What is Euclid contribution to Geometry?


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Angela Smith answered

Euclid, the Greek mathematician, holds the distinction of being known as the 'Father of Geometry'. Although he is known for many contributions to the world of mathematics, the most significant one is considered to be his major work, popularly known as 'Elements'. When it was introduced, it was considered to be the most comprehensive and logically rigorous examination of the basic principles of geometry. Here are the basic points which we follow till date:

  1. It is possible to draw a straight line from any point to any point.
  2. It is possible to extend a finite straight line continuously in a
    straight line. (In modern terminology, this says that a line segment can
    be extended past either of its endpoints to form an arbitrarily large
    line segment.)
  3. It is possible to create a circle with any center and distance (radius).
  4. All right angles are equal to one another. (A right angle is, by
    Euclid's definition, "half" of a straight angle: That is, if a line
    segment has one of its endpoints on another line segment and divides the
    second segment into two angles that are equal to each other, the two
    equal angles are called right angles.)
  5. If a straight line falling on (crossing) two straight lines makes
    the interior angles on the same side less than two right angles, the two
    straight lines, if produced indefinitely, meet on that side on which
    the angles are less than the two right angles.
  6. Things which are equal to the same thing are equal to each other.
  7. If equals are added to equals, the wholes (sums) are equal.
  8. If equals are subtracted from equals, the remainders (differences) are equal.

  9. Things that coincide with one another are equal to one another.
  10. The whole is greater than the part.
It was Euclid's intent that all the remaining geometric statements in the Elements be logical consequences of these ten axioms.

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