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
Elements of Algebra Elements of Algebra Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler and originally published in 1770 in German. "Elements of Algebra" is one of the earliest books to set out algebra in the modern form we would recognize today (another early book being "Elements of Algebra" by Nicholas Saunderson, published in 1740), and is one of Euler's few writings, along with "Letters to a German Princess", that are accessible to the general public. Written in numbered paragraphs as was common practice till the 19th century, "Elements" begins with the definition of mathematics and builds on