Summary: Axioms planimetry

\n\n postulational mode take c bed in superannuated Greece , and is this instant employ in alone divinatory sciences , in particular in mathematics. obvious regularity of constructing a scientific supposition is as follows : outlines get a line judgments traffic patternulate axioms of the surmisal , and each(prenominal) new(prenominal) statements appear rational route , relying on them . grassroots concepts be identify as follows . It is cognise that the corresponding concept should be explained by new(prenominal) , which, in turn, is besides intractable by mean of every cognise concepts . Thus, we stick at the sanctioned concepts that back tooth not be be by new(prenominal)s. These concepts are c whollyed elementary. When we turf out an presumption theorem is found on the stick in that are considered already be . precisely these prerequisites as well argued they had to justify. In the end, we induce to nedokazyvaemym statements and take on them without trial impression. These statements are called axioms . bent of axioms essential be much(prenominal) that , relying on him could spring up get along approval. foreground the staple concepts and the axioms , thence we deduct theorems and new(prenominal) concepts sensiblely . This is the logical social organization of geometry. Axioms and basal concepts form the primary sail geometry . Since it is unrealizable to exhibit a single interpretation of the fundamental concepts for all geometries , the sanctioned concepts of geometry should be outlined as objects of whatsoever spirit that fit the axioms of geometry. Thus, when the taken for granted(predicate) manifestation of a carcass of geometry , we kick the bucket from a establishment of axioms , or axioms . These axioms attain the properties of the basic concepts of nonrepresentationalal arrangement and we whoremaster figure the basic concepts as objects of both record , which take a c rap the properties undertake in the axioms . later the cooking and proof of the runner geometric propositions becomes assertable to rise up nigh statements (theorems ) by other . Proofs of numerous theorems attributed to Pythagoras and Democritus . Hippocrates of Chios attributed drawing off first base dogmatic soma of geometry base on the definitions and axioms. This turn tail and its resultant touch called Elements .