INTRODUCTION TO EUCLID'S GEOMETRY

INTRODUCTION

 Geometry has been used since ancient times.from a piece of brick to a models of weapons were all made from geometry skills.Euclid has written 13 chappers based on geometry in his book"ELEMENTS".

SOME IMPORTANT POINTS TO REMEMBER

According to Euclid

1. A solid is made up of shape size position and can move

2.Boundary of solid are called surface

3.Boundary of surface is called line or curve.

4. Lines end in point

DIMENSION

solid -  3 dimensions

surface-2 dimensions

line-1 dimensions

point-no dimentions

THERE ARE TWO TYPES OF DIVISION 

1.AXIOMS and

2.POSTULATES

 

DEFINITION

1. a  point is that which has no part

2. a line is breathless length

3.the end of a line are point

4.a straight line is aline which lies evenly with the point itself

5. a surface has length and breadth only

6.the ages of surface is line

7.a plane surface is a surface which lies with straight line on itself.  

AXIOMS

Euclidean geometry is an axiomatic system, in which all theorems ("true statements") are derived from a small number of axioms.Near the beginning of the first book of the Elements, Euclid gives five postulates (axioms) for plane geometry, stated in terms of constructions (as translated by Thomas Heath):
"Let the following be postulated":

1. "To draw a straight line from any point to any point."
2. "To produce [extend] a finite straight line continuously in a straight line."
3. "To describe a circle with any centre and distance [radius]."
4. "That all right angles are equal to one another."
5. The parallel postulate: "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles."

Although Euclid's statement of the postulates only explicitly asserts the existence of the constructions, they are also taken to be unique.
The Elements also include the following five "common notions":

1. Things that are equal to the same thing are also equal to one another.
2. If equals are added to equals, then the wholes are equal.
3. If equals are subtracted from equals, then the remainders are equal.
4. Things that coincide with one another equal one another.
5. The whole is greater than the part.