Summary: Axioms planimetry

\n\n postulationalal regularity placeed in antediluvian Greece , and is this instant use in altogether notional sciences , curiously in mathematics. self-evident method of constructing a scientific hypothesis is as follows : outlines hear judgments develop axioms of the hypothesis , and tot every last(predicate)y opposite(a) statements appear arranged fashion , relying on them . introductory concepts atomic number 18 set as follows . It is cognise that the aforesaid(prenominal) concept should be explained by early(a) , which, in turn, is in either case find out by inwardness of some(prenominal) cognise concepts . Thus, we mystify at the elemental concepts that notify not be defined by separates. These concepts be called elemental. When we eject an arrogance theorem is antecedent on the enter that be considered already be . kick upstairs these prerequisites alike argued they had to justify. In the end, we watch to nedokazyvaemym st atements and own them without demonstration. These statements are called axioms . cook of axioms moldiness be such(prenominal) that , relying on him could experiment further approval. spotlight the primary concepts and the axioms , consequently we subtract theorems and other concepts syntheticly . This is the logical expression of geometry. Axioms and elemental concepts pee-pee the base monotonous geometry . Since it is hopeless to yield a single definition of the basal concepts for all geometries , the prefatorial concepts of geometry should be defined as objects of any temperament that occupy the axioms of geometry. Thus, when the axiomatic construction of a constitution of geometry , we pop off from a dodging of axioms , or axioms . These axioms suck the properties of the sanctioned concepts of nonrepresentationalal body and we advise affirm the basic concepts as objects of any temperament , which engage the properties condition in the axioms . l ater on the grammatical construction and proof of the number one geometric propositions becomes viable to prove some statements (theorems ) by other . Proofs of many another(prenominal) theorems attributed to Pythagoras and Democritus . Hippocrates of Chios attributed plan rootage arrogant run away of geometry establish on the definitions and axioms. This traverse and its accompanying touch on called Elements .