*St. Andrew's cross* is found in 1615, although not in a
mathematical context, in Crooke, *Body of Man*: "[They] doe
mutually intersect themselues in the manner of a Saint Andrewes
crosse, or this letter X" (OED2).

The term **ST. PETERSBURG PARADOX** was coined by d'Alembert, who
received a solution by Daniel Bernoulli in 1731 and published it in
Commentarii Akad. Sci. Petropolis 5, 175-192 (1738). The originator
of the St. Petersburg paradox was Niklaus Bernoulli. (Jacques Dutka,
"On the St. Petersburg paradox," *Arch. Hist. Exact Sci.* 39,
No.1, 1988)

**SADDLE POINT** is found in 1922 in *A Treatise on the Theory
of Bessel Functions* by G. N. Watson (OED2).

**SALIENT ANGLE.** The OED2 has a 1687 citation for *Angle
Saliant.*

In 1781 Sir John T. Dillon wrote in *Travels Through Spain*: "He
could find nothing which seemed to confirm the opinion relating to
the salient and reentrant angles" (OED2).

*Mathematical Dictionary and Cyclopedia of Mathematical Science*
(1857) has: "SALIENT ANGLE of a polygon, is an interior angle, less
than two right angles."

See also *convex polygon.*

**SAMPLE SPACE** appears in W. Feller, "Note on regions similar
to the sample space," *Statist. Res. Mem.,* Univ. London 2,
117-125 (1938).

The term may have been used earlier by Richard von Mises (1883-1953).

**SCALAR.** See *vector.*

**SCALAR PRODUCT.** See *vector product.*

**SCALENE.** In Sir Henry Billingsley's 1570 translation of
Euclid's *Elements* *scalenum* is used as a noun: "Scalenum
is a triangle, whose three sides are all unequall."

In 1642
*scalene* is found in a rare use as a noun, referring to a
scalene triangle in *Song of Soul* by Henry More: "But if 't
consist of points: then a Scalene I'll prove all one with an
Isosceles."

The earliest use of *scalene* as an adjective is in
1684 in *Angular Sections* by John Wallis: "The Scalene Cone and
Cylinder."

The earliest use of *scalene* as an adjective to
describe a triangle is in 1734 in *The Builder's Dictionary.*
(All citations are from the OED2.)

**SCATTER DIAGRAM** is found in 1925 in F. C. Mills,
*Statistical Methods* X. 366: "The equation to a straight line,
fitted by the method of least squares to the points on the scatter
diagram, will express mathematically the average relationship between
these two variables" (OED2).

*Scattergram* is found in 1938 in A. E. Waugh, *Elem.
Statistical Method*: "This is the method of plotting the data on a
scatter diagram, or scattergram, in order that one may see the
relationship" (OED2).

**SCIENTIFIC NOTATION.** In 1895 in *Computation Rules and
Logarithms* Silas W. Holman referred to the notation as "the
notation by powers of ten." In the preface, which is dated August
1895, he wrote: "The following pages contain ... an explanation of
the use of the notation by powers of ten ... the notation by powers
of 10, as in the explanation here given. It seems unfortunate that
this simple notation, so useful in computation and so great an aid in
the explanation of numerical relations, is not universally
incorporated into arithmetical instruction." [James A. Landau]

In *A Scrap-Book of Elementary Mathematics* (1908) by William F.
White, the notation is called the *index notation.*

*Scientific notation* appears in *Webster's Second New
International Dictionary* (1934), which says that numbers in this
format are sometimes called *condensed numbers.*

Other terms are *exponential notation* and *standard
notation.*

**SECANT** (in trigonometry) was introduced by Thomas Fincke
(1561-1656) in his *Thomae Finkii Flenspurgensis Geometriae rotundi
libri XIIII,* Basileae: Per Sebastianum Henricpetri, 1583. (His
name is also spelled Finke, Finck, Fink, and Finchius.) Fincke wrote
*secans* in Latin.

Vieta (1593) did not approve of the term *secant,* believing it
could be confused with the geometry term. He used
*Transsinuosa* instead (Smith vol. 2, page 622).

**SELF-CONJUGATE.** Kramer (p. 388) says Galois used this
term, referring to a normal subgroup.

The term **SEMI-CUBICAL PARABOLA** was coined by John Wallis
(Cajori 1919, page 181).

**SEMIGROUP** appears in English in 1904 in the *Bulletin of the
American Mathematical Society* (OED2).

**SEMI-INVARIANT** appears in R. Frisch, "Sur les semi-invariants
et moments employés dans l'étude des distributions
statistiques," Oslo, Skrifter af det Norske Videnskaps Academie, II,
Hist.-Folos. Klasse, no. 3 (1926) [James A. Landau].

