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Euclid geometry

Date post: 06-Dec-2014
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EUCLID GEOMETRY PRESENTED BY:- Ix A1 STARS
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  • 1. EUCLID GEOMETRY PRESENTEDBY:- Ix A1 STARS

2. Introduction to Euclid Geometry 3. CONTENTS 4. INTRODUCTION The word Geometrycomes from Greek word geomeaning the earthand metreinmeaning 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. EUCLIDS 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. EUCLIDS AXIOMs SOME OF EUCLIDS 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.


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