The Elements of Euclid  

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Euclid's Elements have been studied for centuries - in fact until the 20 th century it was the most common reprinted book after the Bible. It consists of 13 books with 465 propositions which deal with geometry, plane and solid, and number theory. It is not absolutely certain whether the author was one man (see a page on Euclid himself) but this doesn't make the achievement less important. Euclid's Elements are made is such an organised and succinct way that mathematicians for centuries tried to find a fault in it, and failed.

Tha - One of the oldest and most complete diagrams from Euclid's Elements of Geometry is a fragment of papyrus found among the remarkable rubbish piles of Oxyrhynchus in 1896-97 by the renowned expedition of B. P. Grenfell and A. S. Hunt. It is now located at the University of Pennsylvania. The diagram accompanies Proposition 5 of Book II of the Elements.

Euclid starts with the 23 definitions, 5 postulates and 5 common notions or general axioms. He then goes on to prove the first theorem, and the second and so forth. If you has enough patience to go through the process, you can encounter such beauty in logic and simplicity that you would rarely find in a piece of art.

Euclidis Megarensis mathematici clarissimi Elementorum geometricorum, published in 1537.

Original of Euclid's Elements have not been preserved, but Arabic mathematicians obviously had a full copy as an Arabic version of The Elements appeared at the end of the 8 th century BC. From this the first western version in 1482 was translated into Latin.

Folio A2r from Euclid's Elements of Geometry printed by Erhard Ratdolt in Venice in 1482, only 27 years after Johannes Gutenberg had produced the first printed book. (Special Collections, Glasgow University Library, Sp Coll BD7-c.5)

The Elements are divided into the following books

  1. triangles
  2. rectangles
  3. circles
  4. polygons
  5. proportion
  6. similarity
  7. number theory
  8. number theory
  9. number theory
  10. number theory
  11. solid geometry
  12. pyramids
  13. platonic solids.

 

   

 

BOOK I of Euclid's Elements

See some animated proofs of Euclid's Elements can be found at this linked page (you need to scroll down the page for further propositions).

 
 

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