...having a third-order osculation with the line $u$ on $(M_3)$ and with the line $v$ on $(M_4)$ [[#References|[1]]]. If two adjacent congruences in a [[Lapl
.../TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> S.P. Finikov, "Projective differential geometry" , Moscow-Leningrad (1937) (In Russian)</TD></TR></
2 KB (229 words) - 09:33, 27 April 2014
$#C+1 = 91 : ~/encyclopedia/old_files/data/P075/P.0705220 Projective determination of a metric
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7 KB (1,055 words) - 10:04, 21 March 2022
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A projective $ n $-
2 KB (353 words) - 13:52, 8 April 2023
A quadruple of points on a straight line with [[Cross ratio|cross ratio]] equal to $-1$. If $(ABCD)$ is a harmonic q
...e) is called a harmonic quadruple of straight lines (planes) if a straight line intersects it in a harmonic quadruple of points.
2 KB (278 words) - 13:42, 29 April 2014
...oint circle. The points $H,T,O,E$ then lie on a straight line (the [[Euler line]]), $E$ being the midpoint of the segment $HO$, and the pair of points $H,T
...ned by a projective base $\{a,b,c,d\}$ (giving a coordinate system) in the projective plane, cf. [[#References|[a2]]], Sects. 16.5.5.1, 16.7.5.
2 KB (345 words) - 19:10, 6 November 2016
$#C+1 = 12 : ~/encyclopedia/old_files/data/P075/P.0705230 Projective differential geometry
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6 KB (838 words) - 08:08, 6 June 2020
$#C+1 = 42 : ~/encyclopedia/old_files/data/P075/P.0705320 Projective representation
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5 KB (667 words) - 18:02, 13 April 2023
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projective (respectively, $ {\mathcal E} $-
3 KB (465 words) - 08:10, 6 June 2020
...dence relation, which are described by certain axioms, one may distinguish projective, affine, hyperbolic, elliptic, and other planes.
...ences|[7]]], Chapt. 3, where the Lenz–Barlotti classification is given for projective and affine planes) or from the realization in the plane of various configur
5 KB (838 words) - 19:20, 28 January 2020
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in the real projective straight line $ P _ {1} ( \mathbf R ) = \widetilde{\mathbf R} $,
6 KB (797 words) - 22:12, 5 June 2020
...ABC)$ of these three points that does not pass through any of them; if the line passes through a point between $A$ and $B$, then it must also pass through
...y]]. By means of Hilbert's other axioms of order it can be proved that the line $a$ cannot intersect both $AC$ and $BC$. M. Pasch stated this axiom in [[#R
2 KB (269 words) - 15:09, 9 April 2014
$#C+1 = 110 : ~/encyclopedia/old_files/data/P075/P.0705160 Projective algebra
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7 KB (1,026 words) - 08:08, 6 June 2020
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...identity transformation. A non-identity involution of the real projective line has just two fixed points (a hyperbolic involution) or has no fixed points
4 KB (550 words) - 22:13, 5 June 2020
...eferences|[a2]]] and [[#References|[a3]]], which is followed here. Given a projective plane, fix four points in [[General position|general position]]: $O$, $X$,
...ioms for a projective plane. Conversely, any ternary field coordinatizes a projective plane. It may happen that different ternary fields coordinatize the same pl
4 KB (678 words) - 08:05, 10 December 2023
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''projective system of probability measures, consistent system of probability measures,
4 KB (573 words) - 17:45, 4 June 2020
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''projective set''
3 KB (535 words) - 04:11, 6 June 2020
$#C+1 = 61 : ~/encyclopedia/old_files/data/P075/P.0705260 Projective limit,
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5 KB (863 words) - 08:08, 6 June 2020
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...in a projective space), the role of the metric connection is played by the projective-metric connection.
2 KB (292 words) - 08:00, 6 June 2020
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A model that realizes the geometry of the three-dimensional projective space $ P _ {3} $
6 KB (820 words) - 08:06, 6 June 2020
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becomes isomorphic to a [[Projective space|projective space]].
5 KB (791 words) - 01:37, 15 January 2022