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Saturday, October 13, 2018

Euclid and the axioms of geometry


Photo source: Wikimedia Commons, Mark A. Wilson

Photo license: CC BY-SA 4.0


Euclid (323-283 BC) was a Greek mathematician best known for his contributions to geometry and Euclid's axioms. Mathematician Eric Temple Bell said,


"With the completion of Euclid's Elements... For the first time in history masses of isolated discoveries were unified and correlated by a single guided principle, that of rigid deduction from explicitly stated assumptions... If the Pythagorean dream of a mathematized science is to be realized, all the sciences must eventually submit to the discipline that geometry accepted from Euclid." (The Development of Mathematics, 1940)


The rest of this post is some quotes from Euclid.




"There is no royal road to geometry." (Quoted in Commentary of the First Book of Euclid's Elements by Proclus)


"A prime number is one (which is) measured by a unit alone." (Elements)


"A line is length without breadth." (


"In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle." (




"The laws of nature are but the mathematical thoughts of God." (


"Handwriting is a spiritual designing, even though it appears by means of a material instrument." (