[Martin Ostwald, Sam Kutler, Robin Hartshorne, David Reed]

**QUADRANGLE** is found in English in the fifteenth century.

The word was later used later by Shakespeare.

**QUADRATIC** is derived from the Latin *quadratus,* meaning
"square." In English, *quadratic* was used in 1668 by John Wilkins
(1614-1672) in *An essay towards a real character, and a philosophical
language* [London: Printed for Sa. Gellibrand, and for John Martyn,
1668]. He wrote: "Those Algebraical notions of Absolute, Lineary, Quadratic,
Cubic" (OED2)

In his *Liber abbaci,* Fibonacci referred to problems involving
quadratic equations as *questiones secundum modum algebre.*

**QUADRATIC FORM** is dated 1859 in MWCD10.

The term **QUADRATIC RESIDUE** was introduced by Euler in a paper
of 1754-55 (Kline, page 611). The term *non-residue* is found in a
paper by Euler of 1758-59, but may occur earlier.

**QUADRATRIX.** The quadratrix of Hippias was probably invented by
Hippias but it became known as a quadratrix when Dinostratus used it for
the quadrature of a circle (DSB, article: "Dinostratus"; *Webster's New
International Dictionary,* 1909).

The term **QUADRATRIX OF HIPPIAS** was used by Proclus (DSB, article:
"Dinostratus").

The quadratrix of Hippias is the first named curve other than circle and line, according to Xah Lee's Visual Dictionary of Special Plane Curves website.

**QUADRILATERAL** appears in English in 1650 in Thomas Rudd's translation
of Euclid.

See also *quadrangle.*

The term **QUADRIVIUM** was used by Anicius Manlius Severinus Boethius
(ca. 480 - 524/525) in his *Arithmetica.* According to the DSB, this
is "probably the first time the word was used."

The term **QUANTICS** was used by Arthur Cayley (1821-1895).

**QUARTILE** is found in D. McAlister, *Proc. R. Soc.* XXIX:
"As these two measures, with the mean, divide the curve of facility into
four equal parts, I propose to call them the 'higher quartile' and the
'lower quartile' respectively. It will be seen that they correspond to
the ill-named 'probable errors' of the ordinary theory" (OED2).

The term **QUASI-PERIODIC FUNCTION** was introduced by Ernest Esclangon
(1876-1954) (DSB, article: Bohl).

The term **QUATERNION** was introduced by William Rowan Hamilton
(1805-1865). He used the word in a paper of 1843.

**QUEUEING.** The OED2 shows a use of "a queueing system" and "a
complex queueing problem" in 1951 in the *Journal of the Royal Statistical
Society,* and a use of "queueing theory" in 1954 in *Science News.*
[An interesting fact about the word *queueing* is that it contains
five consecutive vowels, the longest string of vowels in any English word,
except for a few obscure words not generally found in dictionaries.]

**QUINTIC** was used in English as an adjective in 1853 by Sylvester
in *Philosophical Magazine*: "May, To express the number of distinct
Quintic and Sextic invariants." The word was used as a noun in 1856 by
Cayley: "In the case of a quantic of the fifth order or quintic" (from
his *Works,* 1889) (OED2).

**QUINTILE** is found in 1922 in "The Accuracy of the Plating Method
of Estimating the Density of Bacterial Populations," *Annals of Applied
Biology* by R. A. Fisher, H. G. Thronton, and W. A. Mackenzie: "Since
the 3-plate sets are relatively scanty, we can best test their agreement
with theory by dividing the theoretical distribution of 43 values at its
quintiles, so that the expectation is the same in each group." There are
much earlier uses of this term in astrology [James A. Landau].

**QUOTIENT.** Joannes de Muris (c. 1350) used *numerus quociens.*

In the Rollandus Manuscript (1424) *quotiens* is used (Smith vol.
2, page 131).

Pellos (1492) used *quocient.*

**QUOTIENT GROUP** (for factor group) appears in 1893 in the *Bulletin
of the New York Mathematical Society* (OED2).

**QUOTIENT RING** is found in D. G. Northcott, "Some properties of
analytically irreducible geometric quotient rings," *Proc. Camb. Philos.
Soc.* 47, 662-667 (1951).