After a short historical sketch of the development of non-euclidean geometries, the author proceeds to the critical examination of some recent work tending to prove that non-euclidean geometrical ideas are already to be found in some ancient Greek philosophers, Aristotle alludes to in several places of his works. Before to proceed to a closer examination of Aristotle’s texts about infinity and parallelism, some important euclidean definitions are recalled. Special emphasis is given to Aristotle’s p. 281 b2 (in Bekker’s numbering) considered by the criticized authors as an important theorem of non-euclidean geometry and incommensurability simultaneously. A related scholium to the ‘Elements’ of Euclid is also criticized and proved to be corrupted; a correct version is proposed. In a first conclusion, the author points out that the mentioned text is not a single theorem but two different and independent ones. Another set of more recent Greek texts relating more ancient criticisms of euclidean geometry, is also discussed at some length and judged irrelevant. The overall conclusion is that there is no evidence in more or less ancient Greek texts as to the possible existence of non-euclidean geometries before Euclid and claims there upon are mainly due to a misinterpretation of the existent testimonies. In an appendix some euclidean definitions are briefly discussed. Especially Proclos interpretation of the definition of the straight line is considered as the good one.