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 datum, that among the populations upon which the experiment was tried, those in which p lay in the range dp were equally frequent for all equal ranges dp. The probability that the value of p lay in any range dp was therefore assumed to be simply dp, before the sample was taken. After the selection effected by observing the sample, the probability is clearly proportional to[James A. Landau]
px (1-p)y dp.
After giving this solution, based upon the particular datum stated, BAYES adds a scholium the 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 particular a priori distribution of p. The result, the datum, and the postulate implied by the schodium, 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 1012, 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.