**SENTENTIAL CALCULUS** is dated 1937 in MWCD10.

**SEPARABLE** appears in 1831 in *Elements of the Integral
Calculus* (1839) by J. R. Young: "We shall first consider the
general form X *dy* + Y *dx* = 0, which is the simplest for
which the variables are separable: X being a function of *x*
without *y,* and Y a function of *y* without *x.*

**SEQUENCE.** The OED2 shows a use by Sylvester in 1882
in the *American Journal of Mathematics* with the "rare"
definition of a succession of natural numbers in order.

*Sequence* appears with its modern mathematical definition in
Edward B. Van Vleck, "On Linear Criteria for the Determination of the
Radius of Convergence of a Power Series," *Transactions of the
American Mathematical Society,* Vol. 1, No. 3. (Jul., 1900). [The
term may be considerably older.]

**SERIES.** According to Smith (vol. 2, page 481), "The early
writers often used *proportio* to designate a series, and this
usage is found as late as the 18th century."

John Collins (1624-1683) wrote to James Gregory on Feb. 2, 1668/1669, "...the Lord Brouncker asserts he can turne the square roote into an infinite Series" (DSB, article: "Newton").

*Series* is found in 1676
in Collins in Rigaurd * Corr. Sci. Men* (1841) II. 10:
"The reducibility of Davenant’s problem to infinite series" (OED2).

According to Smith (vol. 2, page 497), "The change to the name 'series' seems to have been due to writers of the 17th century. ... Even as late as the 1693 edition of his algebra, however, Wallis used the expression 'infinite progression' for infinite series."

In the English translation of Wallis' algebra (translated by him and published in 1685), Wallis wrote:

Now (to return where we left off:) Those Approximations (in the Arithmetick of Infinites) above mentioned, (for the Circle or Ellipse, and the Hyperbola;) have given occasion to others (as is before intimated,) to make further inquiry into that subject; and seek out other the like Approximations, (or continual approaches) in other cases. Which are now wont to be called by the name ofTheInfinite Series,orConverging Series,or other names of like import.

The term **SET** first appears in *Paradoxien des Unendlichen*
(Paradoxes of the Infinite), Hrsg. aus dem schriftlichen Nachlasse des
Verfassers von Fr. Prihonsky, C. H. Reclam sen., xi, pp. 157, Leipzig,
1851. This small tract by Bernhard Bolzano (1781-1848) was published
three years after his death by a student Bolzano had befriended
(Burton, page 592).

*Menge* (set) 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].

Georg Cantor (1845-1918) did not define the concept of a set
in his early works on set theory, according to Walter
Purkert in *Cantor's Philosophical Views.*

Cantor's first definition of a set appears in an 1883 paper: "By a
set I understand every multitude which can be conceived as an entity,
that is every embodiment [*Inbegriff*] of defined elements which
can be joined into an entirety by a rule." This quotation is taken
from *Über unendliche lineare Punctmannichfaltigkeiten,*
Mathematische Annalen, 21 (1883).

In 1895 Cantor used the word *Menge* in *Beiträge zur
Begründung der Transfiniten Mengenlehre,* Mathematische
Annalen, 46 (1895):

By a set we understand every collection [This translation was taken fromZusammenfassung]Mof defined, well-distinguished objectsmof our intuition [Zusammenfassung] or our thinking (which are called the elements ofMbrought together to form an entirety.

**SET THEORY** appears in Georg Cantor, "Sur divers
théorèmes de lat théorie des ensembles de points
situés dans un espace continu à n dimensions.
Première communication." *Acta Mathematica* 2, pp. 409-414
(1883) [James A. Landau].

The term is also found in Ivar Bendixson, "Quelques
théorèmes de la théorie des ensembles de points,"
*Acta Mathematica* 2, pp. 415-429 (1883) [James A. Landau].

In a letter to Mittag-Leffler, Cantor wrote on May 5, 1883,
"Unfortunately, I am prevented by *many* circumstances from
working regularly, and I would be fortunate to find, in you and your
distinguished students, coworkers who probably will soon surpass me
in 'set theory.'" This quotation, which is presumably a translation,
was taken from *Cantor's Continuum Problem* by Gregory H. Moore.

*Set theory* is found in English in 1926 in *Annals of
Mathematics* (2d ser.) XXVII. 487: "An important idea in set
theory is that of relativity" (OED2 update).

**SHORT DIVISION** appears in the *Century Dictionary*
(1889-97).

**SIEVE OF ERATOSTHENES** is found in English in 1803 in a
translation of *Bossut's Gen. Hist. Math.*: "The famous sieve of
Eratosthenes..affords an easy and commodious method of finding prime
numbers" (OED2).

**SIGN OF AGGREGATION** is found in 1900 in *Teaching of
Elementary Mathematics* by David Eugene Smith: "Signs of
aggregation often trouble a pupil more than the value of the subject
warrants. The fact is, in mathematics we never find any such
complicated concatenations as often meet the student almost on the
threshold of algebra."

**SIGN TEST** appears in W. MacStewart, "A note on the power of
the sign test," *Ann. Math. Statist.* 12 (1941) [James A.
Landau].

