References in EQF/EPG

[1] Brianchon C. J., Poncelet J.-V.,
Recherche sur la détermination d'une hyperbole équilatère au moyende quatre conditions données,
Annales Mathématiques de 1821
* Page 512 about Euler Circles.

[2a] Jean-Louis Ayme, La droite de Gauss et la droite de Steiner, available at   vol. 4 La droite de Gauss et la droite de Steiner.
[2b] Jean-Louis Ayme, Le point de Kantor-Hervey, available at   vol. 6 Le point de Kantor-Hervey.
[2c] Jean-Louis Ayme, Le Point- d’Euler-Poncelet d‘un Quadrilatère, available at   vol. 8 Le point d’Euler-Poncelet d’un quadrilatère.
* Page 11 Synthetical proof midcircles are concurrent
[3] Jean-Louis Ayme: “Méthodes et techniques en géométrie: A propos de la droite de Newton”.

[4] Jean Pierre Ehrmann - Steiner’s Theorems on the Complete Quadrilateral, Forum Geometricorum 4 (2004) 35-52,

[5] Alexei Myakishev - On Two Remarkable Lines related to a Quadrilateral, Forum Geometricorum 6 (2006) 289-295

[6] Alain Levelut – A note on the Hervey Point of a complete Quadrilateral, Forum Geometricorum 11 (2011) 1-7

[7] Heinrich Dörrie: "100 great problems of Elementary Mathematics"
* Page 213 about “A hyperbola from four points”.
* Page 231 about “The most nearly Circular Ellipse Circumscribing a Quadrilateral”
* Page 265 about “Desargues’ Involution Theorem”.

[8] Dick Klingens, Vlakke Meetkunde, available at
* Stelling van Poncelet-Brianchon
* Euler Cirkels (mentioning of Euler point)
* Aubel, Stelling van Van,
* Tien niet zo bekende eigenschappen van (koorden)vierhoeken

[9] Alexander Bogomolny – Cut The Knot! – The complete Quadrilateral

[10] Francisco Javier García Capitán, Baricentricas.
Description and Notebook on barycentric algebraic formulas, available at

[11] Hyacinthos, Internet forum for discussion on Triangle Geometry.
1. This former Yahoo-forum was closed at December 2019.
The archive is available at:
You can go to a specific message with number nnnn by typing:
You can go to a specific topic with number tttt by typing:
2. A file with all messages can be downloaded at this page:
There also was a Yahoo-forum named Anopolis. This forum also was closed December 2019.
Unfortunately there is no more online program for viewing messages. However many of the Anopolis-messages also were placed in Hyacinthos, but not all of them.

[12] C. Kimberling, Encyclopedia of Triangle Centers, available at

[13] Weisstein, Eric W., MathWorld--A Wolfram Web Resource
, available at
* Anallagmatic Curve
* Anticenter
* Bimedian
* Circular points at infinity
* (Complete) Quadrangle
* (Complete) Quadrilateral
* Crossdifference
* Cyclocevian Conjugate
* Euler Triangle
* Gauss-Bodenmiller Theorem
* First/Second/Third Morley Triangle
* Harmonic Conjugate
* Isoconjugation
* Isotomic Transversal
* Miquel's Pentagram Theorem
* Nine-point Circle
* Orthologic Triangles
* Orthopole
* Petr-Neumann-Douglas Theorem
* Pivotal Isocubic 
* Pivotal Isogonal cubic
* Polar
* Trilinear Pole
* Trilinear Polar
* Van Aubel's Theorem
* Wittenbauer's Parallelogram 

[14] Philippe Chevanne, Mad Maths, Recreational mathematic collection, available at
* Problem equidistance lines:
* Problem inscribed and circumscribed squares:

[15] Eckart Schmidt
[15a] 05-4 Ein weiterer merkwürdiger Viereckspunkt:  
[15b] 05-6 Geometrie auf der ZirkularKurve:
[15c] 07-1 Das Steiner Dreieck von vier Punkten:
[15d] 04-5 Vierecksbezogene Inversionen: (QL-Tf1: Clawson-Schmidt Conjugate)
[15e] 11-1 Die Brennpunktkurve eines Vierecks:
[15f] 11-3 Miquel-, Poncelet- und Bennett-Punkt eines Vierecks:
[15g] 08-6 Miquel Points and Inscribed Triangles:
[15h] 11-2 Parallelogramme eines Vierecks:
[15i] 04-3 Euler-Gerade eines Vierecks:

