| 41. | For the parabola, the center of the directrix moves to the point at infinity ( see projective geometry ).
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| 42. | The converse of this observation ( except for the projective line ) is the fundamental theorem of projective geometry.
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| 43. | In particular, Euclidean geometry was more restrictive than affine geometry, which in turn is more restrictive than projective geometry.
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| 44. | Thus semilinear maps are useful because they define the automorphism group of the projective geometry of a vector space.
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| 45. | This means that the fundamental theorem of projective geometry ( see below ) remains valid in the one-dimensional setting.
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| 46. | Menger and Birkhoff gave axioms for projective geometry in terms of the lattice of linear subspaces of projective space.
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| 47. | His final work was about Projective Geometry, but it was posthumously completed by his students Gustav Fleddermann and Gottfried K�the.
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| 48. | The properties of being ruled or doubly ruled are preserved by projective maps, and therefore are concepts of projective geometry.
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| 49. | Distances and angles are never mentioned in the axioms of the projective geometry and therefore cannot appear in its theorems.
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| 50. | The second geometric development of this period was the systematic study of projective geometry by Girard Desargues ( 1591 1661 ).
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