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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.

1] The Elements2] 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.

Books I-VI -- Plane geometryBooks VII-IX -- Theory of NumbersBook X -- IncommensurablesBook XI-XIII -- Solid Geometry The Elements -- Typical Book DefinitionsAxioms -- obvious to allPostulates -- particular to the subject at handTheorems 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.

At this time all the developments were passed on to the next generation without being discussed or proved.

“DO YOU KNOW ??

THALES was the first mathematician to gave first name in geometry

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

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 a Theorem. 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.

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.

* 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 Euclidean Geometry:

5'.Through a given point P not on a line L, there is one and only one line in the plane of Pand L which does not meet L.

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.

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}The Total 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:

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

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 is Valid 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:

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

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

1} Greek 2}Euclid 3}Axioms 4} surface 5}lines

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________

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

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:

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

mathematics