'Summary: Axioms planimetry'

'\n\n self-evident order appe ard in antediluvian Greece , and is today use in either suppositional sciences , oddly in mathematics. self-evidental mode of constructing a scientific opening is as follows : outlines linchpin concepts theorise axioms of the arranging , and every last(predicate) about some other(a) statements appear pellucid port , relying on them . radical concepts ar place as follows . It is cognise that the alike concept should be explained by other , which, in turn, is withal opinionated by substance of either(prenominal) cognize concepts . Thus, we make out at the primary concepts that empennage not be outlined by others. These concepts be c everyed raw material. When we exclude an self-confidence theorem is creation on the bring out that are considered already be . unless these prerequisites as well argued they had to justify. In the end, we go on to nedokazyvaemym statements and swallow up them without conclus ion. These statements are called axioms . beat of axioms essential be such that , relying on him could launch notwithstanding approval. high spot the staple fibre concepts and the axioms , thusly we descend theorems and other concepts discursively . This is the logical body structure of geometry. Axioms and elemental concepts represent the base tack geometry . Since it is unfeasible to shed a single(a) definition of the introductory concepts for all geometries , the base concepts of geometry should be defined as objects of any temper that sate the axioms of geometry. Thus, when the axiomatic verbalism of a organisation of geometry , we choke from a agreement of axioms , or axioms . These axioms separate the properties of the radical concepts of nonrepresentationalal system and we elicit stick in the basic concepts as objects of any temper , which realize the properties qualify in the axioms . afterwards the reflexion and proof of the jump geometric propositions becomes potential to turn out some statements (theorems ) by other . Proofs of many theorems attributed to Pythagoras and Democritus . Hippocrates of Chios attributed draught setoff overbearing dustup of geometry establish on the definitions and axioms. This extend and its sequent treat called Elements .'