The OED shows a use of *eigenvalue* and *eigenfunction*
from 1927 *Nature* 23 July 117/1:

Among those...trying to acquire a general acquaintance with Schrödinger's wave mechanics there must be many who find their mathematical equipment insufficient to follow his first great problem -- to determine the eigenvalues and eigenfunctions for the hydrogen atom

Paul R. Halmos wrote in *Finite Dimensional Vector Spaces*
(1942, 1958), "Almost every combination of the adjectives proper,
latent, characteristic, eigen and secular, with the nouns root,
number and value, has been used in the literature for what we call a
proper value." Proper value is from the French *valeur propre.*
An eigenfunction is also called an autofunction.

**ELEMENT.** The term *Elemente* (elements) is found in
*Geometrie der Lage* (2nd ed., 1856) by Carl Georg Christian von
Staudt: "Wenn man die Menge aller in einem und demselben reellen
einfoermigen Gebilde enthaltenen reellen Elemente durch n + 1
bezeichnet und mit diesem Ausdrucke, welcher dieselbe Bedeutung auch
in den acht folgenden Nummern hat, wie mit einer endlichen Zahl
verfaehrt, so ..." [Ken Pledger].

Cantor also used the German *Element* in Math. Ann. (1882) XX.
114.

**ELLIPSE** was probably coined by Apollonius, who, according to
Pappus, had terms for all three conic sections. Michael N. Fried says
there are two known occasions where Archimedes used the terms
"parabola" and "ellipse," but that "these are, most likely, later
interpolations rather than Archimedes own terminology."

James A. Landau writes that the curve we call the "ellipse" was
generally called an *ellipsis* in the seventeenth century,
although the word *Elleipse* appears in a letter written by
Robert Hooke in 1679. *Ellipse* appears in a letter written by
Gilbert Clerke in 1687.

**ELLIPSOID** appears in a letter written in 1672 by Sir Isaac
Newton [James A. Landau].

The term **ELLIPTIC FUNCTION** was used by Adrien Marie Legendre
(1752-1833) in 1825 in volume 1 of *Traité des Fonctions
Elliptiques* and may appear in 1811 in volume 1 of his
*Exercises du Calcul Intégral.*

The term was also used in the title *Recherches sur les fonctions
elliptiques* by Niels Henrik Abel (1802-1829), which was published
in *Crelle's Journal* in September 1827.

*Elliptic function* appears in English in its modern sense in
1876 in the title *Elliptic Functions* by Cayley.

**ELLIPTIC INTEGRAL** is found in 1851 in the title *Theory of
Elliptic Integrals* by James Booth [James A. Landau].

**EQUATION** appears in English in 1570 in Sir Henry
Billingsley's translation of Euclid's *Elements*: "Many
rules...of Algebra, with the equations therein vsed." It also appears
in the preface to the translation, by John Dee: "That great
Arithmeticall Arte of Aequation: commonly called...Algebra."

Viete defines the term equation in chapter 8 of *In artem
analyticem isagoge* (1591), according to the DSB.

**EQUILATERAL** appears in English in 1570 in Sir Henry
Billingsley's translation of Euclid's *Elements*.

**EQUIPROBABLE** was used in 1921 by John Maynard Keynes
in *A Treatise on Probability*: "A set of exclusive and
exhaustive equiprobable alternatives" (OED2).

The term **ETHNOMATHEMATICS** was coined by Ubiratan
D'Ambrosio. In 1997 he wrote the following to Julio González
Cabillón (who provided the translation from Spanish to
English):

In 1977, the AAAS hosted a conference on Native American Sciences, where I presented a paper about "Science in Native Cultures," and where I called attention to the need for extending the methodology of Botany (ethnobotany was already in use) to the scientific knowledge as a whole, and to mathematics, doing "something like ethnoscience and ethnomathematics." That paper was never published. Five years later, in a meeting in Suriname in 1982, the concept was mentioned more explicitly. In the following years, I began usingIn the above, ICME 5 refers to the Fifth International Congress on Mathematics Education, held in Adelaide, Australia, in August 1984. The AAAS is the American Association for the Advancement of Science, of which Ubiratan D'Ambrosio is a Fellow.ethnomathematics.But it was not until ICME 5 that the term was "officially" recognized. My bookSocio-cultural Bases for Mathematics Educationbrings the first study about Ethnomathematics.

**EUCLIDEAN** was used in English in 1660 by Isaac Barrow
(1630-1677) in the preface of an edition of the *Elements*
(OED2).

**EUCLIDEAN GEOMETRY** appears in English about 1865 in *The
Circle of the Sciences,* edited by James Wylde.

**EUCLID'S ALGORITHM** appears in the 1907 edition of *Introduction
to Higher Algebra* by Maxime Bôcher [James A. Landau].

The **EULERIAN INTEGRAL** was named by Adrien Marie Legendre
(1752-1833) (Cajori 1919; DSB). He used *Eulerian integral of the
first kind* and *second kind* for the beta and gamma
functions. *Eulerian integral* appears in 1825-26 in the his
*Traité des Fonctions elliptiques et des Intégrales
Eulériennes* [James A. Landau].

**EULER PSEUDOPRIME** first appears in *Solved and
Unsolved Problems in Number Theory, 2nd ed.* by Daniel Shanks
(Chelsea, N. Y., 1979).

**EULER'S CONSTANT** (for 0.577...) appears in 1886 in *Integral
Calculus* by Isaac Todhunter (OED2). He writes, "The quantity
*C* is called Euler's constant." *Eulerian constant,*
referring to the same number, appears in the *Century
Dictionary* (1889-1897).

In his famous address in 1900, David Hilbert (1862-1943) used the term
*Euler-Mascheroni constant* (and the symbol *C*).
*Webster's New International Dictionary* of 1909 refers to the
constant as the *Eulerian constant.*

**EULER'S NUMBERS** (for the coefficients of a series for the
secant function) were so named by H. F. Scherk in 1825 in *Vier
mathematische Abhandlungen* (Cajori vol. 2, page 44).

The term **EVOLUTE** was defined by Christiaan Huygens (1629-1695)
in 1673 in *Horologium oscillatorium.* He used the Latin
*evoluta.* He also described the involute, but used the phrase
*descripta ex evolutione* [James A. Landau].

**EXPECTATION.** The word *expectatio* first appears in van
Schooten's translation of a tract by Huygens (Burton, page 461).

See also *mathematical expectation.*

The term **EXPONENT** was introduced by Michael Stifel (1487-1567)
in 1544 in *Arithmetica integra,* according to the *Dictionary
of Scientific Biography.*

**EXPONENTIAL CURVE** is found in 1704 in *Lexicon
technicum, or an universal English dictionary of arts and sciences*
by John Harris (OED2).

**EXPONENTIAL FUNCTION** appears in an 1843 paper by Sir William
Rowan Hamilton [James A. Landau].

**EXTREMUM** was used in 1904 by Oskar Bolza (1857-1942) in
*Lectures on the Calculus of Variations*: "The word 'extremum'
will be used for maximum and minimum alike, when it is not necessary
to distingish between them" (OED2).