**SIGNED NUMBER.** *Signed magnitude* appears in 1873 in
*Proc. Lond. Math. Soc.*: "A signed magnitude" (OED2).

*Signed number* appears in the title "The [Arithmetic]
Operations on Signed Numbers" by Wilson L. Miser in *Mathematics
Magazine* (1932).

**SIGNIFICANCE TEST.** *Test of significance* is found in
1907 in *Biometrika* V. 183: " Several other cases of probable
error tests of significance deserve reconsideration" (OED2).

*Testing the significance* is found in "New tables for testing
the significance of observations," *Metron* 5 (3) pp 105-108
(1925) [James A. Landau].

*Test of significance* is found in 1935 in *Proc. Cambr.
Philos. Soc.* XXXI. 230: "The test of significance of a
correlation coefficient has been shown..to be little vitiated by
non-normality" (OED2).

See also *rank correlation.*

**SIGNIFICANT DIGIT.** Smith (vol. 2, page 16) indicates
Licht used the term in 1500, and shows a use of "neun bedeutlich
figuren" by Grammateus in 1518.

In 1544, Michael Stifel wrote, "Et nouem quidem priores, significatiuae uocantur."

*Signifying figures* is found in 1542 in Robert Recorde, *Gr.
Artes* (1575): "Of those ten one doth signifie nothing... The
other nyne are called Signifying figures" (OED2).

*Significant figures* is found in 1660 in Milton, *Free
Commw.*: "Only like a great Cypher set to no purpose before a long
row of other significant Figures" (OED2).

*Significant figures* is found in 1827 in Hutton, *Course
Math.*: "The first nine are called Significant Figures, as
distinguished from the cipher, which is of itself quite
insignificant" (OED2).

*Mathematical Dictionary and Cyclopedia of Mathematical Science*
(1857) has this definition:

SIGNIFICANT. Figures standing for numbers are called significant figures. They are 1, 2, 3, 4, 5, 6, 7, 8, and 9.The term

**SIMPLE CLOSED CURVE** occurs in "Theory on Plane Curves in
Non-Metrical Analysis Situs," Oswald Veblen, *Transactions of the
American Mathematical Society,* Vol. 6, No. 1. (Jan., 1905).

**SIMPLEX.** William Kingdon Clifford (1848-1879) used the
term *prime confine* in "Problem in Probability,"
*Educational Times,* Jan. 1886:

Now consider the analogous case in geometry ofndimensions. Corresponding to a closed area and a closed volume we have something which I shall call aconfine.Corresponding to a triangle and to a tetrahedron there is a confine withn+ 1 corners or vertices which I shall call aprime confineas being the simplest form of confine.

*Simplex approach* is found in 1951 by George B. Dantzig (1914-
) in T. C. Koopman's *Activity Analysis of Production and
Allocation* xxi. 339: "The general nature of the 'simplex'
approach (as the method discussed here is known)" (OED2).

**SIMPLY ORDERED SET** was defined by Cantor in *Mathematische
Annalen,* vol. 46, page 496.

**SIMPSON'S RULE** is found in 1875 in *An elementary treatise
on the integral calculus* by Benjamin Williamson (1827-1916):
"This and the preceding are commonly called 'Simpson's rules' for
calculating areas; they were however previously noticed by Newton"
(OED2).

**SIMSON LINE.** The theorem was attributed to Robert Simson
(1687-1768) by François Joseph Servois (1768-1847) in the
Gergonne's Journal, according to Jean-Victor Poncelet in
*Traité des propriétés projectives des
figures.* The line does not appear in Simson's work and is
apparently due to William Wallace. [The University of St. Andrews
website]

**SIMULTANEOUS EQUATIONS** occurs in 1842 in Colenso, *Elem.
Algebra* (ed. 3): "Equations of this kind, ... to be satisfied by
the same pair or pairs of values of *x* and *y,* are called
simultaneous equations" (OED2).

*Simultaneous equations* also appears in 1842 in G. Peacock,
*Treat. Algebra*: "Such pairs or sets of equations in which the
same unknown symbols appear, which are assumed to possess the same
values throughout, are called simultaneous equations" (OED2).

**SINE.** Aryabhata the Elder (476-550) used the word *jya*
for sine in *Aryabhatiya,* which was finished in 499.

According to some sources, *sinus* first appears in Latin in a
translation of the Algebra of al-Khowarizmi by Gherard of Cremona
(1114-1187). For example, Eves (page 177) writes:

The origin of the wordHowever, Boyer (page 278) places the first appearance ofsineis curious. Aryabhata called inardha-jya("half-chord") and alsojya-ardha("chord-half"), and then abbreviated the term by simply usingjya("chord"). Fromjyathe Arabs phonetically derivedjiba,which, following Arabian practice of omitting vowels, was written asjb.Nowjiba,aside from its technical significance, is a meaningless word in Arabic. Later writers, coming acrossjbas an abbreviation for the meaninglessjiba,substitutedjaibinstead, which contains the same letters and is a good Arabic word meaning "cove" or "bay." Still later, Gherardo of Cremona (ca. 1150), when he made his translations from the Arabic, replaced the Arabianjaibby its Latin equivalent,sinus,whence came our present wordsine.

