Non-Euclidean geometry that are both perpendicular to a third line: Euclidean geometry, named after the Greek mathematician Euclid, includes some of the oldest known mathematics, and geometries that deviated from this were not widely accepted as legitimate until the 19th century. The debate that eventually led to the discovery of the non-Euclidean geometries began almost as soon as Euclid's work "Elements" was written. In the "Elements", Euclid began with a limited number of assumptions (23 definitions, five common notions, and five postulates) and sought to prove all the other results (propositions) in the work. The most notorious of the postulates is often
The Crown of Ptolemy The Crown of Ptolemy The Crown of Ptolemy is the third and last book in the "Percy Jackson and the Olympians" and "The Kane Chronicles" crossover series. It was released in the back of the paperback version of "The House of Hades" on March 31, 2015, and later as an ebook and audiobook. The ebook edition was released May 12, 2015. On January 15, 2015, Rick Riordan announced a third crossover story titled "The Crown of Ptolemy" on his Twitter account. His announcement included the fact that the short story would be first published in the paperback version of "The