Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots

V

339 V valence The Latin verb valeo, valere, valui, to be strong, has the present participle valens, valentis with the meaning powerful. From the participle came the late Latin noun valentia, power, from which the French (and English) noun is derived. Finkbeiner and Lindstrom (p. 225) define the valence or degree of a vertex v in a graph G to be the number of edges of G that are incident at v. valid From the Latin verb valeo, valere, valui, which means to be strong, is derived the adjective validus with the meaning strong, powerful. The English adjective is produced by dropping the nominative case ending -us from the Latin adjective. valuation The late Latin noun valuatio, valuationis means worth and is derived from the verb valeo, valere, valui, which developed the meaning to be worth from its original meaning to be strong. If (X, ) is a topological space, a valuation is a mapping f from to [0,satisfying i) f() = 0, ii) if A and B are open sets such that A B, then f(A) f(B), and iii) if A and B are any open sets, then f(A ff(A) + f(B). value The French verb valoir means to be worth; its past participle is valu, from which is derived the French and the English noun value. The French verb is derived from the Latin verb valeo, valere, valui, which means to be strong. vanish The Latin adjective vanus means empty. According to Lewis and Short, its etymology is uncertain, though they call the attention of their readers to the verb vaco, vacare, which means to be empty. The ending -us became -ish through the mispronunciation of the unlearned. The modern technical use of the word as a verb meaning to be zero (of functions) dates back to at least the beginning of the eighteenth century. ‫ڧ‬ ‫ڧ‬ 340 variable Vario is a first-declension Latin verb that is transitive in the sense of to diversify, to alter, and intransitive in the sense of to be different, to vary. From this there developed the medieval Latin adjective variabilis with the meaning to be changeable, whence we get our technical term variable. The use of variable as a noun in the modern mathematical sense is at least as old as the early nineteenth century. variance From the Latin adjective varius, which means manifold, came the verb vario, variare, variavi, variatus with the meaning to diversify; the verb’s present participle is varians, variantis. From this participle was formed the noun variantia, difference, used by Lucretius; it is the origin of the French, and of the English, variance. variate This English noun is derived from the fourth principal part of the Latin verb vario. See the previous two entries. A random variate is an element of the range of a random variable. variation From the Latin adjective varius, which means manifold, came the verb vario, variare, variavi, variatus with the meaning to diversify. From the fourth principal part of the verb came the noun variatio, variationis, used by Livy. This noun is the origin of the English variation. The calculus of variations is that branch of the theory of differential equations that finds the curves that solve certain maxima and minima problems. The method of variation of parameters is due to Lagrange (1736–1813); it is employed to find a particular solution of a non-homogeneous differential equation y΄΄ + by΄ + cy = 0 when the method of undetermined coefficients fails. vault This word is the corruption of the fourth principal part of the Latin verb volvo, volvere, volvi, volutus, which means to roll. A barrel vault is a ceiling in the shape of a half cylinder, the half on one side of a dividing plane through the axis. The nave of St. Peter’s Basilica has the most famous of barrel vaults. The Roman vault is the top half of the solid of intersection of two equal circular cylinders intersected at right angles; I have seen the whole solid of intersection called a bicylinder, and the word is acceptable. The Romans used this type of vault in their public baths. Brunelleschi used the top half of the solid 341 of intersection of four equal right circular cylinders intersected at 45o angles for the dome of the cathedral of Florence. Michelangelo used the top half of the solid of intersection of eight equal right circular cylinders intersected at 22...