One conjecture is that the proof by similar triangles involved a theory of proportions, a topic not discussed until later in the Elements, and that the theory of proportions needed further development at that time. The underlying question is why Euclid did not use this proof, but invented another. To produce a finite straight line continuously in a straight line. Euclid stated five postulates on which he based all his theorems: To draw a straight line from any point to any other. Simply stated, Euclid’s fifth postulate is: through a point not on a given line there is only one line parallel to the given line. The role of this proof in history is the subject of much speculation. Euclid believed that his axioms were self-evident statements about physical reality. In about 300 BC Euclid wrote The Elements, a book which was to become one of the most famous books ever written. Riemannian geometry, also called elliptic geometry, one of the non- Euclidean geometries that completely rejects the validity of Euclid ’s fifth postulate and modifies his second postulate. The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation: a 2 + b 2 = c 2. In Marvin Jay Greenberg’s book Euclidean and Non-Euclidean Geometries, a detailed history of the Euclidean Parallel Postulate is given, including a large portion dedicated to the many attempts to prove the fth postulate. Euclidean geometry, sometimes called parabolic geometry, is a geometry that follows a set of propositions that are based on Euclids five postulates. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |