Pagina 372 di 1391

The terms used in the statement of the problem may be explained

as follows. A perfect number (Greek), as already stated, is one

which is equal to the sum of its divisors. Thus 6, which is the

first perfect or cyclical number, = 1 + 2 + 3. The words (Greek),

'terms' or 'notes,' and (Greek), 'intervals,' are applicable to

music as well as to number and figure. (Greek) is the 'base' on

which the whole calculation depends, or the 'lowest term' from

which it can be worked out. The words (Greek) have been variously

translated-'squared and cubed' (Donaldson), 'equalling and

equalled in power' (Weber), 'by involution and evolution,' i.e.

by raising the power and extracting the root (as in the

translation). Numbers are called 'like and unlike' (Greek) when

the factors or the sides of the planes and cubes which they

represent are or are not in the same ratio: e.g. 8 and 27 = 2

cubed and 3 cubed; and conversely.