Euclid's geometry

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


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


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.

Euclid's geometry

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