The term

**BAR CHART** occurs in Nov. 1914 in *Engineering Magazine*
(OED2).

**BAR GRAPH** is dated 1924 in MWCD10.

The term **BARYCENTRIC CALCULUS** appears in 1827 in the title *Der
barycentrische calkul* by August Ferdinand M?bius (1790-1868).

**BASE** (of a triangle) appears in English in 1570 in Sir Henry
Billingsley's translation of Euclid's *Elements* (OED2).

**BASE** (in logarithms) appears in English in 1874 in *Trigonometry*
by Isaac Todhunter, who refers to the "logarithm of *n* to the base
*a*
(OED2).

**BAYES' THEOREM.** R. A. Fisher, "On the Mathematical Foundations
of Theoretical Statistics," *Philosophical Transactions of the Royal
Society,* Series A, Vol 222 (1922) p. 324 reads:

BAYES introduced the[James A. Landau]datum,that among the populations upon which the experiment was tried, those in whichplay in the rangedpwere equally frequent for all equal rangesdp.The probability that the value ofplay in any rangedpwas therefore assumed to be simplydp,before the sample was taken. After the selection effected by observing the sample, the probability is clearly proportional top(1-^{x}p)^{y}dp.After giving this solution, based upon the particular datum stated, BAYES adds a

scholiumthe purport of which would seem to be that in the absence of all knowledge save that supplied by the sample, it is reasonable to assume this particulara prioridistribution ofp.Theresult,thedatum,and thepostulateimplied by theschodium,have all been somewhat loosely spoken of as BAYES' Theorem.

**BAYESIAN** is found in the phrase *Bayesian prediction* in
1956 in *Statistical Methods & Scientific Inference* by R. A.
Fisher [*OED Additions Series, Volume 1;* provided by Mark Dunn].

**BELL CURVE.** J. V. Uspensky, in *Introduction to Mathematical
Probability* (1937), writes that "the probability curve has a bell-shaped
form" [James A. Landau].

*Bell curve* is dated ca. 1941 in MWCD10.

**BERNOULLI NUMBERS.** According to Cajori (vol. 2, page 42), Leonhard
Euler introduced the name "Bernoullian numbers."

According to the University of St. Andrews website, in its article on Johann Faulhaber, the Bernoulli numbers were "so named by [Abraham] de Moivre" (1667-1754).

**BERNOULLI TRIAL** is dated 1951 in MWCD10, although James A. Landau
has found the phrases "Bernoullian trials" and "Bernoullian series of trials"
in 1937 in *Introduction to Mathematical Probability* by J. V. Upensky.

**BESSEL FUNCTION.** *Philosophical Magazine* in 1872 has "The
value of Bessel's functions is becoming generally recognized" (OED2).

The term **BETTI NUMBER** was coined by Henri Poincar? (1854-1912)
and named for Enrico Betti (1823-1892), according to a history note by
Victor Katz in *A First Course in Abstract Algebra* by John B. Fraleigh.

**BETWEENNESS.** The earliest citation in the OED2 for this word
is in 1892 *Monist* II. 243: "In reality there are not two things
and, in addition to them a betweenness of the two things."

The OED2 also has a 1904 citation which makes reference to "Hilbert's betweenness assumptions."

**BEZOUTIANT** was "used by Sylvester and later writers" (Cajori
1919, page 249).

The term **BICURSAL** was introduced by Cayley (Kline, page 938).

**BILLION** first occurs, with the meaning 10^{12}, in French
in 1484 in *Le Triparty en la Science des Nombres* by Nicolas Chuquet
(1445?-1500?). He used the words *byllion, tryllion, quadrillion, quyllion,
sixlion, septyllion, ottyllion,* and *nonyllion.* A translation
has: "The first dot indicates million, the second dot billion, the third
dot trillion, the fourth dot quadrillion...and so on as far as one may
wish to go."

*Decillion* occurs in English in 1847. *Centillion* is found
in English in an 1889 dictionary, although *centillionth,* with an
imprecise meaning, appears in 1852 in *Tait's Magazine:* "There existed
not a centillionth of the blessing."

**BINARY ARITHMETIC** appears in English in 1796 *A Mathematical
and Philosophical Dictionary* (OED2).

**BINOMIAL** first appears as a noun in English in its modern mathematical
sense in 1557 in *The Whetstone of Witte* by Robert Recorde: "The
nombers that be compound with + be called Bimedialles... If their partes
be of 2 denominations, then thei named Binomialles properly. Howbeit many
vse to call Binomialles all compounde nombers that have +" (OED2).

