About Euclid.Euclid’s definition and relate them

with real life.Meaning of the terms Axioms and

postulates.Axioms and Postulates and their

application for proving other results.

EuclidEuclid of Alexandria was born about 325 BC and he died about 265 BC . He is called “FATHER OF GEOMETRY” and is best known for his treatise may make Euclid the leading mathematics teacher of all time . He most likely came from a rich family because as a young child he went to Plato's school in ancient Greece ,where only rich were educated. After he finished school he went to Alexandria where he discovered and wrote his theories on geometry . Today few historians challenge the consensus that Euclid was older than Archimedes.(290/280-212/211-BC)

1) A straight line is a line which lies evenly with the points on itself

2) The edges of a

surface are

lines

3) A surface is that which has length and breadth only

5) The ends of a line are points

6) A point is that which

has no part

4) A plane surface is a surface which lies evenly

with the straight line itself

7) A line is breadth-less and

has length only

Euclid wrote 23 definition in book-1 of the ‘Elements’, 7 of them are below:-

:-The basic facts which are taken for

granted , without proof, are called AXIOMS

:-Axioms are the general statements .

Postulates are the axioms relating to geometry

AXIOMS Things which are equal to the same thing are equal to one another

If a=b, b=c a=cIf equals are added to equals , the wholes are equal.

If a=b a + c=b + cIf equals are subtracted to equals , the remainders are equal.

If a=b a - c=b - cThings which coincide with one another are equal to one another.The whole is greater than the part.Things which are double of the same things are equal to one another.

If a=b 2a=2bThings which are halves of the same things are equal to one another.

If a=b a/2=b/2If first thing is greater than the second is greater than the third then the

firstis greater than the first is greater than the third.

If a>,b>c a>c

POSTULATESA straight line may be drawn from one point to another point.

A______________BA terminated line can be produced indefinitely.

A _____________B_____________CA circle can be drawn with any center and any radius.

All right angles are equal to one another.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 angles are less than two right angles.

∟1 + ∟2 <180°

SOME BRAIN EXERCISE1. A surface is that which has

(a) length and breadth (b) length only (c) breadth only (d) length and height2. The number of line that can pass through a given point is :

(a) 2 (b) none (c) only one (d) infinitely many3. Which of the following needs proof ?

(a) Axiom (b) theorem (c) postulate (d) definition4. Euclid divided his famous treatise “ The Elements” into

(a) 13 chapters (b) 12 chapters (c) 11 chapters (d) 9 chapters 5. Select the wrong statement :

(a) Only one line can pass through a single point.(b) Only one line can pass through two distinct points .(c) A terminated line can be produced indefinitely on both the sides.(d) If two circles are equal , then their radii are equal.