the sum of the parts of which is equal to its whole. Such a number is 6, whose parts—a third, a half, and a sixth—
