Self-evident Axioms?????

Euclid (330 - 275 BC)

 

A Greek mathematician who, in 13 books known as the Elements, published a systematic account of Elementary Geometry and Number Theory. His aim was to deduce every statement in the Elements logically from a set of ten initial self-evident AXIOMS. These were: -

  1. Things equal to the same thing are also equal to one another.
  2. If equals are added to equals, the sums are equal.
  3. If equals are subtracted from equals, the remainders are equal.
  4. Things that coincide with one another are equal to one another.
  5. The whole is greater than the part.
  6. It is possible to draw a straight line from any point to any other point.
  7. Any straight line can be infinitely extended.
  8. It is possible to describe a circle with any centre and any radius.
  9. All right angles are equal to one another.
  10. Given a straight line and any point not on that line, there is through that point one, and only one line that is parallel to the given line.

Euclid's work has remained the basis of school geometry for more than 2,000 years.


 

(No wonder I could not understand it then. If the above is anything to go by, it's totally confusing and leads you round in circles. Axiompc.)



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