The term

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

**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 (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]

The term *scientific notation* does *not* appear in *Webster's
New International Dictionary* (1909).

The term does appear 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.

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

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

**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 the 1909-1913 *Webster* unabridged dictionary; the OED2
shows a use with the modern definition in 1911 in the *Encyclopaedia
Britannica* article "Number."

**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").

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."

The **SERPENTINE** curve was named by Isaac Newton (1642-1727) in
1701, according to Schwartzman and the University of St. Andrews website.

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).

The term *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].

In 1895 Georg Cantor (1845-1918) used the word *Menge* in *Beiträge
zur Begründung der Transfiniten Mengenlehre:*

By a set we are to understand any collection into a whole ofMof definite and distinguishable objects of our intuition or our thought. These objects are called the elements ofM.

**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.* (OED2).

The term **SIGN OF AGGREGATION** is dated ca. 1942 in MWCD10.

**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."

In English, Robert Recorde wrote, "The other nyne are called Signifying figures."

The original meaning of the term was "any non-zero digit."

The term **SIMILAR** was used in Latin by Leibniz, but may be much
older.

**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).

The term **SIMPLEX** 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).

The term is also found in Robert Dorfman, "Application of the simplex
method to a game theory problem," *Activity Analysis of Production and
Allocation,* Chap. XXII, 348-358 (1951).

Earlier uses of this term occur in geometry.

**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]

**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).

However, Boyer (page 278) places the first appearance of *sinus*
in a translation of 1145. He writes, "It was Robert of Chester's translation
from the Arabic that resulted in our word 'sine.'

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).

**SINGULAR MATRIX.** *Non-singular matrix* (and presumably *singular
matrix* also) occurs in "Resolution into Involutory Substitutions of
the Transformations of a Non-Singular Bilinear form into Itself," Dunham
Jackson, *Transactions of the American Mathematical Society,* Vol.
10, No. 4. (Oct., 1909).

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

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

**SKEWES NUMBER** appears in "The Skewes Number" by R. P. Boas Jr.
Delta 1, No.4, 32-36 (1970).

The term **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 would not have been a slide
rule in the modern sense.

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

The term *slide rule* appears with its modern definition in the
1890 *Funk & Wagnalls* Dictionary. The 1901 *Chambers's Twentieth
Century Dictionary* has *sliding-rule,* with the modern definition.

**SLOPE** occurs as a mathematical term in the *Mathematical Dictionary
and Cyclopedia of Mathematical Science* (New York, 1855) by Charles
Davies and William G. Peck [V. Frederick Rickey].

**SLOPE-INTERCEPT FORM** is dated ca. 1942 in MWCD10.

In *Webster's New International Dictionary* (1909) and in *A
Brief Course in Advanced Algebra* (1937), the term is *slope form.*

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** in English is dated 1816 in MWCD10.

**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 (OED2).

The term apparently is 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). [*Trivia:* The words *spherical geometry* and *versed
sine* were used by Edgar Allan Poe in his short story *The Unparalleled
Adventure Of One Hans Pfaall.*]

The term **SPHERICAL HARMONICS** was used by William Thomson (1824-1907)
and Peter Guthrie Tait (1831-1901) (Todhunter, 1873) [Chris Linton].

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

**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).

**SPIRAL OF ARCHIMEDES** is dated 1650-60 in RHUD2.

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.'"

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."

**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 APPROXIMATION** appears in 1938 in *Biometrika*
(OED2).

**STIRLING'S FORMULA** is found in "On the Degree of Convergence
of Laplace's Series," T. H. Gronwall, *Transactions of the American Mathematical
Society,* Vol. 15, No. 1. (Jan., 1914).

**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* 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."

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.

**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.**

*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* appears (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].

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

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

**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.*

**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).

Recorde (c. 1542) used "rebate" as a synonym for "subtract."

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" (OED2).

**SUM.** Nicolas Chuquet used *some* in his *Triparty en la
Science des Nombres* in 1484.

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."

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

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

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

**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.

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 1964 in *Elem. Gen. Topology* by S.-T.
Hu (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].

**Note: This page previously stated that Robert Tucker coined the term
symmedian.
He actually coined symmedian point.**

The term **SYMMEDIAN POINT** (point of concurrence of the symmedians
of a triangle) 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").

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

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 English in 1881 in *Elements
of Algebra* by G. A. Wentworth [James A. Landau].

**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).