4. INTRODUCTIONThe word Geometrycomes from Greek word geo
meaning 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 DEFINITONS Some of the definitions made by Euclid in
volume I of The Elementsthat 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.