Fibonacci used the term *sinus rectus arcus.*

Regiomontanus (1436-1476) used *sinus, sinus rectus,* and
*sinus versus* in *De triangulis omnimodis* (On triangles
of all kinds; Nuremberg, 1533) [James A. Landau].

Copernicus and Rheticus did not use the term sine (DSB).

The earliest known use of *sine* in English is by Thomas Fale in
1593:

This Table of Sines may seem obscure and hard to those who are not acquainted with Sinicall computation.The citation is above is from

The term **SINGLE-VALUED FUNCTION** (meaning analytic function)
was used by Yulian-Karl Vasilievich Sokhotsky (1842-1927).

The term **SINGULAR INTEGRAL** is due to Lagrange (Kline, page 532).

The term is found in 1831 in *Elements of the Integral Calculus*
(1839) by J. R. Young:

We see, therefore, that it is possible for a differential equation to have other integrals besides the complete primitive, but derivable from it by substituting in it, for the arbitrary constantc,each of its values given in terms ofxandyby the equation (5). Such integrals are calledsingular integrals,orsingular solutionsof the proposed differential equation.

**SINGULAR POINT** appears in a paper by George Green published in
1828. The paper also contains the synonymous phrase "singular value"
[James A. Landau].

In *An Elementary Treatise on Curves, Functions and Forces*
(1846), Benjamin Peirce writes, "Those points of a curve, which
present any peculiarity as to curvature or discontinuity, are called
*singular points.*"

**SKEW DISTRIBUTION** appears in 1895 in a paper by Karl Pearson
[James A. Landau].

**SKEW SYMMETRIC MATRIX.** *Skew symmetric determinant*
appears in 1849 in Arthur Cayley, *Jrnl. für die reine und
angewandte Math.* XXXVIII. 93: "Ces déterminants peuvent
être nommés ‘gauches et symmétriques’" (OED2).

*Skew symmetric determinant* appears in 1911 in T. Muir,
*Hist. Determinants*: "Any skew determinant is expressible in
terms of skew symmetric determinants and those of the original
determinant which are not included in the latter" (OED2).

*Skew symmetric matrix* appears in "Linear Algebras," Leonard
Eugene Dickson, *Transactions of the American Mathematical
Society,* Vol. 13, No. 1. (Jan., 1912).

**SKEWES NUMBER** appears in 1949 in Kasner & Newman,
*Mathematics and the Imagination*: "A veritable giant is
Skewes' number, even bigger than a gogolplex" (OED2).

**SLIDE RULE.** In 1630, the terms *Grammelogia* and
*mathematical ring* were used for a new device which,
unlike Gunter's scale, had moving parts.

In 1632, the terms *circles of proportion* and *horizontal
instrument* were used to describe Oughtred's device, in a 1632
publication, *Circles of Proportion.*

*Slide rule* appears in the Diary of Samuel Pepys (1633-1703) in
April 1663: "I walked to Greenwich, studying the slide rule for
measuring of timber." However, the device referred to may not have
been a slide rule in the modern sense.

*Slide rule* appears in 1838 in *Civil Eng. & Arch. Jrnl.*:
"To assist in facilitating the use of the slide rule among working
mechanics" (OED2).

Amédée Mannheim (1831-1906) designed (c. 1850) the Mannheim Slide Rule.

*Sliding-rule* and *sliding-scale* appear in 1857 in
*Mathematical Dictionary and Cyclopaedia of Mathematical
Science,* defined in the modern sense.

*Slide rule* appears in 1876 in *Handbk. Scientif. Appar.*:
"The slide rule,--an apparatus for effecting multiplications and
divisions by means of a logarithmic scale" (OED2).

**SLOPE** is found in 1857 in *Mathematical Dictionary and
Cyclopedia of Mathematical Science*:

SLOPE. Oblique direction. The slope of a plane is its inclination to the horizon. This slope is generally given by its tangent. Thus, the slope, 1/2, is equal to an angle whose tangent is 1/2; or, we generally say, the slope is 1 upon 2; that is, we rise, in ascending such a plane, a vertical distance of 1, in passing over a horizontal distance of 2. The slope of a curved surface, at any point, is the slope of a plane, tangent to the surface at that point.

*Slope-intercept form* is dated ca. 1942 in MWCD10.

The term **SOCIAL MATHEMATICS** was used by Condorcet (1743-1794)
and may have been coined by him.

**SOLID GEOMETRY** appears in 1733 in the title *Elements
of Solid Geometry* by H. Gore (OED2).

**SOLID OF REVOLUTION** is found in English in 1816 in the
translation of Lacroix's *Differential and Integral Calculus*:
"To find the differentials of the volumes and curve surfaces of
solids of revolution" (OED2).

