Euclid is known for writing The Elements, one of the most influential works in mathematics. The Elements laid out the basics of geometry and number theory through definitions, postulates, and 465 theorems proved through deduction. It covered areas like plane geometry, solid geometry, and early number theory. Euclid divided The Elements into 13 books covering topics such as commensurable and incommensurable lines. The work was widely studied and established Euclid as the "father of geometry."

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3. Euclid is known to almost every high school
student as the author of The Elements, the long
studied text on geometry and number theory. No
other book except the Bible has been so widely
translated and circulated. From the time it was
written it was regarded as an extraordinary work
and was studied by all mathematicians, even the
greatest mathematician of antiquity --
Archimedes, and so it has been through the 23
centuries that have followed. It is unquestionably
the best mathematics text ever written and is
likely to remain so into the distant future.

4. 1]The Elements
2] Data -- a companion volume to the first six books of
the Elements written for beginners. It includes
geometric methods for the solution of quadratics.
3] Division of Figures -- a collection of thirty-six
propositions concerning the division of plane
configurations. It survived only by Arabic
translations.
4] Phenomena -- on spherical geometry, it is similar to
the work by Autolysis
5] Optics -- an early work on perspective including
optics, catoptrics, and dioptrics.

5. Books I-VI -- Plane geometry
BooksVII-IX --Theory of Numbers
Book X -- Incommensurables
Book XI-XIII -- Solid Geometry
The Elements --Typical Book
Definitions
Axioms -- obvious to all
Postulates -- particular to the subject at hand
Theorems
The Elements -- Book I
Definitions -- 23
1. A point is that which has no part
2. A line is breathless length.
3.The extremities of a line are points.
4. A straight line is a line which lies evenly with the points on itself.

6.  At this time all the developments were
passed on to the next generation without
being discussed or proved.
“DOYOU KNOW ??
THALES was the first
mathematician to gave
first name in geometry

7.  A teacher of mythical Egypt Assembled almost
all the main work of geometry and 3D geometry
in one book elements. It has been divided into 13
chapter Each called a book
 Elements almost contain
 almost everything plain geometry,
sphere, Curve and other 3D figures
that is why Euclid is known as the
FATHER OF GEOMETRY

8. One interesting question about the assumptions for Euclid's system of geometry is
the difference between the "axioms" and the "postulates." "Axiom" is from Greek
axiom, "worthy." An axiom is in some sense thought to be strongly self-evident. A
"postulate," on the other hand, is simply postulated, e.g. "let" this be true.There
need not even be a claim to truth, just the notion that we are going to do it this way
and see what happens. Euclid's postulates, indeed, could be thought of as those
assumptions that were necessary and sufficient to derive truths of geometry, of some
of which we might otherwise already be intuitively persuaded. As first principles of
geometry, however, both axioms and postulates, on Aristotle's understanding, would
have to be self-evident.This never seemed entirely quite right, at least for the Fifth
Postulate -- hence many centuries of trying to derive it as aTheorem. In the modern
practice, as in Hilbert's geometry, the first principles of any formal deductive system
are "axioms," regardless of what we think about their truth -- which in many cases
has been a purely conventionalist attitude. Given Kant's view of geometry, however,
the Euclidean distinction could be restored: "axioms" would be analytic propositions,
and "postulates" synthetic. Whether any of Euclid's original axioms are analytic is a
good question.

9.  The elements started with 23 definitions, five postulates, and five "common
notions," and systematically built the rest of plane and solid geometry upon
this foundation.The five Euclid's postulates are
1. It is possible to draw a straight line from any point to another point.
2. It is possible to produce a finite straight line continuously in a straight line.
3. It is possible to describe a circle with any center and radius.
4. All right angles are equal to one another.
5. If a straight line falling on two straight lines makes the interior angles on the
same side less than two right angles, the straight lines (if extended
indefinitely) meet on the side on which the angles which are less than two
right angles lie.
(Dunham 1990). Euclid's fifth postulate is known as the parallel postulate. After
more than two millennia of study, this postulate was found to be
independent of the others. In fact, equally valid non-Euclidean geometries
were found to be possible by changing the assumption of this postulate.
Unfortunately, Euclid's postulates were not rigorously complete and left a
large number of gaps. Hilbert needed a total of 20 postulates to construct a
logically complete geometry.

13. * In 1795, John Playfair (1748-1819) offered an
alternative version of the Fifth Postulate.This
alternative version gives rise to the identical
geometry as Euclid's. It is Playfair's version of
the Fifth Postulate that often appears in
discussions of EuclideanGeometry:
5'.Through a given point P not on a line L,
there is one and only one line in the plane of P
and L which does not meet L.

15. Euclidean geometry is a mathematical system attributed to the
Alexandrian Greek mathematician Euclid, which he described in his
textbook on geometry the Elements. Euclid's method consists in
assuming a small set of intuitively appealing axioms, and deducing
many other propositions (theorems) from these. Although many of
Euclid's results had been stated by earlier mathematicians, Euclid was
the first to show how these propositions could fit into a comprehensive
deductive and logical system.The Elements begins with plane
geometry, still taught in secondary school as the first axiomatic system
and the first examples of formal proof. It goes on to the solid geometry
of three dimensions. Much of the Elements states results of what are
now called algebra and number theory, explained in geometrical
language.

16.  1} the number of dimensions, a point has.
 2}Boundaries of surfaces are:
 3}it is known that if, x+y=10 than,x+y+z=10+z the
Euclid’s axiom that illustrates this statement is :
 4}TheTotal number of propositions in the elements are:
 5]Euclid divided his famous treatise ‘The Elements'into:
 6}lines are parallel if they do not intersect’ is stated in
the form of :
 7} Pythagoras was a student of ________?
 8}Greek’s emphasised on:

17.  1} zero{0}
 2}Curves.
 3}By second axiom x+y=10
=x+y+z =10+z
(If equals are added to equals, the wholes are
equal) (axiom2)
 4} 465
 5}13 chapter.
 6}A postulate.
 7}Thales
 8}deductive reasoning

18.  1} In 1795, John Playfair (1748-1819) offered an alternative version
of the
 2}Through a given point P not on a line L, there is one and only
one line in the plane of P and L which does not meet
 3} Euclid listed __definitions in book 1 of the 'Elements'.
 4 }Theorems are mathematical statements which are proved
using________
 5 } _____and already proved statements and deductive reasoning
 6}The Euclidlidean Geometry isValid Only For Figures in the
______.
 7} his book Elements was used well into the ____________as the
standard textbook for teaching geometry.
 8}How many Axioms are their:

19.  Fifth Postulate
 L.
 23
 Definitions
 Axioms
 Plane
 8} 20th century
 }seven

20.  1}Thales Belongs to _____country.
 2}Father of geometry.
 3} Common notion are:
 4}_____Having length and breadth Only.
 Edges of a surface are ?

21.  1} Greek
 2}Euclid
 3}Axioms
 4} surface
 5}lines

22.  1}according to Euclid’s definition, and of line
are :
 2}Two distant lines L and M cannot have:
 3}Euclid belong to which country:
 4}Undefined terms are? :
 5} Euclid's most well-known collection of
works, called________

23.  1} Points{.}
 2} two point in common.
 3}Greece
 4}Point,line,plane.
 5} Elements

24.  1} A two points has_____ .
 2}A number of dimensions a solid has:
 3}A pyramid is a solid figure, the base of
which is:
 4}a one points has ____ lines:
 5}axioms are assumed as:

25.  1} one line
 2} 3
 3}Triangle, rectangle, ect..
 4} Infinite
 5}universal truths in all branches of
mathematics