This document discusses Euclid and the foundations of geometry. It explains that Euclid was the first to take a deductive approach to geometry based on definitions, axioms, and postulates. Some of Euclid's key definitions included points, lines, planes, and relationships between them. His axioms stated basic logical truths like "equals added to equals are equal." Euclid also introduced five postulates, such as being able to draw straight lines between points and produce lines indefinitely. Overall, the document outlines Euclid's foundational work in clearly defining terms and establishing logical principles, making him the father of geometry.

1. PRESENTED BY:-
Lohitha hari babu
IX m

3. TABLE OF CONTENT
•Introduction
•Euclid’s Definition
•Euclid’s Axioms
•Euclid’s Five Postulates

4.  The word ‘Geometry’comes from Greek word ‘geo’
meaning the ‘earth’and ‘metrein’meaning to
‘measure’. Geometry appears to have originated from
the need for measuring land.
 Euclid was the first Greek Mathematician who
initiated a new way of thinking the study of geometry.
 He introduced the method of proving a geometrical
result by deductive reasoning based upon previously
proved result and some self evident specific
assumptions called AXIOMS.
 The geometry of plane figure is known as ‘ Euclidean
Geometry ’. Euclid is known as the father of geometry.
 His work is found in Thirteen books called ‘ The
Elements ’.

5. Some of the definitions made by Euclid in
volume I of ‘The Elements’are as follows :-
 A point is that of which has no part.
 A line is a width less length.
 A straight line is which lies evenly with the points
on itself
 The extremities of lines are called points
 A surface is that which has only length and
breadth
 The edges of surface are lines
 A plane surface is a surface which lies evenly with
straight lines on itself.

6. o Axioms or postulates are the
assumptions which are obvious
universal truths. They are not
proved.

7. SOME OF EUCLID’S AXIOMS ARE :-
 Things which are equal to the same thing are
equal to one another.
i.e. if a=c and b=c then a=b.
Here a, b and c are same kind of things.
 If equals are added to equals, the wholes are
equal.
i.e. if a=b and c=d, then a+c = b+d
Also a=b then this implies that a+c = b+c .

8.  If equals are subtracted, the remainders are
equal.
 Things which coincide with one another are
equal to one another.
 Things which are double of the same things are
equal to one another

9.  The whole is greater than the part.
That is if a > b then there exists c such that
a =b + c.
Here, b is a part of a and therefore, a is greater
than b.
 Things which are halves of the same things are
equal to one another.

10. EUCLID’S POSTULATES WERE :-
 POSTULATE 1 :-
 A straight line may be drawn from any one point to
any other point
 POSTULATE 2 :-
 A terminated line can be produced infinitely
 POSTULATE 3 :-
 A circle can be drawn with any centre and any
radius
 POSTULATE 4 :-
 All right angles are equal to one another

11.  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 angles.