**SOLIDUS** (the diagonal fraction bar). Arthur Cayley
(1821-1895) wrote to Stokes, "I think the 'solidus' looks very well
indeed...; it would give you a strong claim to be President of a
Society for the Prevention of Cruelty to Printers" (Cajori vol. 2,
page 313).

The word *solidus* appears in this sense in the *Century
Dictionary* of 1891.

**SOLUBLE (referring to groups).** Ferdinand Georg Frobenius
(1849-1917) wrote in a paper of 1893:

Jede Gruppe, deren Ordnung eine Potenz einer Primzahl ist, ist nach einem Satze von Sylow die Gruppe einer durch Wurzelausdrücke auflösbaren Gleichung oder, wie ich mich kurz ausdrücken will, einer auflösbare Gruppe. [Every group of prime-power order is, by a theorem of Sylow, the group of an equation which is soluble by radicals or, as I will allow myself to abbreviate, a soluble group.]Peter Neumann believes this is likely to be the passage that introduced the term "auflösbar" ["soluble"] as an adjective applicable to groups into mathematical language.

**SOLUTION SET** appears in 1959 in *Fund. Math.* by
Allendoerfer and Oakley: Given a universal set *X* and an
equation *F*(*x*) = *G*(*x*) involving *x,*
the set {*x*|*F*(*x*) = *G*(*x*)} is called
the solution set of the given equation" (OED2).

The term may occur in found in Imsik Hong, "On the null-set of a
solution for the equation $\Delta u+k^2u=0$," *Kodai Math. Semin.
Rep.* (1955).

The term **SPECIALLY MULTIPLICATIVE FUNCTION** was coined by D. H.
Lehmer (McCarthy, page 65).

The term **SPECTRUM** (the set of eigenvalues of a Hermitian
operator) was coined by Hilbert (DSB).

**SPHERICAL CONCHOID** was coined by Herschel.

**SPHERICAL GEOMETRY** appears in 1728 in Chambers'
*Cyclopedia* (OED2).

The words *spherical geometry* and *versed sine* were used
by Edgar Allan Poe in his short story *The Unparalleled Adventure
Of One Hans Pfaall.*

**SPHERICAL HARMONICS.** A. H. Resal used the term *fonctions
spheriques* (Todhunter, 1873) [Chris Linton].

*Spherical harmonics* was used in 1867 by William Thomson
(1824-1907) and Peter Guthrie Tait (1831-1901) in * Nat.
Philos.*: "General expressions for complete spherical harmonics of
all orders" (OED2).

**SPHERICAL TRIANGLE** Menelaus of Alexandria (fl. A. D. 100) used
the term *tripleuron* in his *Sphaerica,* according to
Pappus. According to the DSB, "this is the earliest known mention of
a spherical triangle."

**SPHERICAL TRIGONOMETRY** is found in the title *Trigonometria
sphaericorum logarithmica* (1651) by Nicolaus Mercator
(1620-1687).

The term is found in English in a letter by John Collins to the Governors of Christ's Hospital written on May 16, 1682, in the phrase "plaine & spherick Trigonometry, whereby Navigation is performed" [James A. Landau].

**SPINOR** appears in 1931 in *Physical Review.* The citation
refers to spinor analysis developed by B. Van der Waerden (OED2).

The term **SPORADIC GROUP** was coined by William Burnside
(1852-1927) in the second edition of his *Theory of Groups of
Finite Order,* published in 1911 [John McKay].

**SQUARE MATRIX** was used by Arthur Cayley in 1858 in
*Collected Math. Papers* (1889): "The term matrix might be used
in a more general sense, but in the present memoir I consider only
square or rectangular matrices" (OED2).

The term **STANDARD DEVIATION** was introduced by Karl Pearson
(1857-1936) in 1893, "although the idea was by then nearly a century
old" (Abbott; Stigler, page 328). According to the DSB, "The term
'standard deviation' was introduced in the lecture of 31 January
1893, as a convenient substitute for the cumbersome 'root mean square
error' and the older expressions 'error of mean square' and 'mean
error.'"

**STANDARD ERROR** is found in 1897 in G. U. Yule, *Jrnl. R.
Statist. Soc.* 60: "We see that [sigma]_{1}[sqrt](1 -
*r*^{2}) is the standard error made in estimating
*x*" (OED2).

**STANDARD POSITION** is dated 1950 in MWCD10.

The term **STAR PRIME** was coined in 1988 by Richard L.
Francis (Schwartzman, p. 206).

**STATISTICS** originally referred to political science and it is
difficult to determine when the word was first used in a purely
mathematical sense. The earliest citation of the word
*statistics* in the OED2 is in 1770 in W. Hooper's translation of
*Bielfield's Elementary Universal Education:* "The science, that
is called statistics, teaches us what is the political arrangement of
all the modern states of the known world." However, there are earlier
citations for *statistical* and Latin and German forms of
*statistic,* all used in a political sense.

