Introduction to Euclid's Geometry

The word 'Geometry' is derived from the Greek words 'Geo' means 'Earth' and 'Metron' means to 'Measure'. 
Around 325 BC Euclid, a teacher of mathematics at Alexandria in Egypt, collected all the known work and arranged it in his famous treatise, called 'Elements'.
He divided the 'Elements' into thirteen chapters, each called a book. These books influenced the whole world's understanding of geometry for generations to come. 

Euclid's Definitions:
1: A point is that which has no part.
2: A line is breadthless length.
3: The ends of a line are points
4: A straight line is a line which lies evenly with the points on itself. 
5: A surface is that which has length and breadth only.
6: The edges of a surface are lines.
7: A plane surface is a surface which lies evenly with the straight lines on itself.
Euclid's Postulates:
1: line can be drawn from any point to any point.
2: A terminated line can be produced indefinitely. 
3: It is possible to describe a circle with any centre any distance.
4: All right angles are equal to one another.
5: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
Euclid's Axioms:
1: Things which are equal to the same things are also equal to one another.
2: If equals are added to equals, then the wholes are equal.
3: If equals are subtracted from equals, then the remainders are equal.
4: Things which coincide with one another are equal to one another.
5: The whole is greater than the part.
6 : Things which are double of the same things are equal to one another.
7 : Things which are halves of the same things are equal to one another.
length, line, breadthless, points, rays, two distinct point , unique line

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