[16] Daniel Baumgartner, Roland Stärk, Ein merkwürdiger Punkt des Vierecks, available at

[17a] Points and Mappings:
[17b] Jean-Pierre Ehrmann and Bernard Gibert,
Special Isocubics in the Triangle Plane, available at:
[17c] Note on Circular Isocubics,
[17d] Inscribed Cardioids and Eckart Cubics,

[18] H.M. Cundy and C.F. Parry,
Geometrical properties of some Euler and circular cubics. Part 2.
Journal of Geometry 68, 2000,
p.63 on isoptic (or Bennett) point of a quadrangle

[19] Michael Fox, Constructions for Sketchpad

[20] P.S. Modenow and A.S. Parkmohenko,
Geometric Transformations, Volume 2: Projective Transformations
p.24 Two fundamental Theorems on Projective Transformations

[21] Jim Loy, Jim Loy's Mathematics Page
* Inscribing a Square in a Quadrilateral:

[22] J.W. Clawson, The complete Quadrilateral – American Mathematical Monthly, Volume 20 (1919) pages 232-262,

[23] Eckart Schmidt, Mittelsenkrechtenvierecke eines Vierecks, PM 2/44 (Jg. 2002), S. 84-87

[24] Lang Fred, The pedal circle center transformation. – July 9, 2007.

[25] J.L. Coolidge, Harvard University, Two geometrical applications of the method of least squares,

[26] Chris van Tienhoven, Perspective Fields,
[26a] Perspective Fields part I
[26b] Perspective Fields part II

[27] Olga Radko and Emmanuel Tsukerman - The perpendicular bisector construction, isoptic point and Simson line, 161—189,
Forum Geometricorum, Volume 12 (2012),

[28] A.V. Akopyan, A.A. Zaslavski, Geometry of Conics, American Mathematical Society. ISBN 978-08218-4323-9

[29] C.M. Herbert, The inscribed and Circumscribed Squares of a Quadrilateral and Their Significance in Kinematic Geometry – Annals of Mathematics, Second Series, Vol. 16, No 1/4 (1914 – 1915), pages 38-42,

[30] Alexei Myakishev, On two remarkable lines related to a quadrilateral, Forum Geometricorum, 6 (2006) 289--295.

[31] J.W. Clawson, More theorems on the Complete Quadrilateral – American Mathematical Monthly, Volume 23, No. 1 (Sep., 1921) pages 40-44,

[32] Eisso J. Atzema - An Elementary Proof of a Theorem by Emelyanov, Forum Geometricorum 8 (2008) 201-204

[33] Anopolis, Internet forum for discussions on Elementary Geometry,
This former Yahoo-forum was closed at December 2019.
Unfortunately there is no more online program for viewing messages.
However many of the Anopolis-messages also were placed in Hyacinthos (see [11]), but not all of them.
[34] Quadri-Figures-Group, Internet forum for discussions on topics related to Quadrilaterals, Quadrangles, etc.
This former Yahoo-forum was closed at December 2019.
1. The archive is available at:
When you are looking for a QFG-message with a specific number (e.g. #255), then use the Search option with keyword “Message: 255” and you will be directed to the right message.
2. Also available at:
You can go to a specific message with number nnnn by typing:
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[35] Wikipedia, The Free Encyclopedia, about the Möbius Transformation.
[35b] Wikipedia, The free Encyclopedia, about the Petr-Douglas-Neumann Theorem.

Benedetto Scimemi, Central Points of the Complete Quadrangle - Milan. J. Math., 75 (2007) 333–356.

[37] F. Morley, 
Extensions of Cliffords Chain-Theorem, Amer J Math, 51 (1929) 465-472.

[38] S. Kantor,
Quelques théorèmes nouveaux sur l’hypocycloïde à trois rebroussements,
Bulletin des sciences mathématiques et astronomiques (1879).

M. Victor Thébault, Sur le quadrilatere complet, C. R. Acad. Sci., Paris 217, 97-99 (1943),

[40] J.W. Clawson, An Inversion of the complete Quadrilateral – American Mathematical Monthly, Volume 24, No 2 (Feb., 1917) pages 71-73,

[41] Martin Josefsson - Characterizations of Trapezoids, Forum Geometricorum Volume 13 (2013) 23–35.

[42] Darij Grinberg,
Poncelet points and antigonal conjugates,

[43] Bernard Keizer,
La Géométrie du Quadrilatère Complet.