**STEP FUNCTION** is dated ca. 1929 in MWCD10.

**STEREOGRAPHIC.** According to Schwartzman (p. 207), "the term
seems to have been used first by the Belgian Jesuit François
Aguillon (1566-1617), although the concept was already known to the
ancient Greeks."

In *Flattening the Earth: Two Thousand Years of Map
Projections,* John P. Snyder attributes the term to d'Aguillon in
1613 [John W. Dawson, Jr.].

**STIELTJES INTEGRAL** is found in Henri Lebesgue, "Sur
l'intégrale de Stieltjes et sur les opérations
linéaires," *Comptes Rendus Acad. Sci. Paris* 150 (1910)
[James A. Landau].

The terms **STIRLING NUMBERS OF THE FIRST** and **SECOND KIND**
were coined by Niels Nielsen (1865-1931), who wrote in German
"Stirlingschen Zahlen erster Art" [Stirling numbers of the first kind]
and "Stirlingschen Zahlen zweiter Art" [Stirling numbers of the second
kind]. Nielsen's masterpiece, "Handbuch der Theorie der
Gammafunktion" [B. G. Teubner, Leipzig, 1906], had a great influence,
and the terms progressively found their acceptance (Julio
González Cabillón).

John Conway believes the newer terms *Stirling cycle* and
*Stirling (sub)set* numbers were introduced by R. L. Graham, D.
E. Knuth, and O. Patshnik in *Concrete Mathematics* (Addison
Wesley, 1989 & often reprinted).

**STIRLING'S FORMULA.** Lacroix used *Théorème de
Stirling* in *Traité élémentaire de calcul
différentiel et de calcul intégral* (1797-1800).

*Stirling's approximation* appears in 1938 in *Biometrika*
(OED2).

**STOCHASTIC** is found in English as early as 1662 with the
obsolete meaning "pertaining to conjecture."

In its modern sense, the term was used in 1917 by Ladislaus
Josephowitsch Bortkiewicz (1868-1931) in *Die Iterationem* 3:
"Die an der Wahrscheinlichkeitstheorie orientierte, somit auf 'das
Gesetz der Grossen Zahlen' sich gründende Betrachtng empirischer
Vielheiten mö ge als Stochastik ... bezeichnet werden" (OED2).

*Stochastic process* is found in A. N. Kolmogorov, "Sulla forma
generale di un prozesso stocastico omogeneo," *Rend. Accad. Lincei
Cl. Sci. Fis. Mat.* 15 (1) page 805 (1932) [James A. Landau].

*Stochastic process* is also found in A. Khintchine
"Korrelationstheorie der stationäre stochastischen Prozesse,"
*Math. Ann.* 109 (1934) [James A. Landau].

*Stochastic process* occurs in English in "Stochastic processes
and statistics," * Proc. Natl. Acad. Sci. USA* 20 (1934).

**STOKES'S THEOREM.** According to Finney and Thomas
(page 987), Stokes learned of the theorem from Lord Kelvin in 1850 and
"a few years later, thinking it would make a good examination
question, put it on the Smith Prize examination. It has been known as
Stokes's theorem ever since."

*Stokes' theorem* is found in 1893 in J. J. Thomsom, *Notes
Recent Res. Electr. & Magnetism* (OED2).

**STRAIGHT ANGLE** appears in English in 1889 in Dupuis, *Elem.
Synth. Geom.*: "One-half of a circumangle is a straight angle, and
one-fourth of a circumangle is a right angle" (OED2).

There are earlier citations in the OED2 for the term with the obsolete meaning of "a right angle."

The term **STRANGE ATTRACTOR** was coined by David Ruelle
and Floris Takens in their classic paper "On the Nature of Turbulence"
[*Communications in Mathematical Physics,* vol. 20, pp. 167-192,
1971], in which they describe the complex geometric structure of an
attractor during a study of models for turbulence in fluid flow.

**STRATIFIED SAMPLING** occurs in J. Neyman, "On the two different
aspects of the representative method; the method of stratified
sampling and the method of purposive selection," *J. R. Satatist.
Soc* 97 (1934) [James A. Landau].

**STRONG LAW OF LARGE NUMBERS** is found in A. N. Kolmogorov, "Sur
la loi forte des grandes nombres," *Comptes Rendus de l'Acade/mie
des Sciences,* Paris 191 page 910 (1930) [James A. Landau].

**STRONG PSEUDOPRIME** is found in Pomerance, Carl; Selfridge,
J.L.; Wagstaff, Samuel S. Jr. "The pseudoprimes to 25 x
10^{9}," *Math. Comput.* 35, 1003-1026 (1980).

**STROPHOID** was coined by E. Montucci in 1846, according to
Schwartzman (page 209) and Smith (vol. 2, page 330). (However, Julio
González Cabillón says that, in reading the article "La
Strophoide" (1846), it does not seem that Montucci is introducing a
new term.)

**STUDENT'S t-DISTRIBUTION.** The letter

*"Student's" t-distribution* appears in 1929 in *Nature*
(OED2).

