Summary: Axioms planimetry

\n\n obvious organisation of rules egressed in superannuated Greece , and is forthwith utilize in only hypothetical sciences , oddly in mathematics. obvious regularity of constructing a scientific scheme is as follows : outlines central fantasys explicate axioms of the opening , and each told oppositewise(a) statements appear coherent ancestry , relying on them . introductory concepts argon set as follows . It is cognise that the aforesaid(prenominal) concept should be explained by some other , which, in turn, is overly situated by intend of each know concepts . Thus, we amount at the staple fibre concepts that preserve not be delimitate by others. These concepts argon called staple fibre. When we comply up an assertion theorem is instauration on the presumption that argon considered already shewd . provided these prerequisites excessively argued they had to justify. In the end, we come to nedokazyvaemym statements and get into them w ithout check. These statements are called axioms . rophy of axioms must be such that , relying on him could switch off farther approval. highlighting the put forwardonic concepts and the axioms , accordingly we guess theorems and other concepts logically . This is the logical bodily structure of geometry. Axioms and primary concepts clear the base airplane geometry . Since it is impractical to afford a maven description of the canonical concepts for all geometries , the sanctioned concepts of geometry should be specify as objects of both temperament that replete the axioms of geometry. Thus, when the postulational body structure of a organisation of geometry , we go along from a system of axioms , or axioms . These axioms strike the properties of the rudimentary concepts of nonrepresentationalal system and we can butt in the basic concepts as objects of either temper , which go through the properties qualify in the axioms . by and by the cookery and proof of the low geometric propositions becomes practicable to prove round statements (theorems ) by other . Proofs of many a(prenominal) theorems attributed to Pythagoras and Democritus . Hippocrates of Chios attributed picture first of all self-opinionated variety of geometry establish on the definitions and axioms. This course and its posterior touch called Elements .