6. _All straight angles are equal._ It is possible to prove this, and therefore, from the standpoint of strict logic, it is unnecessary as a postulate. On the other hand, it is poor educational policy for a beginner to attempt to prove a thing that is so obvious. The attempt leads to a loss of interest in the subject, the proposition being (to state a paradox) hard because it is so easy. It is, of course, possible to postulate that straight angles are equal, and to draw the conclusion that their halves (right angles) are equal; or to proceed in the opposite direction, and postulate that all right angles are equal, and draw the conclusion that their doubles (straight angles) are equal. Of the two the former has the advantage, since it is probably more obvious that all straight angles are equal. It is well to state the following definite corollaries to this postulate: (1) _All right angles are equal_; (2) _From a point in a line only one perpendicular can be drawn to the line_, since two perpendiculars would make the whole (right angle) equal to its part; (3) _Equal angles have equal complements, equal supplements, and equal conjugates_; (4) _The greater of two angles has the less complement, the less supplement, and the less conjugate._ All of these four might appear as propositions, but, as already stated, they are so obvious as to be more harmful than useful to beginners when given in such form. The postulate of parallels may properly appear in connection with that topic in Book I, and it is accordingly treated in Chapter XIV. There is also another assumption that some writers are now trying to formulate in a simple fashion. We take, for example, a line segment _AB_, and describe circles with _A_ and _B_ respectively as centers, and with a radius _AB_. We say that the circles will intersect as at _C_ and _D_. But how do we know that they intersect? We assume it, just as we assume that an indefinite straight line drawn from a point inclosed by a circle will, if produced far enough, cut the circle twice. Of course a pupil would not think of this if his attention was not called to it, and the harm outweighs the good in doing this with one who is beginning the study of geometry. With axioms and with postulates, therefore, the conclusion is the same: from the standpoint of scientific geometry there is an irreducible minimum of assumptions, but from the standpoint of practical teaching this list should give place to a working set of axioms and postulates that meet the needs of the beginner.