Editing History of geometry (section)

=== Plato ===
[[Plato]] (427–347 BC) was a philosopher, highly esteemed by the Greeks. There is a story that he had inscribed above the entrance to his famous school, "Let none ignorant of geometry enter here." However, the story is considered to be untrue.<ref>{{cite web|last1=Cherowitzo|first1=Bill|title=What precisely was written over the door of Plato's Academy?|url=http://www.math.ucdenver.edu/~jloats/APresentations_2010/PlatosAcademy_Jim's10.ppt.pdf |archive-url=https://web.archive.org/web/20130625173419/http://www.math.ucdenver.edu/~jloats/APresentations_2010/PlatosAcademy_Jim%27s10.ppt.pdf |archive-date=2013-06-25 |url-status=live|website=www.math.ucdenver.edu/|access-date=8 April 2015}}</ref> Though he was not a mathematician himself, his views on mathematics had great influence. Mathematicians thus accepted his belief that geometry should use no tools but compass and straightedge – never measuring instruments such as a marked [[ruler]] or a [[protractor]], because these were a workman's tools, not worthy of a scholar. This dictum led to a deep study of possible [[compass and straightedge]] constructions, and three classic construction problems: how to use these tools to [[trisect an angle]], to construct a cube twice the volume of a given cube, and to construct a square equal in area to a given circle. The proofs of the impossibility of these constructions, finally achieved in the 19th century, led to important principles regarding the deep structure of the real number system. [[Aristotle]] (384–322 BC), Plato's greatest pupil, wrote a treatise on methods of reasoning used in deductive proofs (see [[Logic]]) which was not substantially improved upon until the 19th century.