Page 2 - Lesson Notes-Euclid Definitions,Axioms and Postulates Ch-5(Introduction to Euclid')
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5. Circles
6. Regular polygons
7. Conic sections
Solid geometry
1. Volume
2. Regular solids
What is Euclidean Geometry?
Euclidean Geometry is considered as an axiomatic system, where all the theorems
are derived from the small number of simple axioms. Since the term “Geometry”
deals with things like points, line, angles, square, triangle, and other shapes, the
Euclidean Geometry is also known as the “plane geometry”. It deals with the
properties and relationship between all the things.
Non-Euclidean is different from Euclidean geometry. There is a difference between
these two in the nature of parallel lines. In Euclid geometry, for the given point and
line, there is exactly a single line that passes through the given points in the same
plane and it never intersects.
Euclid‟s Elements
Euclid‟s Elements is a mathematical and geometrical work consisting of 13 books
written by ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt.
Further, the „Elements‟ was divided into thirteen books which popularized geometry
all over the world. As a whole, these Elements is a collection of definitions,
postulates (axioms), propositions (theorems and constructions), and mathematical
proofs of the propositions.
Book 1 to 4th and 6th discuss plane geometry. He gave five postulates for plane
geometry known as Euclid’s Postulates and the geometry is known as Euclidean
geometry. It was through his works; we have a collective source for learning
geometry; it lays the foundation for geometry as we know now.
Euclid was a teacher of mathematics at Alexandria in Egypt, popularly known as
‘Father of Geometry”.
He introduced the method of proving mathematical results by using deductive logical
reasoning and the previously proved result.
He collected all his work in a book called “Elements”. This book is divided into
thirteen chapters and each chapter is called a book.
In this chapter, we shall discuss Euclid‟s approach to Geometry and shall try to relate
it with present day geometry.
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