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1. EUCLID
GEOMETRY
PRESENTEDBY:-
Ix A1 STARS

2. Introduction to Euclid Geometry

3. CONTENTS

4. INTRODUCTION
• 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.
• Nearly 5000 years ago geometry originated in
Egypt as an art of earth measurement. Egyptian
geometry was the statements of results.
• The knowledge of geometry passed from
Egyptians to the Greeks and many Greek
mathematicians worked on geometry. The Greeks
developed geometry in a systematic manner.

5. • 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 ’.

6. EUCLID’S DEFINITIONS
Some of the definitions made by Euclid in volume I of ‘The Elements’
that we take for granted today are as follows :-
 A point is that which has no part
 A line is breadth less length
 The ends of a line are points
 A straight line is that which has length only

7. Continued…...
The edges of a surface are lines
A plane surface is a surface which lies
evenly with the straight lines on itself
o Axioms or postulates are the
assumptions which are obvious universal
truths. They are not proved.

8. EUCLID’S AXIOMs
SOME OF EUCLID’S AXIOMS WERE :-
 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 .

9. Continued…..
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

10. Continued…..
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.