**BINOMIAL COEFFICIENT** occurs in English in 1889 in the *Century*
Dictionary.

According to Kline (page 272), this term was introduced by Michael Stifel
(1487-1567) about 1544. However, Julio Gonz?lez Cabill?n believes this
information is incorrect. He says Stifel could not have used the word *coefficient,*
which is due to Vieta (1540-1603).

**BINOMIAL DISTRIBUTION** is found in 1911 in *Introd. Theory Statistics*
xv. 305, by G. U. Yule (OED2).

**BINOMIAL THEOREM** appears in 1742 in *Treatise of Fluxions*
by Colin Maclaurin (Struik, page 339).

**BIPARTITE.** In 1858, Cayley referred to "bipartite binary quantics."

In 1879, George Salmon (1819-1904) referred to "a bipartite curve" in
*Higher
Plane Curves* (OED2).

The term **BIQUATERNION** was coined by William Kingdon Clifford
(1845-1879).

**BIT** was coined by John W. Tukey, according to a 1948 article
by Claude Elwood Shannon (1916- ) in *Bell Systems Technical Journal.*

Abbott (1985) writes that Shannon used the term *bit,* and seems
to imply that Shannon coined the term.

**BIVARIATE** is found in 1929 in *Biometrika* XIII. 37 (OED2).

**BOOLEAN** is found in 1851 in the *Cambridge and Dublin Mathematical
Journal* vi. 192: "...the Hessian, or as it ought to be termed, the
first Boolian Determinant" (OED2).

**BOOLEAN ALGEBRA** appears in the *Century Dictionary* of 1889,
where it is spelled "Boolian."

According to E. V. Hutington in "New Sets of Independent Postulates
for the Algebra of Logic with Special Reference to Whitehead and Russell's
Principia Mathematica," Trans. Amer. Math. Soc., 35: 274-304 (1933), the
term *Boolean algebra* was introduced by H. M. Sheffer in the paper
"A Set of Five Independent Postulates for Boolean Algebras with Application
to Logical Constants", *Trans. Amer. Math. Soc.,* 14 : 481-488 (1913).

In an illuminating passage of "Algebraic Logic", Halmos writes (p. 11):

Terminological purists sometimes object to the Boolean use of the word "algebra". The objection is not really cogent. In the first place, the theory of Boolean algebras has not yet collided, and it is not likely to collide, with the theory of linear algebras. In the second place, a collision would not be catastrophic; a Boolean algebra is, after all, a linear algebra over the field of integers modulo 2. (...) While, to be sure, a shorter and more suggestive term than "Boolean algebra" might be desirable, the nomenclature is so thoroughly established that to change now would do more harm than good.[Carlos C?sar de Ara?jo]

The term **BRACHISTOCHRONE** was introduced by Johann Bernoulli (1667-1748).
Smith (vol. 2, page 326) says the term is "due to the Bernoullis."

The terms **BRA VECTOR** and **KET VECTOR** were introduced by
Paul Adrien Maurice Dirac (1902-1984).

**BRIGGSIAN LOGARITHM.** The phrase *Briggs logarithm* is found
in the 1771 edition of the *Encyclopaedia Britannica* [James A. Landau].

**BROKEN LINE.** According to Schwartzman (page 38), this term, meaning
a curve composed of connected straight line segments, was adopted "around
1898" by David Hilbert (1862-1943).

**BRUN'S CONSTANT** was coined by R. P. Brent in "Irregularities
in the distribution of primes and twin primes," *Math. Comp.* 29 (1975),
according to *Algorithmic Number Theory* by Bach and Shallit [Paul
Pollack].

The term **BYTE** was coined in 1956 by Dr. Werner Buchholz of IBM.
A question-and-answer session at an ACM conference on the history of programming
languages included this exchange:

JOHN GOODENOUGH: You mentioned that the term "byte" is used in JOVIAL. Where did the term come from?

JULES SCHWARTZ (inventor of JOVIAL): As I recall, the AN/FSQ-31, a totally different computer than the 709, was byte oriented. I don't recall for sure, but I'm reasonably certain the description of that computer included the word "byte," and we used it.

FRED BROOKS: May I speak to that? Werner Buchholz coined the word as part of the definition of STRETCH, and the AN/FSQ-31 picked it up from STRETCH, but Werner is very definitely the author of that word.

SCHWARTZ: That's right. Thank you.