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Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had ...
Optics (Greek: Ὀπτικά) is a work on the geometry of vision written by the Greek mathematician Euclid around 300 BC. The earliest surviving manuscript of Optics is in Greek and dates from the 10th century AD. The work deals almost entirely with the geometry of vision, with little reference to either the physical or psychological aspects ...
The Elements (Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean ...
The early writers discussed here treated vision more as a geometrical than as a physical, physiological, or psychological problem. The first known author of a treatise on geometrical optics was the geometer Euclid (c. 325 BC–265 BC). Euclid began his study of optics as he began his study of geometry, with a set of self-evident axioms.
Ptolemy also presents a theory of vision. In his view, rays (or flux) are emitted from the eye. The rays are sensitive, and convey information back to the observer's intellect about the distance and orientation of surfaces. Size and shape were determined by the visual angle subtended at the eye combined with perceived distance and orientation.
Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie [1][2][3][4] (tr. The Foundations of Geometry) as the foundation for a modern treatment of Euclidean geometry. Other well-known modern axiomatizations of Euclidean geometry are those of Alfred Tarski and of George Birkhoff.
In geometry, the parallel postulate, also called Euclid 's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right ...
Theon of Alexandria (/ ˌθiːən, - ɒn /; Ancient Greek: Θέων ὁ Ἀλεξανδρεύς; c. AD 335 – c. 405) was a Greek [1] scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid 's Elements and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.