Initial initial concepts of arithmetics and geometry cannot be defined in the classical way (i.e. are brought under wider generic term with the instruction on specific distinguish because there are no broader fundamental categories of mathematical character. For this reason of definition of a point, a straight line and other initial concepts are given by Euclid at the intuitive level and at the further proof of theorems actually were not used. A geometrical point (according to Euclid) it that has no parts; the line has no thickness, it is a trace of a moving point; the plane – result of the movement of a straight line, etc. However, and much later many scientists were compelled to give definition of initial mathematical concepts at the intuitive level.
The quantity is and external, both internal, and various in objects, similar on quality, and, at the same time, similar in things, various on the quality. It is such definiteness of subjects, phenomena which characterizes their size, a form, intensity of properties, rates of development, etc.