Editing History of geometry (section)

====Euclid====
[[Image:EuclidStatueOxford.jpg|thumb|Statue of Euclid in the [[Oxford University Museum of Natural History]]]]

[[Image:Woman teaching geometry.jpg|thumb|''Woman teaching geometry''. Illustration at the beginning of a medieval translation of Euclid's [[Element (mathematics)|Elements]] (c. 1310)]]
<!--[[Image:Title page of Sir Henry Billingsley's first English version of Euclid's Elements, 1570 (560x900).jpg|right|200px|thumb|The [[frontispiece]] of Sir Henry Billingsley's first English version of Euclid's ''Elements'', 1570]]-->
[[Euclid]] (c. 325–265 BC), of [[Alexandria]], probably a student at the Academy founded by Plato, wrote a treatise in 13 books (chapters), titled ''[[Euclid's Elements|The Elements of Geometry]]'', in which he presented geometry in an ideal [[axiom]]atic form, which came to be known as [[Euclidean geometry]]. The treatise is not a compendium of all that the [[Hellenistic]] mathematicians knew at the time about geometry; Euclid himself wrote eight more advanced books on geometry. We know from other references that Euclid's was not the first elementary geometry textbook, but it was so much superior that the others fell into disuse and were lost. He was brought to the university at Alexandria by [[Ptolemy I Soter|Ptolemy I]], King of Egypt.

''The Elements'' began with definitions of terms, fundamental geometric principles (called ''axioms'' or ''postulates''), and general quantitative principles (called ''common notions'') from which all the rest of geometry could be logically deduced. Following are his five axioms, somewhat paraphrased to make the English easier to read.

# Any two points can be joined by a straight line.
# Any finite straight line can be extended in a straight line.
# A circle can be drawn with any center and any radius.
# All right angles are equal to each other.
# If two straight lines in a plane are crossed by another straight line (called the transversal), and the interior angles between the two lines and the transversal lying on one side of the transversal add up to less than two right angles, then on that side of the transversal, the two lines extended will intersect (also called the [[parallel postulate]]).

Concepts, that are now understood as [[algebra]], were expressed geometrically by Euclid, a method referred to as [[Greek geometric algebra]].