Content of type 'section'
Ancient Extensions of the Theory of Book X
From the hints given by the author of the commentary found in Arabic by Woepcke (cf. pp. 3—4 above) it would seem probable that Apollonius’ extensions of the theory of irrationals took two directions : (1) generalising the medial straight line of Euclid, and (2) forming compound irrationals by the addition and subtraction of more than two terms of the sort composing the binomials, apotomes, etc. The commentator writes (Woepcke’s article, pp. 694 sqq.) :