Euclid of Alexandria lived around 300 BCE and wrote The Elements, the most influential and widely used mathematics textbook in history. The Elements collected, organized, and proved many geometric ideas and theorems that were known at the time. Euclid began with definitions, common notions, and postulates as foundations for geometry. He then used deductive reasoning to prove hundreds of theorems, establishing geometry as a logical science. While little is known about Euclid's life, his work The Elements has had an immense impact and remains highly influential to this day.

1. THE SWAMINARAYAN SCHOOL
PROJECT :- HISTORY OF MATHEMATICION THE *EUCLID*
SUBJECT :- MATHS
ROLL NO :- 4
NAME :- AGASTYA DEKATE
CLASS :- IX OR 9th (C)

2. EUCLID'S LIFE
Euclid of Alexandria (lived c. 300 BCE) systematized ancient Greek and
Near Eastern mathematics and geometry. He wrote The Elements, the most
widely used mathematics and geometry textbook in history. Older books
sometimes confuse him with Euclid of Megara. Modern economics has been
called "a series of footnotes to Adam Smith," who was the author of The
Wealth of Nations (1776 CE). Likewise, much of Western mathematics has
been a series of footnotes to Euclid, either developing his ideas or
challenging them. Almost nothing is known of Euclid's life. Around 300 BCE,
he ran his own school in Alexandria, Egypt. We do not know the years or
places of his birth and death. He seems to have written a dozen or so
books, most of which are now lost. The philosopher Proclus of Athens (412-
485 CE), who lived seven centuries later, said that Euclid "put together the
Elements, collecting many of Eudoxus's theorems, perfecting many of
Theaetetus's, and bringing to irrefragable demonstration things which were
only somewhat loosely proved by his predecessors." The scholar Stobaeus
lived at about the same time as Proclus. He collected Greek manuscripts
that were in danger of being lost. He told a story about Euclid that has the
ring of truth.

3. GEOMETRY BEFORE EUCLID’S CONTRIBUTION
In The Elements, Euclid collected, organized, and proved geometric ideas that were
already used as applied techniques. Except for Euclid and some of his Greek
predecessors such as Thales (624-548 BCE), Hippocrates (470-410 BCE),
Theaetetus (417-369 BCE), and Eudoxus (408-355 BCE), hardly anyone had tried to
figure out why the ideas were true or if they applied in general. Thales even became
a celebrity in Egypt because he could see the mathematical principles behind rules
for specific problems, then apply the principles to other problems such as
determining the height of the pyramids. The ancient Egyptians knew a lot of
geometry, but only as applied methods based on testing and experience. For
example, to calculate the area of a circle, they made a square whose sides were
eight-ninths the length of the circle's diameter. The area of the square was close
enough to the area of the circle that they could not detect any difference. Their
method implies that pi has a value of 3.16, slightly off its true value of 3.14... but
close enough for simple engineering. Most of what we know about
ancient Egyptian mathematics comes from the Rhind Papyrus, discovered in the mid-
19th century CE and now kept in the British Museum. Ancient Babylonians also knew
a lot of applied mathematics, including the Pythagorean theorem. Archaeological
excavations at Nineveh discovered clay tablets with number triplets satisfying the
Pythagorean theorem, such as 3-4-5, 5-12-13, and with considerably larger numbers.
As of 2006 CE, 960 of the tablets had been deciphered.

4. INVENTION DONE IN
LIFE TIME OF THE EUCLID ( 325 BCE – 265 BCE )
EUCLIIDS THOUGHT’S
From studies of the space and solids in the space around them, an abstract geometrical notion of a solid object
was developed. A sold has shape, size, position, and can be moved from on place to another. Its boundaries are
called surfaces. They separate on part of the space from another, and are said to have no thickness. The
boundary of the surfaces are curves or straight lines. These lines end in a points. The three steps from solid
to point (solids-surfaces-lines-points ). In each step we lose on extension, also called a dimension. A solid has
three dimensions, a surface has two dimension, a line has only one and a point has none. EUCLID gave these
statements as definitions He began his exposition by listing 23 definitions in Book 1 of the “Elements”. A few
of them are given below :-
1. A point is that which has no part.
2. A line is breadthless length.
3. The end of a lines are points.
4. A straight line is a line which lies evenly with the point on itself.
5. The surface is that which has length and breadth only.
6. The edge of the surface are line.
7. A plane surface is a surface which lies evenly with the straight lines on itself.

