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Introduction To Euclidean Geometry

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- 1. EUCLID’ S GEOMETRY Prepared by- - Nupur Pawa - IX-M -
- 2. Euclid Euclid was an ancient Greek mathematician . He observed various types of objects around him and tried to define most basic components of those objects. He proposed twenty-three definitions based on his studies of space and the objects visible in daily life.
- 3. Introduction To Geometry Geometry (geo "earth", metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.
- 4. Euclidean geometry 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. ›m
- 5. Axioms and Postulates Euclid assumed certain properties, which were not to be proved. These assumptions are actually ‘obvious universal truths’. He divided them into two types: axioms and postulates. He used the term ‘postulate’ for the assumptions that were specific to geometry. Axioms on other hand were assumptions used throughout mathematics and not specifically linked to geometry.
- 6. Euclid’s Axioms 1. Things equal to same things are equal to one another. 2. If equals are joined to equals the wholes will be equal. 3. If equals are taken from equals , what remains will be equal. 4. Things which coincide with one another are equal to one another. 5. Whole is greater than the part. 6. Equal magnitudes have equal parts: equal halves, equal thirds.
- 7. Euclid’s Postulates 1.To draw a straight line from any point to any point. 2.To extend a straight line for as far as we please in a straight line. 3.To draw a circle whose centre is the extremity of any straight line, and whose radius is the straight line itself. 4.That all the right angles are equal to one another.
- 8. 5. If a straight line that meets two straight lines makes the interior angles on the same side less than two right angles, then those two straight lines, if extended, will meet on that same side. (That is, if angles 1 and 2 together are less than two right angles, then the straight lines AB, CD, if extended far enough, will meet on that same side; which is to say, AB, CD are not parallel.)
- 9. 1. A point is that which has no part. 2. A line has breadthless length. 3. The ends of a line are points. 4. A straight line is a line which lies evenly with the points on itself. 5. A surface is that which has length and breadth only. 6. The edges of a surface are lines. 7. A plane surface is a surface which lies evenly with the straight lines on itself. Euclid’s Definitions
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