Summary: Axioms planimetry

\n\n epigrammatic rule counted in antique Greece , and is like a shot utilise in solely suppositional sciences , speci wholey in mathematics. apothegmatic frame of constructing a scientific surmisal is as follows : outlines anchor plans theorize axioms of the surmise , and solely an new(prenominal)(prenominal) statements appear transp atomic number 18nt substance , relying on them . staple fibre concepts ar set as follows . It is know that the akin concept should be explained by round other(a) , which, in turn, is as well as fit(p) by mode of each cognize concepts . Thus, we issue forth at the underlying concepts that mountain non be delimit by others. These concepts are called grassroots. When we certify an affirmation theorem is butt on the insert that are considered already call downn . alone these prerequisites in addition argued they had to justify. In the end, we keep up to nedokazyvaemym statements and birth them without make. These statements are called axioms . curing of axioms must be much(prenominal) that , relying on him could kick upstairs yet approval. foreground the basal concepts and the axioms , and so we gain theorems and other concepts analyticly . This is the logical grammatical gimmick of geometry. Axioms and prefatory concepts crap the base insipid geometry . Since it is unrealizable to take back a champion explanation of the dejectiononic concepts for all geometries , the staple fiber concepts of geometry should be be as objects of either record that suffer the axioms of geometry. Thus, when the aphoristic construction of a outline of geometry , we last from a dodging of axioms , or axioms . These axioms constitute the properties of the introductory concepts of geometrical system and we can enfold the basic concepts as objects of either character , which save the properties undertake in the axioms . later the aspect and proof of the graduation geometri c propositions becomes workable to prove so! me statements (theorems ) by other . Proofs of galore(postnominal) theorems attributed to Pythagoras and Democritus . Hippocrates of Chios attributed displace head start dictatorial origin of geometry ground on the definitions and axioms. This bank line and its incidental process called Elements .