*t-distribution* appears (without Student) in A. T. McKay,
"Distribution of the coefficient of variation and the extended 't'
distribution," *J. Roy. Stat. Soc.,* n. Ser. 95 (1932).

*Student's distribution* (without "t") appears in R. A. Fisher,
"Applications of 'Student's' Distribution," *Metron,* 3, 90-114.
This paper is dated both 1925 and 1926 in separate bibliographies
[James A. Landau].

"Student" was the pseudonym of William Sealy Gossett (1876-1937).

**STUDENTIZATION.** According to Hald (p. 669), William Sealy
Gossett (1876-1937) used the term *Studentization* in a letter
to E. S. Pearson of Jan. 29, 1932 [James A. Landau].

*Studentized D ^{2} statistic* is found in R. C. Bose and
S. N. Roy, "The exact distribution of the Studentized D

**STURM'S THEOREM** appears 1853 in J. J. Sylvester, *Phil.
Trans.* CXLIII. 483: "Reverting now to the simplified Sturmian
residues, since..these differ from the unsimplified complete residues
required by the Sturmian method only in the circumstance of their
being divested of factors, which are necessarily..positive, these
simplified Sturmians may of course be substituted for the complete
Sturmians for the purposes of M. Sturm’s theorem" (OED2).

**SUBFACTORIAL** was introduced in 1878 by W. Allen Whitworth in
*Messenger of Mathematics* (Cajori vol. 2, page 77).

**SUBFIELD** is found in "On the Base of a Relative Number-Field,
with an Application to the Composition of Fields," G. E. Wahlin,
*Transactions of the American Mathematical Society,* Vol. 11,
No. 4. (Oct., 1910).

**SUBGROUP.** Felix Klein used the term *untergruppe.*

*Subgroup* appears in 1887 in *Amer. Jrnl. Math.* IX. 51:
"I use 'self-conjugate sub-group' in translating Klein’s
‘ausgezeichnete Untergruppe’ and Jordan’s ‘groupe permutable’"
(OED2).

**SUBRING** is found in English in 1937 in the phrase *invariant
subring* in *Modern Higher Algebra* (1938) by A. A. Albert
(OED2).

**SUBSET** occurs in "A Simple Proof of the Fundamental
Cauchy-Goursat Theorem," Eliakim Hastings Moore, *Transactions of
the American Mathematical Society,* Vol. 1, No. 4. (Oct., 1900).

**SUBTRACT.** When Fibonacci (1201) wishes to say "I subtract," he
uses some of the various words meaning "I take": *tollo,
aufero,* or *accipio.* Instead of saying "to subtract" he
says "to extract."

In a manuscript written by Christian of Prag (c. 1400), the word
"subtraction" is at first limited to cases in which there is no
"borrowing." Cases in which "borrowing" occurs he puts under the
title *cautela* (caution), and gives this caption the same
prominence as *subtractio.*

In *Practica* (1539) Cardano used *detrahere* (to draw or
take from).

In 1542 in the *Ground of Artes* Robert Recorde used
*rebate*: "Than do I rebate 6 out of 8, & there resteth 2."

In 1551 in *Pathway to Knowledge* Recorde used *abate*:
"Introd., And if you abate euen portions from things that are equal,
those partes that remain shall be equall also" (OED2).

Digges (1572) writes "to subduce or substray any sume, is wittily to pull a lesse fro a bigger number."

Schoner, in his notes on Ramus (1586 ed., p. 8), uses both
*subduco* and *tollo* for "I subtract."

In his arithmetic, Boethius uses *subtrahere,* but in geometry
attributed to him he prefers *subducere.*

The first citation for *subtract* in the OED2 is in 1557 by
Robert Recorde in *The whetstone of witte:* "Wherfore I subtract
16. out of 18."

Hylles (1592) used "abate," "subtact," "deduct," and "take away" (Smith vol. 2, pages 94-95).

From Smith (vol. 2, page 95):

The word "subtract" has itself had an interesting history. The Latinsubappears in French assub, soub, sou,andsous, subtraherebecomingsoustraireandsubtractiobecomingsoustraction.Partly because of this French usage, and partly no doubt for euphony, as in the case of "abstract," there crept into the Latin works of the Middle Ages, and particularly into the books printed in Paris early in the 16th century, the formsubstractio.From France the usage spread to Holland and England, and form each of these countries it came to America. Until the beginning of the 19th century "substract" was a common form in England and America, and among those brought up in somewhat illiterate surroundings it is still to be found. The incorrect form was never popular in Germany, probably because of the Teutonic exclusion of international terms.

Tonstall (1522) devoted 15 pages to *Subductio.* He wrote, "Hanc
autem eandem, uel deductionem uel subtractionem appellare Latine
licet" (1538 ed., p. 23; 1522 ed., fol. E 2, r).

Gemma Frisius (1540) has a chapter *De Subductione siue
Subtractione.*

Clavius (1585 ed., p. 26) says "Subtractio est ... subductio."

