3. ABOUT
EUCLID
Euclid, also known as the Euclid of Alexandria, was a Greek mathematician, often
referred to as the "Father of Geometry". He was active in Alexandria during the reign of
Ptomeli1 (323–283 BC). His E is one of the most influential works in the history of
mathematics, serving as the main textbook for teaching (especially geometry) from the
time of its publication until the late 19th or early 20th century. ] In the Elements, Euclid
deduced the principles of what is now called Euclidean geometry from a small set of
axioms. Euclid also wrote works on perspective, conic sections, spherical geometry,
number theory and rigor.
"Euclid" is the anglicized version of the Greek name Εὐκλείδης, meaning "Good Glory".[
4. One of the oldest surviving fragments of Euclid's
Elements, found at Oxyrhynchus and dated to circa
AD 100 . The diagram accompanies Book II,
Proposition 5.
ELEMENTS
Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to
present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of
rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.
There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are "from the
edition of Theon" or the "lectures of Theon", while the text considered to be primary, held by the Vatican, mentions no author.
The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly in his
Commentary on the Elements ascribes Euclid as its author.
5. Definitions of
Euclid
1. A point is that which has no
parts .
1. A line is breadth less length .
2. A straight line is a line which lies evenly with
the points on itself.
3. A surface is that which has length and
breadth only .
6. 4. The edges of a surface are
lines .5. A plane surface is a surface which lies
evenly with the straight lines on it self ..
Euclid’s Axioms
1. Things which are equal to the same thing are
equal to ne another .
2. If equals are added to equals ,the wholes are
equals
7. 3. If equal are subtracted from equals ,the
remainders are equals .
4. Things which coincide with one another are
equal to one another .
5. The whole is greater than the part .
6. things which are double of the same thing are
equal to one another .
7. things which are half of the same thing are
equal to one another .
8. Euclid’s postulate's
A Straight line may be drawn from any one
point to any other point .
1.
Note: that this postulates tell us that at least one straight line
passes through the two distinct points ,but it does not say
that there cannot be one such line.
9. 2. A terminated line can be produced
indefinitely.
Note: that we call a line segment now a days what Euclid call a
terminated line. So , according to the present day terms , the second
postulate says that a line segment can be extended on either side to
form a line .
A
B
10. 3.
A circle can be drawn with any
centre and any radius.
4.
All right angles are
equal to one another .
11. 5. If a straight line falling on two straight
line makes the interior angles on the
same side of it taken together less than
two right angles , then the two straight
lines , if produced indefinitely, meet on
that side on which the sum of angles is
less than two right angles .
A
B
C
D E
F
12. Line ,Ray ‘N’Line segment
Line :
A straight line extends indefinitely in
both directions . It has no definite
length .Ray
: A ray is a part of line with on end & the other part
extends indefinitely .
14. Prove that equilateral triangle can be constructed
by any given line segment .
In the statement above, a line segment of any length is given say
AB
Using Euclid’s postulates 3 you can draw a circle with point A as
the centre and AB as the radius. Similarly, draw another circle with
point B as the center and BA as the radius. The two circles meet at
a point say C .Now draw the line segment AC and BC to form a
triangle ABC .
15. AB =AC, since they are the radii of the same circle
AB=BC,(radii of the same circle)
From these two facts and Euclid’s axiom that things which are
equal to the same things are equal to one another, you can conclude
that AB=BC=AC
A B
i
A B
C
ii A
C
B
iii
So, ABC is a
equilateral triangle
16. Euclid’s
Achievements
Euclid is best known for his treatise on mathematics, The Elements. His book is one of
the most influential works in the history of mathematics, serving as the main textbook
for teaching math, especially geometry, from the time of its publication until the late
19th or early 20th century. The Elements is a mathematical and geometric treatise
consisting of 13 books written in Alexandria at around 300 BC. It is divided into
thirteen books which cover plane geometry, arithmetic and number theory, irrational
numbers, and solid geometry, such as definitions, propositions, theorems,
constructions, the five postulates (axioms), and mathematical proofs of the
propositions. Axioms are statements that are
