Euclid's Elements Book I, Definitions. Level: High School, SAT Prep, College.

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Euclid's Book 1 begins with 23 definitions — such as point, line, and surface. Following a visual illustration.

Euclid Elements Book I, 23 definitions
 

     The first few definitions are:

  • Definition 1. A point is that which has no part.

  • Definition 2. A line is breadthless length.

  • Definition 3. The extremities of a line are points.

  • Definition 4. A straight line is a line which lies evenly with the points on itself.

 
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The Elements: Books I-XIII (Barnes & Noble Library of Essential Reading)
by Euclid, Thomas L. Heath (Translator), Andrew Aberdein (Introduction)
(Paperback - Complete and Unabridged)

Euclid's Elements is a fundamental landmark of mathematical achievement. Firstly, it is a compendium of the principal mathematical work undertaken in classical Greece, for which in many cases no other source survives. Secondly, it is a model of organizational clarity which has had a deep influence on the way almost all subsequent mathematical research has been conducted. Thirdly, it is the most successful textbook ever written, only seriously challenged as an account of elementary geometry in the nineteenth century, more than two thousand years after its first publication.

Euclid reportedly lived some time between the death of Plato (427-347 BC) and the birth of Archimedes (287-212 BC). He most likely learned mathematics at Plato's Academy in Athens and taught at Alexandria in Egypt. Scholars believe Euclid was hired as one of the original faculty at a school of advanced study, patterned after those in Athens, and known as the Museum.


 

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