[24] There is some reason to think that the Pythagoreans distinguished between discrete and continuous quantity. G. J. Allman, in his _Greek Geometry from Thales to Euclid_, says (p. 23): "The Pythagoreans made a fourfold division of mathematical science, attributing one of its parts to the how many, τὸ πόσον, and the other to the how much, τὸ πηλίκον; and they assigned to each of these parts a twofold division. For they said that discrete quantity, or the _how many_, either subsists by itself or must be considered with relation to some other; but that continued quantity, or the _how much_, is either stable or in motion. Hence they affirmed that arithmetic contemplates that discrete quantity which subsists by itself, but music that which is related to another; and that geometry considers continued quantity so far as it is immovable; but astronomy (τὴν σφαιρικήν) contemplates continued quantity so far as it is of a self-motive nature. (Proclus, ed. Friedlein, p. 35. As to the distinction between τὸ πηλίκον, continuous, and τὸ πόσον, discrete quantity, see Iambl., _in Nicomachi Geraseni Arithmeticam introductionem_, ed. Tennulius, p. 148.)" _Cf._ p. 48. [25] Referred to by Burnet, _op. cit._, p. 120. [26] iv., 6. 213b, 22; H. Ritter and L. Preller, _Historia Philosophiæ Græcæ_, 8th ed., Gotha, 1898, p. 75 (this work will be referred to in future as "R. P."). This seems to imply that they regarded matter as consisting of atoms with empty space in between. But if so, they must have thought space could be studied by only paying attention to the atoms, for otherwise it would be hard to account for their arithmetical methods in geometry, or for their statement that "things are numbers."