See also *addition.*

**SUBTRAHEND** is an abbreviation of the Latin *numerus
subtrahendus* (number to be subtracted).

**SUCCESSIVE INDUCTION.** This term was suggested by Augustus De
Morgan in his article "Induction (Mathematics)" in the *Penny
Cyclopedia* of 1838. See also *mathematical induction,
induction, complete induction.*

The phrase **SUFFICIENT STATISTIC** is found in 1922 in R. A.
Fisher in *Philosophical Transactions of the Royal Society*:

In the case of the normal curve of distribution it is evident that the second moment is a sufficient statistic for estimating the standard deviation; in investigating a sufficient solution for grouped normal data, we are therefore in reality finding the optimum correction for grouping; the Sheppard correction having been proved only to satisfy the criterion of consistency.

The term **SUMMABLE** (referring to a function that is Lebesgue
integrable such that the value of the integral is finite) was
introduced by Lebesgue (Klein, page 1045).

**SUPPLEMENT.** "Supplement of a parallelogram" appears in English
in 1570 in Sir Henry Billingsley's translation of Euclid's
*Elements.*

In 1704 *Lexicon Technicum* by John Harris has "supplement of an
Ark."

In 1796 Hutton *Math. Dict.* has "The complement to 180° is
usually called the supplement.

In 1798 Hutton in *Course Math.* has "supplemental arc" (one of
two arcs which add to a semicircle) (OED2).

Supplement II to the 1801 *Encyclopaedia Britannica* has, "The
supplement of 50° is 130°; as the complement of it is 40
°" (OED2).

In 1840, Lardner in *Geometry* vii writes, "If a quadrilateral
figure be inscribed in a circle, its opposite angles will be
supplemental" (OED2).

*Supplementary angle* is dated ca. 1924 in MWCD10.

**SURD.** According to Smith (vol. 2, page 252), al-Khowarizmi
(c. 825) referred to rational and irrational numbers as 'audible' and
'inaudible', respectively.

This was translated as *surdus* ("deaf" or "mute") in Latin.

As far as is known, the first known European to adopt this terminology was Gherardo of Cremona (c. 1150).

Fibonacci (1202) adopted the same term to refer to a number that has no root, according to Smith.

*Surd* is found in English in Robert Recorde's *The Pathwaie
to Knowledge* (1551): "Quantitees partly rationall, and partly
surde" (OED2).

According to Smith (vol. 2, page 252), there has never been a general
agreement on what constitutes a surd. It is admitted that a number
like sqrt 2 is a surd, but there have been prominent writers who have
not included sqrt 6, since it is equal to sqrt 2 X sqrt 3. Smith
also called the word *surd* "unnecessary and ill-defined" in his
*Teaching of Elementary Mathematics* (1900).

G. Chrystal in *Algebra,* 2nd ed. (1889) says that "...a surd
number is the incommensurable root of a commensurable number," and
says that sqrt *e* is not a surd, nor is sqrt (1 + sqrt 2).

**SURJECTION** appears in 1964 in *Foundations of
Algebraic Topology* by W. J. Pervin (OED2).

**SURJECTIVE** appears in 1956 in C. Chevalley, *Fund. Concepts
Algebra*: "A homomorphism which is injective is called a
monomorphism; a homomorphism which is surjective is called an
epimorphism" (OED2).

The term **SURREAL NUMBER** was introduced by Donald Ervin Knuth
(1938- ) in 1972 or 1973, although the notion was previously
invented by John Horton Conway (1937- ) in 1969.

The term **SYLOW'S THEOREM** is found in 1893 in *Proceedings of
the London Mathematical Society* XXV 14 (OED2).

The term **SYMMEDIAN** was introduced in 1883 by Philbert Maurice
d'Ocagne (1862-1938) [Clark Kimberling].

The term **SYMMEDIAN POINT** (point of concurrence of symmedians)
was coined by the Robert Tucker (1832-1905) in the interest of
uniformity and amity. The point had been called the Lemoine point in
France and the Grebe point (after E. W. Grebe) in Germany (DSB,
article "Lemoine").

The term **SYMPLECTIC GROUP** was proposed in 1939 by
Herman Weyl in *The Classical Groups.* He wrote on page 165:

The name "complex group" formerly advocated by me in allusion to line complexes, as these are defined by the vanishing of antisymmetric bilinear forms, has become more and more embarrassing through collision with the word "complex" in the connotation of complex number. I therefore propose to replace it by the corresponding Greek adjective "symplectic." Dickson calls the group the "Abelian linear group" in homage to Abel who first studied it.[This information was provided by William C. Waterhouse.]

**SYNTHETIC DIVISION** is found in 1857 in *Mathematical
Dictionary and Cyclopedia of Mathematical Science.*

**SYNTHETIC GEOMETRY** appears in 1889 in the title *Elementary
Synthetic Geometry of the Point, Line and Circle in the Plane,* by
N. F. Dupuis (OED2). It also appears in the *Century
Dictionary* (1889-97).