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 with Tarquin Publications published a digitized copy based on Hewlett's translation of the first four sections (or Part I) of the book. In 2015, Scott Hecht published both print and Kindle versions of "Elements of Algebra" () with Euler's Part I (Containing the Analysis of Determinate Quantities), Part II (Containing the Analysis of Indeterminate Quantities), Lagrange's Additions, and footnotes by Johann Bernoulli and others. 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