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1
CRC Concise Encyclopedia of Mathematics, Second Edition
Note that a complete quadrilateral is different from a COMPLETE QUADRANGLE.
The midpoints of the sides of any complete quadrangle and the three diagonal
points all lie on a CONIC known as the NINE-POINT CONIC. If it is an ORTHO- ...
2
Euclid's Elements of geometry [book 1-6, 11,12] with ...
The complete figure formed by the production of the opposite sides of the simple
quadrilateral to meet each other, or two adjacent sides to meet the other two
sides is called a complete quadrilateral. Thus the same complete quadrilateral is
...
Euclides, Robert Potts,
1845
A complete quadrilateral (see Figure 1.8a) is the figure formed by four coplanar
lines, no three of which are concurrent. The four lines are called the sides of the
complete quadrilateral, and the six points of intersection of pairs of the sides are ...
Howard Whitley Eves,
1995
But before we do that let us recall that a complete quadrilateral is a quadrilateral
in which the pairs of opposite sides have been extended until they meet. For that
reason, a complete quadrilateral has six vertices and three diagonals. Example.
Razvan Gelca, Titu Andreescu,
2007
5
Machine Proofs in Geometry: Automated Production of Readable ...
By a complete quadrilateral, we mean the figure consisting of four points (any
three of them are not collinear) and the six lines joining any two of them. As in
Figure 6-235, A, B, C, D are the vertices of the complete quadrilateral. AB and CD
, AC ...
Shang-Ching Chou, Xiao-Shan Gao, Jingzhong Zhang,
1994
6
Perspectives on Projective Geometry: A Guided Tour Through ...
In our labeling there are three pairs of points (a,d), (b,e), and (c,f) such that the
points of each pair do not share a line of the configuration. Every line of the
complete quadrilateral is obtained by selecting exactly one point from each of the
pairs.
Jürgen Richter-Gebert,
2011
7
Fundamental Concepts of Geometry
A complete quadrilateral has been defined as the figure composed of four
coplanar lines (sides), no three of which are on the same point, and the six points
(vertices) determined by them. We now define a quadrangular set of lines as any
point ...
A complete quadrilateral (Figure 7.1) is the figure formed by four coplanar lines
no three of which are concurrent. The four lines p., p_, p_, p. are called the sides
of the complete quadrilateral, and the six points P,, P2, P,, P, P,., Pfi of
intersection ...
9
Geometry, Its Elements and Structure: Second Edition
G E D A B C H D C A B F We should be able to verify this by constructing another
complete quadrilateral with H at the intersection of ←→ AC and ←→EF. Then the
other diagonal should cut ←→EF at G. In this figure, we construct ABCDEF.
Alfred S. Posamentier, J. Houston Banks, Robert L. Bannister,
2014
10
Encyclopedia of the History of Arabic Science
Arab scientists engaged in the study of the complete quadrilateral. They called
Menelaus's theorem the proposition on the secants (shakl al-qat(ar ) and the
complete quadrilateral itself was the 'figure of secants' in their terminology.
Among the ...
Rushdī Rāshid, Régis Morelon,
1996