Eukleidovy Základy

Šárka Voráčová

Spis známý pod názvem Základy (latinsky Elementa) ovlivnil zásadním způsobem nejen matematiku, ale evropskou vědu vůbec.


  • 1. Euclid's Elements, Book 3 Propositions 7 & 8
  • 2. Elements Book I, Proposition 26
  • 3. Euclid Bk 1: Prop 37
  • 4. Elements I: Proposition 1
  • 5. Elements I: Proposition 3
  • 6. Elements I: Proposition 4
  • 7. Elements I: Proposition 5
  • 8. Elements I: Proposition 6
  • 9. Elements I: Proposition 7
  • 10. Elements I, Proposition 8 (Setup)
  • 11. Elements I: Proposition 8
  • 12. Elements I: Proposition 9
  • 13. Elements I: Proposition 10
  • 14. Elements I: Proposition 11
  • 15. Elements I: Proposition 12
  • 16. Elements I: Proposition 13
  • 17. Elements I: Proposition 14
  • 18. Elements I: Proposition 15
  • 19. Elements I: Proposition 16
  • 20. Euclid's Twelfth Proposition in the Poincaré Disk
  • 21. Euclid's First Proposition in the Poincaré disk
  • 22. Eukleides, kniha I, věta 1.
  • 23. Eukleides, kniha I, věta 2
  • 24. Eukleides, kniha I, věta 3
  • 25. Pythagorova věta - důkazy
  • 26. Eukleides, kniha I, věta 43
  • 27. Saccheriho čtyřúhelník
  • 28. Eukleides, kniha II, věta 14
  • 29. Eukleides, kniha I, věta 45
  • 30. Eukleides, kniha I, věta 44
  • 31. Eukleides, kniha I, věta 42
  • 32. Eukleides: Základy, Kniha X, Věta 6
  • 33. Elements X.33
  • 34. Eukleides, kniha IV, věta 11
  • 35. Eukleides, kniha IV, věta 10
  • 36. Eukleides, kniha II, věta 11
  • 37. Eukleides, Základy, Kniha II. Věta 5
  • 38. Proof Without Words
  • 39. Pythagorova věta
  • 40. Pythagorova věta
  • 41. Eukleidovy věty o pravoúhlém trojúhelníku
  • 42. Dodekaedr
  • 43. Konstrukce dodekaedru z krychle

1.

Euclid's Elements, Book 3 Propositions 7 & 8

We made this sketch in class to try to make sense of these propositions. Proposition 7. If on the diameter of a circle a point is taken which is not the center of the circle, and from the point straight lines fall upon the circle, then that is greatest on which passes through the center, the remainder of the same diameter is least, and of the rest the nearer to the straight line through the center is always greater than the more remote; and only two equal straight lines fall from the point on the circle, one on each side of the least straight line. Proposition 8. If a point is taken outside a circle and from the point straight lines are drawn through to the circle, one of which is through the center and the others are drawn at random, then, of the straight lines which fall on the concave circumference, that through the center is greatest, while of the rest the nearer to that through the center is always greater than the more remote, but, of the straight lines falling on the convex circumference, that between the point and the diameter is least, while of the rest the nearer to the least is always less than the more remote; and only two equal straight lines fall on the circle from the point, one on each side of the least.

Text from David Joyce's translation & illustration of Euclid at [url]http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/bookIII.html[/url]
– mtpberg

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