[44] Schwerpunkte von Vierecken (I),Wurzel 48-2/2014, 35-41 (mit Günter Pickert)
English Version: Rudolf Fritsch and Guenter Pickert, The Seebach-Walser Line of a Quadrangle.
CRUX Mathematicorum 39-4/2014, 178-184

[45] M. Léon Ripert, Notes sur le quadrilatère, available at:
(pages 106-118)

[46] H.V. Mallison, Pedal Circles and the Quadrangle.
Math. Gazette 42 (1958), 17-20,

F. Morley, On Reflexive Geometry, Trans Amer Math Soc, 8 (1907) 14-24
available at:

F. Morley, On the Metric Geometry of the N-Line, Trans Amer Math Soc, 1 (1900) 97-115
available at:

F. Morley, Orthocentric properties of the plane n-Line, Trans Amer Math Soc, 4 (1903) 1-12
available at:

[50] Advanced Plane Geometry, an Internet forum for discussions on Advanced Plane Geometry,
This former Yahoo-forum was closed at December 2019.
1. The archive is available at:
You can go to a specific message with number nnnn by typing:
You can go to a specific topic with number tttt by typing:
2. A file with all messages can be downloaded at this page:

[51] M. Chasles, Annales De Mathematique 18 (1827-1828), p.297,

[52] Paris Pamfilos, Gallery Geometrikon,
The item “All rectangular hyperbolas tangent to four lines

[53] H.S.M. Coxeter - The Real Projective Plane. Springer-Verlag, 1993

[54] Angel Montesdeoca - Apuntes de Geometrıa Proyectiva Conicas y Cuadricas

[55] Goormaghtigh, R., The Hervey Point on the general n-Line, The American Mathematical Monthly, Vol. 54, No. 6 (Jun. - Jul., 1947), pp. 327-331, 

[56] Edward C. Phillips,  On the Pentacardioid, University of Michigan, 1909.

[57] Guy, R. K.. (2007). The Lighthouse Theorem, Morley & Malfatti: A Budget of Paradoxes. The American Mathematical Monthly114(2), 97–141.

[58] Clark Kimberling, "Hofstadter points", Nieuw Archief voor Wiskunde 12 (1994) 109-114.

[59] Art of Problem Solving (AoPS), an Internet forum for High School Olympiads.
Available at:
[59a] Vu Thunh Tang - 4 Orthotransversals are concurrent
[59b] Vu Thunh Tang - Points of Concurrent orthotransversals Problem
[59c] Telv Cohl – Radical center of Five circles

[60] Rolinek, Michal & Anh Dung, Le. The Miquel points, pseudocircumcenter, and Euler-Poncelet point of a complete quadrilateral. Forum Geometricorum, 14 (2014) 145--153.
Available at:

[61] Jacob Steiner, Jacob Steiner’s Gesammelte Werke, vol. I.
Auflösung einer geometrischen Aufgabe aus Gergonne’s Annales de Mathem. t. XVII, p. 284.
Available at:, page 123.


[63] Roger Cuppens, Faire de la Géomètrie supérieure en jouant avec Cabri-Géomètre II, Tome II
APMEP Brochure no 125, ISBN: 2-912846-38-2

[64] A.S. Hart - Construction by the Ruler alone to determine the ninth Point of Intersection of two Curves of the third Degree.  Cambridge and Dublin Mathematical Journal 6 (1851) 181-182.

[65] Math Forum, about “Naming Polygons and Polyhedra”

[66] Quadri-and-Poly-Geometry (QPG), Internet forum for discussions on topics related to the Geometry of Quadrilaterals & Polygons,

[67] Sandor Nagydobai Kiss, On the Wittenbauer Type Parallelograms, INTERNATIONAL JOURNAL OF GEOMETRY, Vol. 4 (2015), No. 1, 27 – 36

[68] Dario Pellegrinetti, The six-point circle for the quadrangle, INTERNATIONAL JOURNAL OF GEOMETRY, Vol. 8 (2019), No. 2, 5 – 13

[69] Qingchun Ren, Jürgen Richter-Gebert & Bernd Sturmfels (2015) Cayley–Bacharach Formulas, The American Mathematical Monthly, 122:9, 845-854, DOI: 10.4169

[70] Tran Quang Hung - Some new theorems on Pentagon and Pentagram,

[71] Cabri Geometry - Solution of a difficult problem: the Quartic page

Chris van Tienhoven,
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