Transcript
PRESENTED BY:-
Lohitha hari babu
IX m
TABLE OF CONTENT
•Introduction
•Euclid’s Definition
•Euclid’s Axioms
•Euclid’s Five Postulates
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 ’.
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.
oAxioms or postulates are the
assumptions which are obvious
universal truths. They are not
proved.
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 .
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
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.
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
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.
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