## Definitions

• WordNet 3.6
• n quadrilateral a four-sided polygon
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Webster's Revised Unabridged Dictionary
• Quadrilateral (Geom) A plane figure having four sides, and consequently four angles; a quadrangular figure; any figure formed by four lines.
• Quadrilateral An area defended by four fortresses supporting each other; as, the Venetian quadrilateral, comprising Mantua, Peschiera, Verona, and Legnano.
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Century Dictionary and Cyclopedia
• quadrilateral Having four sides; composed of four lines.
• n quadrilateral A figure formed of four Straight lines. In the old geometry the lines are supposed to terminate at four intersections; in modern geometry the lines are regarded as infinite, and a plane quadrilateral as having six angles. Such a figure has three diagonals or axes, being straight lines through opposite vertices, and three centers, which are the intersections of the axes.
• n quadrilateral Milit., the space inclosed between, and defended by, four fortresses: as, the Bulgarian quadrilateral. The most famous quadrilateral was that in northern Italy, inclosed by the fortresses of Peschiera, Mantua, Verona, and Legnago.
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Chambers's Twentieth Century Dictionary
• n Quadrilateral (geom.) a plane figure having four sides: the four fortresses—Mantua, Verona, Peschiera, and Legnago—which form the points of a quadrilateral
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## Etymology

Webster's Revised Unabridged Dictionary

## Usage

### In literature:

A figure that is bounded by four straight lines is termed a quadrangle, quadrilateral or tetragon.
"Mechanical Drawing Self-Taught" by Joshua Rose
"Archeological Expedition to Arizona in 1895" by Jesse Walter Fewkes
These latter are nothing more or less than clumsy lugs or quadrilaterals.
"The Sailor's Word-Book" by William Henry Smyth
For, in spite of Solferino, it was probable that the tide of victory would be hurled back from the Quadrilateral.
"The Dodge Club" by James De Mille
No more fitting site could be found for the chateau than the quadrilateral formed by these two streams.
"In Château Land" by Anne Hollingsworth Wharton
This left in the hands of the Austrians still an important part of northern Italy known as the Quadrilateral.
"The Story of the Great War, Volume I (of 8)" by Various
Thus the quadrilateral space MDCA contains the Rolandic area.
"Manual of Surgery Volume Second: Extremities--Head--Neck. Sixth Edition." by Alexander Miles
The Quadrilateral was passed; then came Franchard.
"The Works of Robert Louis Stevenson" by Robert Louis Stevenson
British and Belgian troops held Antwerp and the fortresses of the Belgian Quadrilateral in force.
"The Angel of the Revolution" by George Griffith
"A Monograph on the Sub-class Cirripedia (Volume 1 of 2)" by Charles Darwin
The peculiar, oblong, quadrilateral form was probably common to both.
"Cathedrals of Spain" by John A. (John Allyne) Gade
Rectilinear figures cannot be divided into triangles and quadrilaterals because there are rectilinear figures which have more than four sides.
"Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 5" by Various
It is quadrilateral in shape, consisting of four unequal sides flanked by towers and built round a courtyard.
"Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 7" by Various
Upon entering, one finds himself in a quadrilateral court, which is open to the sky.
"Mentone, Cairo, and Corfu" by Constance Fenimore Woolson
Bernard wished to construct one great fortress, like Antwerp or the once famous strongholds of the Quadrilateral.
"Nooks and Corners of the New England Coast" by Samuel Adams Drake
In its centre a quadrilateral marble basin, which still exists, formerly caught the rain-water that dripped from the roof of the portico.
"One of Cleopatra's Nights and Other Fantastic Romances" by Thophile Gautier
There are ten quadrilateral prisms, the largest of which has a base of 10 centimetres, the others decreasing by 1 centimetre.
"The Montessori Method" by Maria Montessori
The walled part of the town is a quadrilateral with faces of about 1200 yds.
"Encyclopaedia Britannica, 11th Edition, Volume 15, Slice 7" by Various
After Solferino the allies prepared to besiege the Quadrilateral.
"Encyclopaedia Britannica, 11th Edition, Volume 15, Slice 1" by Various
They form an enormous quadrilateral terrace, round which a portico of granite columns ran.
"Old Rome" by Robert Burn
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### In science:

Thus, S and T differ in Z within the quadrilateral deﬁned by the largest and smallest barred and unbarred vertices of Z ; in S the larger ones are connected, while in T the two smaller ones are conected.
Tamari lattices and noncrossing partitions in type B and beyond
It is the space of pairs of quadrilaterals abcd and ABCD , where the second is inscribed into the ﬁrst, considered up to pro jective transformations.
Moduli spaces of convex projective structures on surfaces
Moreover for any pair of adjacent triangles AiAj Ak and Aj AkAl forming a quadrilateral AiAj AkAl inscribed into the quadrilateral aiaj ak al one can also compute a pair of cross-ratios and assign it to two points on the diagonal Aj Ak .
Moduli spaces of convex projective structures on surfaces
We assign to every triple of ﬂags at the vertices of a Farey triangle their triple ratio, and to every quadruple of ﬂags at the vertices of a Farey quadrilateral the related two cross-ratios, pictured at the diagonal.
Moduli spaces of convex projective structures on surfaces
Figure 2: Notation for a triangle (a) and for a quadrilateral (b).
On simple ideal hyperbolic Coxeter polytopes
Let Q be a quadrilateral 2-face with vertices V , Vi , Vj and Vij .
On simple ideal hyperbolic Coxeter polytopes
Figure 4: Example of a quadrilateral V ViVij Vj .
On simple ideal hyperbolic Coxeter polytopes
Therefore, the nodes vi and vj are joined in the diagram ΣV , that implies that each quadrilateral face containing the vertex V corresponds to a pair of neighboring nodes in ΣV .
On simple ideal hyperbolic Coxeter polytopes
Hence, V belongs to at most n quadrilateral 2-faces.
On simple ideal hyperbolic Coxeter polytopes
While proving Lemma 5 we estimated the number of pairs (vi , vj ) such that the 2-face corresponding to the diagram ΣV \{vi , vj } may be quadrilateral.
On simple ideal hyperbolic Coxeter polytopes
Clearly, this estimate of the number of quadrilaterals is rough.
On simple ideal hyperbolic Coxeter polytopes
Clearly, the number of quadrilateral 2-faces containing the vertex V is bounded by M (ΣV ).
On simple ideal hyperbolic Coxeter polytopes
If 0 < r < R < 1 2 diam(E ), then γZ (r) and γZ (R) are the sides of some quadrilateral QZ (r, R) ⊂ Ω whose other two sides are parts of the boundary L.
Constructive Function Theory on Sets of the Complex Plane through Potential Theory and Geometric Function Theory
Let mZ (r, R) be the module of this quadrilateral, i.e., the module of the family of arcs that separate the sides γZ (r) and γZ (R) in QZ (r, R) (see , ).
Constructive Function Theory on Sets of the Complex Plane through Potential Theory and Geometric Function Theory
This quadrilateral can be chosen such that the two ﬁnite length adjacent sides are of length arcsinh1.
Minimal length of two intersecting simple closed geodesics
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