INTRODUCTION TO EUCLD’S GEOMETRY.ppt

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INTRODUCTION TO

EUCLD’S GEOMETRY.

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The word ‘geometry’ comes form theGreek words ‘geo’ ,meaning the ‘earth’,

And ‘metrein’, meaning ‘to measure‘.Geometry appears to have originatedfrom the need for measuring land. Thisbranch of mathematics was studyvarious from in every ancient civilisation,be it in Egypt, Babylonia, China, India,Greece, the Incas, etc.

Introduction.

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A GREEK MATHEMATICIAN.

A Greek mathematician,thales is credited withgiving the first knownproof. This proof the

statement that a circle isbisected, by itsdiameter. One of thalesmost famous pupils wasPythagoras(572BCE)wh

om you have heardabout. A that timeEuclid, a teacher

Alexandria in Egypt.

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GREEK MATHEMATICIAN THALES

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EUCLID’S DEFINITIONS.

A solid has shapes, size, position, andcan be moved from one place to another.Its called surfaces.The boundaries of the surfaces arecurves or straight lines. These lines endin points.

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ELUID’S ELEMENTS.

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 a line which lies evenly withthe points on itself. A surface is that which has length and breadthonly.The edges of a surface are lines.

A plane surface is a surface which lies evenlywith the straight lines on itself.

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EULID’S AXIOMS.

Things which are equal to the thing are equal to oneanother.If equals added to equals, the wholes are equal.If equals are subtracted from equals, the reminders

are equals.Things which coincide with one another are equal toone another.The whole is greater than the part.Things which are double of the same things are equal

to one another.Things which are halves of the same things are equalto one another.

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EUCLID’S FIVE POSTULATES.

A straight line may be drawn from anypoint to any other point.Axiom5.1: Given two distinct points,

there is a unique line that passesthrough them.

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POSTULATE 2

A terminated line can be producedindefinitely.

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POSTULATE 3

A circle can be drawn with any center and radius.

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POSTULATES 4

All right angles are equal to one another.

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POSTULATES 5

If a straight line falling on two straightlines make the interior. Angles on thesame side of it taken together less thanto right angles then the two straight linesof produced indefinitely, meet on thatside on which the some of angles is less

than two right angles.

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