EUCLIDE
(325BC – 265BC)
Born

325 BC

Died

265 BC

Residence

Egypt, Athens, Alexandria,

Nationality

Greek

Fields

Mathematics (geometry),

Institutions

Royal school at Alexandria in Egypt

Plato academy in Athens


Teacher

Archimedes

Eulcid,
best known for his treatise on mathematics, ‘Elements’ was born about 325 BC.
Little is known about his life except that he taught mathematics about 300 BC
in Royal School at Alexandria in Eqypt that has been founded by Ptolemy, the
successor of Alexander the great. He must have studies in Plato’s academy in
Athens and learnt the geometry of Eudoxus and theaetetus of which he was
familiar. He is considered a one of the great Greek mathematicians.
Euclid Elements / BOOKS:
Books
are given the content of subject matter of the thirteen books of the elements.
Ü Book1
: Proves elementary theorems about triangles and parallelograms and ends
with Pythagorean theorem.
Ü Book
–2 : has been known as “geometric algebra” because it states algebraic
identities as theorems about equivalent
geometric figures. This book contains a
construction of “the section”, the division of a line into two parts such that
the ratio of the original line to the larger segment. It also generalizes the
Pythagrorean theorem to arbitrary triangles, a result that is equivalent to the
law of cosines.
Ü Book
–3 : gives details of properties of circles.
Ü Book
–4 : deals with the construction of regular polygons, in particular the
pentagon.
Ü Book
–5 : develops a general theory of ratios and proportions. It formed the
foundation for a geometric theory of numbers the foundation for a geometric
theory of numbers until an analytic theory developed in the late 19^{th}
century.
Ü Book6
: applies the theory of ratios to plane geometry, mainly triangles and
parallelograms, culminating in the “application of areas” a procedure for
solving Quadratic problems by geometric means.
Ü Book7
: describes a method, antanaresis (now known as Euclidean algorithms), for
finding the greatest common divisor of two or more numbers.
Ü Book8
: examines numbers in continued proportions, now known as geometric sequences
(such as ax, ax2, ax3, ax4).
Ü Book9
: proves that there are infinite numbers.
Ü Book10
: which comprises roughly onefourth of the Elements seems
disproportionate to the importance of
its classification of incommensurable lines and areas.
Ü Book11
: deals with the intersections of planes, lines and parallelepipeds (solids
with parallel parallelograms as opposite faces).
Ü Book12
: provides Eudoxus’ method of exhaustion to prove that areas of a circle are to
one another as the squares of their diameters and the volumes of spheres are to one another as the
cubes of their diameters.
Ü Book13
: culminates with the construction of the five regular Platonic solids
(pyramid, cube, octahedron, dodecahedron, icosahedron) in a given spheres.
Book 1.
Triangles, parallelogram,
Pythagorean theorem
Book 2.
Geometric algebra :
Algebraic identities.
Book 3.
Properties of Circles
Book 4.
Construction of regular
polygons
Book 5.
Geometrical Theory :
Theory of ratios and Proportion
Book 6.
Idea of proportion applied
to similar figure
Book 7.
Even, odd numbers,
numerical theory of proportion
Book 8.
Continued proportion
Book 9.
Number theory
Book 10.
Irrational
Book 11.
Solid geometry
Book 12.
Method of exhaustion used
to show that circles are
Proportional
to their diameters etc.
Book 13.
Regular solids.
Euclid also wrote other books in
mathematics and a few in physics. The important of them are ‘data’, ‘on
Division of Figures’, ‘Phenomena’, ‘optics’, etc.
@
Data:
Data
deals with the nature and implications of "given" information in
geometrical problems; the subject matter is closely related to the first four
books of the Elements. It comprising
supplementary geometrical material concerned with algebraic problems is important in the development of algebra.
@
Division of figures:
consists of 36 propositions
concerning the division of various figures into two or more equal parts or
parts in given ratios.
@
Phenomena:
Phenomena, a treatise on spherical astronomy survives in Greek; it
deals with the celestial
sphere and contains 25 geometrical propositions.
@ Optics:
apparent shapes of cylinder and cones with viewed from different
angles.
Euclid Contributions:
Ø Euclid
proved what is generally known as Euclid’s second theorem that prime
numbers are infinite.
Ø He
thought about the three current problems of time namely
Dividing
an angle into three equal parts
Making
double of a cube
Obtaining
square from a cube
Ø He
solved unresolved problems related to irrational numbers
Ø He
also discussed the so called Euclidean algorithm for finding the
greatest common divisor of two numbers
Ø He
is created with the wellknown proof of the Pythagorean Theorem.
Ø He
also formulated few mathematical riddles.
Ø Euclid axioms:
Ø We
connect two points in a straight line
Ø We
extend the line in both sides
Ø Right
angle triangle consists of 90 degree
GETTING GREAT KNOWLEDGE
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