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2. Hilbert's axioms - Wikipedia

   en.wikipedia.org/wiki/Hilbert's_axioms

   To a system of points, straight lines, and planes, it is impossible to add other elements in such a manner that the system thus generalized shall form a new geometry obeying all of the five groups of axioms. In other words, the elements of geometry form a system which is not susceptible of extension, if we regard the five groups of axioms as valid.

3. Parallel postulate - Wikipedia

   en.wikipedia.org/wiki/Parallel_postulate

   A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry. Geometry that is independent of Euclid's fifth postulate (i.e., only assumes the modern equivalent of the first four postulates) is known as absolute geometry (or sometimes "neutral geometry").

4. Foundations of geometry - Wikipedia

   en.wikipedia.org/wiki/Foundations_of_geometry

   Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.

5. Geometry - Wikipedia

   en.wikipedia.org/wiki/Geometry

   Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, [a] which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental ...

6. Playfair's axiom - Wikipedia

   en.wikipedia.org/wiki/Playfair's_axiom

   Antecedent of Playfair's axiom: a line and a point not on the line Consequent of Playfair's axiom: a second line, parallel to the first, passing through the point. In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate):

7. Exclusive: Quizlet acquires Slader as it aims to become the ...

   www.aol.com/news/quizlet-schools-reopening...

   The go-to learning portal for high school and college students is bulking up its curriculum. Quizlet, best known for its flashcards and study tools, is acquiring education tech platform Slader ...

8. Parallel (geometry) - Wikipedia

   en.wikipedia.org/wiki/Parallel_(geometry)

   The corresponding angles formed by a transversal property, used by W. D. Cooley in his 1860 text, The Elements of Geometry, simplified and explained requires a proof of the fact that if one transversal meets a pair of lines in congruent corresponding angles then all transversals must do so. Again, a new axiom is needed to justify this statement.

9. AOL Mail

   mail.aol.com/d?reason=invalid_cred

   Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!