Euclid of Alexandria, known as the "Father of Geometry", wrote his influential treatise Elements around 300 BC. In it, he defined fundamental geometric terms like points, lines, and planes and established basic principles called axioms and postulates that could be used to prove other geometric results without needing further proof. Some of Euclid's key definitions included that a point has no size, a line has length but no width, and a plane surface has length and width. His axioms and postulates laid the groundwork for deductive reasoning in geometry.

7. 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.

8. Euclid
Euclid 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)

9. Euclid wrote 23 definition in book-1 of
the ‘Elements’, 7 of them are below:-
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
4) A plane surface is a
surface which lies evenly
with the straight line itself
6) A point is
that which
has no part
7) A line is
breadth-less
and
has length
only

10. :-
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

11. AXIOMS
Things which are equal to the same thing are equal to one another
If a=b, b=c a=c
If equals are added to equals , the wholes are equal.
If a=b a + c=b + c
If equals are subtracted to equals , the remainders are equal.
If a=b a - c=b - c
Things 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=2b
Things which are halves of the same things are equal to one another.
If a=b a/2=b/2
If first thing is greater than the second is greater than the third then the
first
is greater than the first is greater than the third.
If a>,b>c a>c

12. POSTULATES
A straight line may be drawn from one point to another point.
A______________B
A terminated line can be produced indefinitely.
A _____________B_____________C
A 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°

13. SOME BRAIN EXERCISE
1. A surface is that which has
(a) length and breadth (b) length only (c) breadth only (d) length and height
2. The number of line that can pass through a given point is :
(a) 2 (b) none (c) only one (d) infinitely many
3. Which of the following needs proof ?
(a) Axiom (b) theorem (c) postulate (d) definition
4. 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.