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On The Heavens   

Book I


THE science which has to do with nature clearly concerns itself

for the most part with bodies and magnitudes and their properties

and movements, but also with the principles of this sort of substance,

as many as they may be. For of things constituted by nature some are

bodies and magnitudes, some possess body and magnitude, and some are

principles of things which possess these. Now a continuum is that

which is divisible into parts always capable of subdivision, and a

body is that which is every way divisible. A magnitude if divisible

one way is a line, if two ways a surface, and if three a body.

Beyond these there is no other magnitude, because the three dimensions

are all that there are, and that which is divisible in three

directions is divisible in all. For, as the Pythagoreans say, the

world and all that is in it is determined by the number three, since

beginning and middle and end give the number of an 'all', and the

number they give is the triad. And so, having taken these three from

nature as (so to speak) laws of it, we make further use of the

number three in the worship of the Gods. Further, we use the terms

in practice in this way. Of two things, or men, we say 'both', but not

'all': three is the first number to which the term 'all' has been

appropriated. And in this, as we have said, we do but follow the

lead which nature gives. Therefore, since 'every' and 'all' and

'complete' do not differ from one another in respect of form, but

only, if at all, in their matter and in that to which they are

applied, body alone among magnitudes can be complete. For it alone

is determined by the three dimensions, that is, is an 'all'. But if it

is divisible in three dimensions it is every way divisible, while

the other magnitudes are divisible in one dimension or in two alone:

for the divisibility and continuity of magnitudes depend upon the

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