Term
| Fundamental Theorem of Projective Geometry |
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Definition
| A projectivity is determined when three collinear points and the corresponding three collinear points are given. |
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Definition
| If the six vertices of a hexagon lie alternately on two lines, the three pairs of opposite sides meet in collinear points |
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Definition
| Every projectivity relating ranges on two distinct lines determines another special line, the "axis", which contains the intersection of the cross-joins of any two pairs of corresponding points. |
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Definition
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| any two harmonic sets are related... |
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Definition
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| A projectivity relating ranges on two distinct lines is a perspectivity iff... |
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Definition
| the common point of the two lines is invariant. |
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Definition
| a cycle of three triangles, each inscribed in the next |
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| if two triangles are doubly perspective... |
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Definition
| they are triply perspective |
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Term
| Axiom 3.11: any two lines are incident... |
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Definition
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Term
| Axiom 3.12: there exists four points... |
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Definition
| of which no three are collinear |
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Definition
| every definition and every theorem remain true when we interchange the words point for line (and join and meet, collinear and concurrent, vertex and side, etc.) |
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| three dimensional duality |
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Definition
| points, lines and planes are interchanged with planes, lines and points |
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Term
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Definition
(m_c, n_d) where mc=nd and c of the n lines pass through each of the m points while d of the poiunts lie on each of the n lines.
(m points have c lines pass through and n lines contain d points) |
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Definition
| a configuration where (n_d,n_d) like 3_2 which is a triangle, another example is a 10_3 |
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Term
| harmonic conjugate of c with respect to a and b |
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Definition
| any three concurrent lines a, b, c determine a fourth line f, concurrent with them (see page 28 for construction help) |
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Term
| 3.31: a harmonic set of points is projected from any point outside the line by... |
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Definition
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| 3.32: Any section of a harmonic set of lines, by a line not passing through the point of concurrence ... |
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Definition
| is a harmonic set of points |
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| 3.33 If ABCD is perspective (or projective) to A'B'C'F' and H(AB,CF), then... |
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Definition
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| 3.35 If H(AB,CF), then... |
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Definition
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Term
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Definition
| lines passing through vertices of a triangle (examples include the "median" and "altitude" |
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