5. EUCLIDS ASSUMPTION
Euclid assumed certain properties, which were not to be proved. These assumptions
are actually “universal truths”. He divided them into two types: axioms and
postulates. He use this term “postulate” for the assumptions that were specific to
geometry. Common notion (called axioms), were assumptions used throughout
mathematics and not specifically linked to geometry. For details about axioms and
postulates, refer to Appendix 1. some of EUCLID’S axioms, are given below :
1.Things which are equal to the same thing are equal to one another.
2.If equals are added to equals, the whole would be equal.
3.If equals are subtracted from equals, the remainders are equal.
4.Things which coincide one another are equal to one another.
5.The whole is greater then parts.
6.Things which are double of same things are equal to one another.
7.Things which are halves of the same thing are equal to one another.
These “common notions” refer to the magnitudes of some kind.

6. EUCLID’S FIVE POSTULATES
POSTULATE 1. A straight line may be drawn from any one point to any other point.
EXPLANATION: The postulate says that a line passes through two point. But, it does not say that only
one line passes through 2 distinct points
POSTULATE 2. A terminated line can be produced indefinitely.
EXPLANATON: A terminated line is that part of a line which has two fixed points i.e. terminated
line has definite end points because of which we can measure the length of the terminated line.
POSTULATE 3. A circle can be drawn with any center and any radius.
EXPLANATION: If one of these points is taken as the center of a circle and the radius of the circle is
taken as equal to the length of the segment, a circle can be drawn with its diameter twice than the length
of the line segment.
POSTULATE 4. All right angles are equal to one another.
EXPLANATION: Euclid stated that all right angles are equal to each other in the form of fourth
postulate. The correct answer is a postulate. He said that because one line perpendicular to another can
help make the right angle and this makes one angle equal to another.
POSTUATE 5. If a straight line falling on two straight lines 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.
It is only explained.

7. EUCLID'S OTHER WORKS
• About half of Euclid's works are lost. We only know about them because other ancient writers
refer to them. Lost works include books on conic sections, logical fallacies, and "porisms."
We're not sure what porisms were. Euclid's works that still exist are The
Elements, Data, Division of Figures, Phenomena, and Optics. In his book about optics, Euclid
argued for the same theory of vision as the Christian philosopher St. Augustine. ‘Elements’
was Euclid’s most famous work and continues to influence mathematics even to this day but he
wrote a number of other books as well. At least 5 works of Euclid have survived to this day.
• Data: This book holds 94 propositions and basically deals with the nature and implications of
"given" information in geometrical problems.
• On Divisions of Figures: Another important work of Euclid but survives only partially in Arabic
translation. It resembles a work (3rd century) of ‘Heron of Alexandria’
• Catoptrics: It is another important work that is related to the mathematical theory of
mirrors. J J O'Connor and E F Robertson, however, consider 'Theon of Alexandria' as the real
author.
• Phaenomena: It throws light on spherical astronomy. It is strikingly similar to ‘On the Moving
Sphere’ by Autolycus of Pitane, who flourished around 310 BC.
• Optics: This work shares knowledge about theory of perspective and is the earliest surviving
Greek treatise on perspective.
• Apart from the five abovementioned extant works, there are some other works attributed to
Euclid, but have been lost. These are ‘Conics’, ‘Porisms’, ‘Pseudaria’ and ‘Surface Loci’. In
addition to these, various Arabic sources consider Euclid as author of several works on
mechanics.

8. THANKYOU TO SEE MY SLIDS
CONCLUSION
EUCLID was a great mathematation on the earth he has a great contribution
on the geometry and other also .
Thank you ! Jai swaminarayann!!