- Euclid was a Greek mathematician who introduced deductive reasoning and proofs to geometry through his work "The Elements". He defined fundamental geometric concepts like points, lines, and planes and established axioms and theorems to prove geometric properties. Some of Euclid's key definitions included that a point has no parts, a line has length but no breadth, and a plane surface lies evenly with straight lines on it. His work established the foundation for Euclidean geometry.

1. Euclid's geometry

2. INTRODUCTION TO EUCLID’S
GEOMETRY

3. INTRODUCTION
- THE WORD ‘GEOMENTRY’ COMES FROM
GREEK WORDS ‘GEO’ MEANING THE ‘EARTH’ AND
‘METREIN’ MEANING TO ‘MEASURE’. GEOMENTRY
APPEARS TO HAVE ORIGINATED FROM THE
NEED FOR MEASURING LAND.
- NEARLY 5000 YEARS AGO GEOMENTRY
ORIGINATED IN EGYPT AS AN ART OF EARTH
MEASUREMENT. EGYPTIAN GEOMENTRY WAS
THE STATMENTS OF RESULTS.

4. WHO IS EUCLID?
- 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 PREVIOSYLY 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 GEOMTRY.

5. EUCLID’S 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

6. CONTINUED….
THE EDGES OF A SURFACE ARE LINES.
A PLANE SURFACE IS A SURFACE WHICH LIES EVENLY
WITH THE STRAIGHT LINES ON ITSELF.
AXIOMS OR POSTULATES ARE THE ASSUMPTIONS
WHICH ARE OBVIOUS UNIVERSAL TRUTHS. THEY
ARE NOT PROVED.
THEOREMS ARE STATEMENTS WHICH ARE PROVED,
USING DEFINITIONS.

7. EUCLID’S AXIOMs
SOME OF EUCLID’S 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.

8. CONTINUED…
IF EQUALS ARE SUBTRACTED, THE
REMAINDERS ARE EQUAL.
THINGS WHICH COINCIDE WITH ONE ANOTHER
ARE EQUAL TO ONE ANOTHER.
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 THEN B.
THINGS WHICH ARE DOUBLE OF THE SAME
THINGS ARE EQUAL TO ONE ANOTHER.