Introduction to Euclids Geometry
Euclid, also known as Euclid of Alexandria, was a Greek mathematician. He is famously known for Euclidean geometry and Euclid’s Elements. Euclid’s Elements consists of 13 books written by him
Some of the definitions given by Euclid are
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 assumptions are actually ‘obvious universal truths’. He divided them into two types: Axioms and Postulates. Some of Euclid’s axioms are :
1) Things which are equal to the same thing are equal to one another.
2) If equals are added to equals, the wholes are equal.
3) If equals are subtracted from equals, 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.
Euclid’s postulates are :
Postulate 1 : A straight line may be drawn from any one point to any other point.
Postulate 2 : A terminated line can be produced indefinitely.
Postulate 3 : A circle can be drawn with any centre and any radius.
Postulate 4 : All right angles are equal to one another.
Postulate 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
Two equivalent versions of Euclid’s fifth postulate are:
(i) ‘For every line l and for every point P not lying on l, there exists a unique line m
passing through P and parallel to l’.
(ii) Two distinct intersecting lines cannot be parallel to the same line.