Note 3 — Chapter XXII

Pure number is ἀριθμὸς μοναδικός: applied number is αριθμὸς φυσικὸς or σωματικός. Aristotle, Metaph. N. 5, speaks of αριθμὸς πύρινος ἤ γήϊνος. But this is only Greek idiom: as we say 'Greek history' instead of 'History of Greece:' or vice versa, when we translate Populus Romanus by 'people of Rome.' Aristotle is speaking of 'proportions' or 'amounts' of fire or earth in the compounds of these elements.