PPT: Introduction to Euclid`s Geometry | Mathematics (Maths) Class 9 PDF Download

 Page 1


 
 
Euclid's Geometry
Euclid's Geometry
I n t r o d u c t i o n
t o
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Euclid's Geometry
Euclid's Geometry
I n t r o d u c t i o n
t o
Geometry, a mathematical discipline exploring
various shapes and sizes prevalent in our daily
experiences, was revolutionized by the Greek
mathematician Euclid. In this chapter's introduction
to Euclid's geometry, we delve into the foundations
laid by Euclid, encompassing new definitions, axioms,
and postulates that form the basis of contemporary
geometry.
Introduction 
Page 3


 
 
Euclid's Geometry
Euclid's Geometry
I n t r o d u c t i o n
t o
Geometry, a mathematical discipline exploring
various shapes and sizes prevalent in our daily
experiences, was revolutionized by the Greek
mathematician Euclid. In this chapter's introduction
to Euclid's geometry, we delve into the foundations
laid by Euclid, encompassing new definitions, axioms,
and postulates that form the basis of contemporary
geometry.
Introduction 
Euclid's Definitions
Euclid was a Greek mathematician, who
introduced the method of proving a geometrical
result by using logical reasonings on previously
proved and known results.
The statement is a sentence that can be judged
to be true or false.
A Theorem is a statement that requires proof.
Page 4


 
 
Euclid's Geometry
Euclid's Geometry
I n t r o d u c t i o n
t o
Geometry, a mathematical discipline exploring
various shapes and sizes prevalent in our daily
experiences, was revolutionized by the Greek
mathematician Euclid. In this chapter's introduction
to Euclid's geometry, we delve into the foundations
laid by Euclid, encompassing new definitions, axioms,
and postulates that form the basis of contemporary
geometry.
Introduction 
Euclid's Definitions
Euclid was a Greek mathematician, who
introduced the method of proving a geometrical
result by using logical reasonings on previously
proved and known results.
The statement is a sentence that can be judged
to be true or false.
A Theorem is a statement that requires proof.
Euclid's Definitions
The corollary is a statement whose truth can
easily be deduced from a theorem.
Axioms are the basic facts that are taken for
granted without proof.
Postulates are the basic facts that are taken for
granted specific to geometry, without proof.
Page 5


 
 
Euclid's Geometry
Euclid's Geometry
I n t r o d u c t i o n
t o
Geometry, a mathematical discipline exploring
various shapes and sizes prevalent in our daily
experiences, was revolutionized by the Greek
mathematician Euclid. In this chapter's introduction
to Euclid's geometry, we delve into the foundations
laid by Euclid, encompassing new definitions, axioms,
and postulates that form the basis of contemporary
geometry.
Introduction 
Euclid's Definitions
Euclid was a Greek mathematician, who
introduced the method of proving a geometrical
result by using logical reasonings on previously
proved and known results.
The statement is a sentence that can be judged
to be true or false.
A Theorem is a statement that requires proof.
Euclid's Definitions
The corollary is a statement whose truth can
easily be deduced from a theorem.
Axioms are the basic facts that are taken for
granted without proof.
Postulates are the basic facts that are taken for
granted specific to geometry, without proof.
Euclid’s Axioms
The whole is greater than the part. 1.
Things which are double of the same things are equal to one another. 2.
Things which are halves of the same things are equal to one another. 3.
Things which are equal to the same thing are equal to one another. 4.
Things which coincide with one another are equal to one another. 5.
If equals are added to equals, the wholes are equal. 6.
If equals are subtracted from equals, the remainders are equal. 7.