AXIOM (Gk. 6.;:iwpa, axiOnia, that which is thought worthy, fit, self-evident). A general statement, the truth of which is accepted without proof. Plato probably limited it to geometric propositions, but Aristotle applied it to state ments of a more general nature. Euclid fol lowed Aristotle's use of the term, regarding axioms as 'common notions' not limited to geometry, and applying the term postulate to a premise specifically geometric in character. The early English translators of Euclid failed to consult the most trustworthy sources, and hence the terms axiom, and postulate have come to be confused. Heiberg, the latest and best editor of the Elements, has made clear the distinction which Euclid recognized, and has shown that he gave five axioms and five postulates. Euclid re garded as an axiom that, equals be added to equals, the sums are equal:" as a postulate that (stated in simpler language than his), "Through a given point only one line can be drawn paral lel to a given line." The first statement is general, the second is specifically geometric. Mathematicians formerly sought to limit the list of axioms and postulates to the smallest num ber upon which the subject in question, as geome try, could be built; the modern tendency is rather to seek a list, however extended, of the really independent properties of space. To the followers of Kant seems due the common defini tion of axiom as 'a self-evident truth,' a defini tion no longer recognized as valid. See A Paroni and GEOMETRY.
AXIS (Lat. axis, axle). In mathematics. a line of reference called by various names, ac cording to its different uses. In geometry, a line which bisects at right angles the lines joining corresponding points in symmetric systems is called an axis of symmetry; e.g. the altitude of an isosceles triangle. An axis of a geometric solid is a diameter about which the points of the solid are symmetrically distributed; e.g. the di ameters of spheres and ellipsoids. Axes of co ordinates are the lines of reference from which the coordinates are measured. ( See ANALYTIC GEOMETRY.) The radical axis of two circles is the line joining their points of intersection; the line is real, even when the circles cut in imag inary points. The transrcrse axis of a conic is
the diameter which passes through the foci. The conjugate axis is the line through the origin per pendicular to the transverse axis.
In physics. the optic axis of a lens is the straight line passing through its optical centre and perpendicular to its surfaces. The axis of a trleseope is the straight line joining the centres of its lenses (objective and ocular). The axis of rotation is a straight line which remains at rest while a body rotates around it, as the line joining the poles of the earth.
AXIS (Lat., of unknown origin). A species of deer (('errus axis) abundant throughout India and in many islands of the Eastern Archipelago. One of its Indian names is chittra, and by Brit ish sportsmen in India it is generally called the spotted hog-deer. It was known to the ancients as axis. The axis resembles in size and color the European fallow-deer; it. is generally of a rich fawn color, beautifully spotted with white, nearly black along the back, the under parts snow-white. The horns are slender, sharp-pointed, little branched, and not at all palmated. The female has no horns. The axis frequents thick jungles in the vicinity of water, and feeds during the night. It is commonly found in herds of 15 or 20, of which three or four are males. Its sense of smell is remarkably acute, and it is generally very shy and timid, so that sportsmen find it difficult to get within shot. The male, however, sometimes exhibits great courage in defense of the young. It is very easily domes ticated, is gentle in its manners, and breeds freely in captivity, so that it is commonly seen in zoological parks. See colored plate of DEER.
In architecture, axis is either the temporary central line used in making drawings or the imaginary central line of a building. Sometimes buildings have a curved axis, sometimes several have a common axis. The relation of the axis of neighboring monumental structures has al ways been a matter of careful study in architec tural history.