Euclid was an ancient
Greek mathematician . He
observed various types of
objects around him and
tried to define most basic
components of those
objects. He proposed
based on his studies of
space and the objects
visible in daily life.
3. Introduction To Geometry
Geometry (geo "earth",
metron "measurement") is
a branch of mathematics
concerned with questions
of shape, size, relative
position of figures, and the
properties of space. A
mathematician who works
in the field of geometry is
called a geometer.
4. Euclidean geometry
Euclidean geometry is
a mathematical system
attributed to the -
which he described in
his textbook on geometry: the Elements.
Euclid's method consists in assuming a
small set of intuitively appealing axioms,
and deducing many other
propositions (theorems) from these.
5. Axioms and Postulates
Euclid assumed certain properties, which
were not to be proved. These assumptions
are actually ‘obvious universal truths’. He
divided them into two types: axioms and
postulates. He used the term ‘postulate’ for
the assumptions that were specific to
geometry. Axioms on other hand were
assumptions used throughout mathematics
and not specifically linked to geometry.
6. Euclid’s Axioms
1. Things equal to same things are equal to one
2. If equals are joined to equals the wholes will
3. If equals are taken from equals , what
remains will be equal.
4. Things which coincide with one another are
equal to one another.
5. Whole is greater than the part.
6. Equal magnitudes have equal parts: equal
halves, equal thirds.
7. Euclid’s Postulates
1.To draw a straight line from any point to
2.To extend a straight line for as far as we
please in a straight line.
3.To draw a circle whose centre is the
extremity of any straight line, and
whose radius is the straight line itself.
4.That all the right angles are equal to
8. 5. If a straight line that meets two straight lines
makes the interior angles on the same side less
than two right angles, then those two straight
lines, if extended, will meet on that same side.
(That is, if angles 1 and 2 together are less than
two right angles, then the straight lines AB, CD,
if extended far enough, will meet on that same
side; which is to say, AB, CD are not parallel.)
9. 1. A point is that which has no part.
2. A line has breadthless length.
3. The ends of a line are points.
4. A straight line is a line which lies evenly with
the points on itself.
5. A surface is that which has length and
6. The edges of a surface are lines.
7. A plane surface is a surface which lies evenly
with the straight lines on itself.