Euclid's parallel postulate

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• Parallel postulate — In geometry, the parallel postulate, also called Euclid s fifth postulate since it is the fifth postulate in Euclid s Elements , is a distinctive axiom in what is now called Euclidean geometry. It states that: If a line segment intersects two… …   Wikipedia

• parallel postulate — Geom. the axiom in Euclidean geometry that only one line can be drawn through a given point so that the line is parallel to a given line that does not contain the point. Also called parallel axiom. * * * One of the five postulates, or axioms, of… …   Universalium

• Schopenhauer's criticism of the proofs of the parallel postulate — Arthur Schopenhauer criticized mathematicians attempts to prove Euclid s Parallel Postulate because they try to prove from indirect concepts that which is directly evident from perception. Throughout his writings [ I wanted in this way to stress… …   Wikipedia

• Euclid's Elements — (Greek: polytonic|Στοιχεῖα) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions… …   Wikipedia

• Parallel (geometry) — Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid s… …   Wikipedia

• parallel axiom — noun only one line can be drawn through a point parallel to another line • Syn: ↑Euclid s fifth axiom • Hypernyms: ↑Euclid s axiom, ↑Euclid s postulate, ↑Euclidean axiom * * * noun : parallel postul …   Useful english dictionary

• Euclid's axiom — noun (mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry • Syn: ↑Euclid s postulate, ↑Euclidean axiom • Topics: ↑mathematics, ↑math, ↑maths …   Useful english dictionary

• Euclid's postulate — noun (mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry • Syn: ↑Euclid s axiom, ↑Euclidean axiom • Topics: ↑mathematics, ↑math, ↑maths • …   Useful english dictionary

• Euclid's fifth axiom — noun only one line can be drawn through a point parallel to another line • Syn: ↑parallel axiom • Hypernyms: ↑Euclid s axiom, ↑Euclid s postulate, ↑Euclidean axiom …   Useful english dictionary

• mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

• Non-Euclidean geometry — Behavior of lines with a common perpendicular in each of the three types of geometry Non Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate,… …   Wikipedia