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On The Heavens   


again destroyed. This had been asserted in the first instance by

Hesiod and his followers, but afterwards outside his circle by the

earliest natural philosophers. But what these thinkers maintained

was that all else has been generated and, as they said, 'is flowing

away, nothing having any solidity, except one single thing which

persists as the basis of all these transformations. So we may

interpret the statements of Heraclitus of Ephesus and many others. And

some subject all bodies whatever to generation, by means of the

composition and separation of planes.

Discussion of the other views may be postponed. But this last theory

which composes every body of planes is, as the most superficial

observation shows, in many respects in plain contradiction with

mathematics. It is, however, wrong to remove the foundations of a

science unless you can replace them with others more convincing.

And, secondly, the same theory which composes solids of planes clearly

composes planes of lines and lines of points, so that a part of a line

need not be a line. This matter has been already considered in our

discussion of movement, where we have shown that an indivisible length

is impossible. But with respect to natural bodies there are

impossibilities involved in the view which asserts indivisible

lines, which we may briefly consider at this point. For the impossible

consequences which result from this view in the mathematical sphere

will reproduce themselves when it is applied to physical bodies, but

there will be difficulties in physics which are not present in

mathematics; for mathematics deals with an abstract and physics with a

more concrete object. There are many attributes necessarily present in

physical bodies which are necessarily excluded by indivisibility;

all attributes, in fact, which are divisible. There can be nothing

divisible in an indivisible thing, but the attributes of bodies are

all divisible in one of two ways. They are divisible into kinds, as

colour is divided into white and black, and they are divisible per

accidens when that which has them is divisible. In this latter sense

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