1. Euclid's Geometry

2. Index
• What is Euclid's Geometry?
• Difference between Axioms and
Postulates.
• All Axioms and Postulates.
• Different Mathematicians and their
contribution towards Mathematics.

3. What is Euclid’s Geometry 1.1
• Euclidean geometry, the study of plane and solid
figures on the basis of axioms and theorems
employed by the Greek
mathematician Euclid (c. 300 BCE). In its rough
outline, Euclidean geometry is the plane and solid
geometry commonly taught in secondary schools.
Indeed, until the second half of the 19th century,
when non-Euclidean geometries attracted the
attention of mathematicians, geometry meant
Euclidean geometry.

4. What is Euclid’s Geometry 1.2
• It is the most typical expression of general
mathematical thinking. Rather than the
memorization of simple algorithms to solve equations
by rote, it demands true insight into the subject,
clever ideas for applying theorems in special
situations, an ability to generalize from known facts,
and an insistence on the importance of proof. In
Euclid’s great work, the Elements, the only tools
employed for geometrical constructions were the
ruler and the compass—a restriction retained in
elementary Euclidean geometry to this day.

5. Difference between Axioms
and Postulates.
 Postulates - The assumptions
that were specific to geometry are
called postulates.
Axioms - The assumptions that
are used throughout mathematics
and not specifically linked to
geometry are called Axioms.

6. All Axioms and Postulates.
Axioms:-
• Things that equal the same thing also equal one another.
• If equals are added to equals, then the wholes are equal.
• If equals are subtracted from equals, then the remainders
are equal.
• Things that coincide with one another equal one another.
• The whole is greater than the part.
• Things which are double of the same things are equal to
one and other.
• Things which are halves of the same things are equal to one
another.

7. Postulates
1. A straight line segment can be drawn joining any two
points.
2. Any straight line segment can be extended indefinitely in a
straight line.
3. Given any straight line segment, a circle can be drawn
having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. if a straight line falling on 2 straight lines makes the
interior angles on the same side of it taken together less
than 2 right angles, then 2 straight lines, if produced
indefinitely, meet on that side on which the sum of angles is
less than 2 right angles.

8. Euclid’s 1 to 4 Postulates

9. 5th Postulate

10. Different Mathematicians
and their contribution towards
Mathematics.
Euclid of Alexandria
Srinivasa Ramanujan
Rene Descartes
Aryabhatta
Thales

11. Euclid of Alexandria
• Euclid of Alexandria is the most
prominent mathematician of antiquity
best known for his treatise on
mathematics The Elements. The long
lasting nature of The Elements must
make Euclid the leading mathematics
teacher of all time. However little is
known of Euclid's life except that he
taught at Alexandria in Egypt.

12. Srinivasa Ramanujan
Srinivasa Ramanujan was one of India's
greatest mathematical geniuses. He made
substantial contributions to the analytical
theory of numbers and worked on elliptic
functions, continued fractions, and infinite
series.
Ramanujan was shown how to solve cubic
equations in 1902 and he went on to find his own
method to solve the quartic. The following year,
not knowing that the quintic could not be solved
by radicals, he tried (and of course failed) to solve
the quintic.

13. Rene Descartes
Rene Descartes was a great philosopher and
thinker, many overlook his contribution to math
because of his overwhelming additions to the field
of philosophy, however we would like to point out
this mans work on mathematics so that he gets
even more credit to his name. By the way he
passed away from a cold, away from him native
France, and could have probably made an even
bigger impact on modern science if he had not
passed away in a relatively early age.

14. Aryabhatta
• Aryabhatta is a renowned mathematician and
astronomer of ancient India. He was born in 476 AD
in Kerala. He studied at the University of Nalanda.
One of his major work was Aryabhatiya written in 499
AD. The book dealt with many topics like astronomy,
spherical trigonometry, arithmetic, algebra and plane
trigonometry. He jotted his inventions in mathematics
and astronomy in verse form. The book was translated
into Latin in the 13th century. Through the translated
Latin version of the Aryabhattiya, the European
mathematicians learned how to calculate the areas of
triangles, volumes of spheres as well as how to find out the
square and cube root.

15. Thales
Thales, an engineer by trade, was the first of the Seven Sages, or
wise men of Ancient Greece. Thales is known as the first
Greek philosopher, mathematician and scientist. He founded the
geometry of lines, so is given credit for introducing abstract
geometry.
Thales is credited with the following five theorems of geometry:
A circle is bisected by its diameter.
Angles at the base of any isosceles triangle are equal.
If two straight lines intersect, the opposite angles formed are
equal.
If one triangle has two angles and one side equal to another
triangle, the two triangles are equal in all respects. (See
Congruence)
Any angle inscribed in a semicircle is a right angle. This is
known as Thales' Theorem.