 A detailed examination of geometry as Euclid presented it reveals a number of problems. It is worth considering these in some detail because the epistemologically convincing status of Euclid’s Elements was uncontested by almost everyone until the later decades of the 19th century. Chief among these problems are a lack of clarity in the definitions of straight line and plane, and a confusion between shortest and straightest as a, or the, fundamental geometrical property. (See the many comments collected in Heath’s edition of Euclid’s Elements.) The implications for the parallel postulate will be treated separately, see the section on   Non-Euclidean geometry.