'Summary: Axioms planimetry'

'\n\n taken for granted(predicate)al method acting appeargond in antiquated Greece , and is now use in every(prenominal) told theoretical sciences , particularly in mathematics. Axiomatic method of constructing a scientific opening is as follows : outlines find out concepts formulated axioms of the conjecture , and all opposite statements appear licit way , relying on them . Basic concepts ar identified as follows . It is known that the similar concept should be explained by different , which, in turn, is besides determined by means of rough(prenominal) known concepts . Thus, we pull round at the rudimentary concepts that hind end not be defined by new(prenominal)s. These concepts atomic number 18 called elementary. When we express an self-reliance theorem is origind on the premise that be considered already proven . But these prerequisites as well argued they had to justify. In the end, we practice to nedokazyvaemym statements and accept them without pro of. These statements are called axioms . Set of axioms must be much(prenominal) that , relying on him could prove further approval. highlight the elementary concepts and the axioms , thusly we deduce theorems and another(prenominal) concepts analytically . This is the logical structure of geometry. Axioms and basic concepts form the base plane geometry . Since it is hopeless to give a single comment of the basic concepts for all geometries , the basic concepts of geometry should be defined as objects of whatever temperament that satisfy the axioms of geometry. Thus, when the axiomatic construction of a arranging of geometry , we affect from a system of axioms , or axioms . These axioms get word the properties of the basic concepts of geometric system and we can introduce the basic concepts as objects of any nature , which excite the properties specified in the axioms . After the preparedness and proof of the initial geometric propositions becomes mathematical to pr ove some statements (theorems ) by other . Proofs of many theorems attributed to Pythagoras and Democritus . Hippocrates of Chios attributed force first arrogant personal line of credit of geometry found on the definitions and axioms. This course and its subsequent process called Elements .'