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Euclid of alexandria


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Euclid of alexandria

  1. 1. Euclid of Alexandria
  2. 2. Euclid of Alexandria Alexandria Death of Alexander the Great Ptolemies Museum and Library Ptolemy II Euclid Elements (Stoichia) Obscure!!! Ptolemy I
  3. 3. Euclid of Alexandria Lost works DID YOU KNOW THAT!!! Of what Euclid wrote, more than half has been lost!!! Treatise on conics in four books Treatise on Solid Loci (the Greek name for the conic sections) Surface Loci Pseudaria (or fallacies) three books on Porisms the loss of Euclidean Porisms Pappus Porism is intermediate between a theorem, in which something is proposed for demonstration , and a problem, in which something is proposed for construction. A proposition in which one determines a relationship between known and variable or undetermined quantities
  4. 4. Euclid of Alexandria Extant works Elements Data Division of Figures Phaenomena Optics Optical Phenomena optics catoptrics dioptrics The geometry of direct vision The geometry of refracted rays The geometry of reflected rays
  5. 5. Euclid of Alexandria Extant works Euclid’s Optics “emission” theory of visionEuclidean Division of Figures Arabic Scholars Arabic Translations Latin Current modern languages
  6. 6. Euclidean Division of Figures Euclid of Alexandria Includes a collection of thirty-six propositions concerning the division of plane configurations Proposition 1 Calls for the construction of a straight line that shall be parallel to the base of a triangle and shall divide the triangle into two equal areas. Proposition 6 Call for the division of a parallelogram into two equal parts by a line drawn through a given point on one of the sides or (proposition 10) through a given point outside the parallelogram. Final Preposition (36) Asks for the division of a quadrilateral in a given ratio by a line through a point on one of the sides of the quadrilateral.
  7. 7. Euclid of Alexandria Euclid’s Data Fifteen definitions magnitu des lo ci Ninety-five statements Conditions and magnitudes If two magnitudes a and b are given, their ratio is given, and that if one magnitude is given and
  8. 8. Euclid of Alexandria E B D CFA We are told that if a given (rectangular) area AB is laid off along a line segment of given length AC and if the area BC by which the area AB falls short of the entire rectangle AD is given, the dimensions of the rectangle BC are known.
  9. 9. Euclid of Alexandria The elements First textbook Introductory textbook covering all elementary mathematics A bearing to the rest of mathematics the same sort of relation as that which the letters of the alphabet have in relation to language.
  10. 10. Euclid of Alexandria The elements Thirteen books First half- dozen Elementary Plane Geometry “The extremities of a line are points” “A straight line is a line in which lies evenly with the points on itself.” “The extremities of a surface are lines”
  11. 11. Postulat es 1. To draw a straight line from any point to any point 2. To produce a finite straight line continuously in a straight line. 3. To describe a circle with any center and radius. 4. That all angles are equal. 5. That, if a straight line falling on two straight line makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than the two right angles. Euclid of Alexandria
  12. 12. Common notions: 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another. 5. The whole is greater than the part. Euclid of Alexandria
  13. 13. End.. Sa Wakas!!!! Euclid of Alexandria
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  15. 15. Euclid of AlexandriaEuclid of Alexandria
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  17. 17. Euclid of Alexandria
  18. 18. Euclid of Alexandria
  19. 19. Euclid of Alexandria