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

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170 according to whether c b. The parametric equations of the hypotrochoid are x = (a – b)cos q + c cos [(a – b)/b]q y = (a – b)sin q – c sin[(a – b)/b]q. I -ical Words ending in this way are usually the offspring of ignorance. The stem -al of the Latin adjectival suffix -alis has been superimposed upon an adjective ending in the stem -ic of the Greek adjectival suffix -ikÒj. This was done because those who did so did not recognize that the word they were dealing with was already an adjective; it was all Greek to them. For example, from the noun m£qhma, maq»matoj, learning, the Greeks formed their adjective maqhmatikÒj, pertaining to learning. The Romans adopted this adjective, which in their language became mathematicus. There is no Latin word mathematicalis since mathematicus, being already an adjective, did not require the addition of the suffix -alis to its root to make it so. The adjective mathematicus became in English mathematic or mathematick, and is a recognized adjective in Johnson’s Dictionary. Some authors, however, superimposed the Latin ending on the word mathematic to produce mathematical, and the latter adjective, which also appears in Johnson’s Dictionary, has displaced the former, which has altogether disappeared from modern prose. In some instances, however, as in the case of dynamic and dynamical, both the true and the inflated adjectives have survived. Thus, we hear both of the method of translation called dynamic equivalence and of the subject dynamical systems. As a general rule, when making new words, -al should not be added to what are already adjectives of Greek origin ending in -ic. In the case of words like mathematical and dynamical, their use is sanctioned by immemorial custom. 171 icosian This is a word invented by William Rowan Hamilton for the name of one of his games. The Greek word for twenty is e‡kosi; to this word Hamilton added the stem of the Latin adjectival ending -anus to produce icosian. The game consists of starting at one vertex of a dodecahedron and moving along the edges until one has touched every vertex exactly once but has passed through no edge more than once; the path must be a cycle, that is, it must end at the vertex whence it began. The solution path has twenty edges, hence the name of the game. ideal The Greek noun „dša means something seen by the eye of the mind, from „de‹n, to see. It was taken over into Latin as idea, ideae, from which the adjective idealis meaning existing as an idea proceeded. idempotent The Romans did not use the adjective idem, same, as a prefix; therefore, whoever coined this word made a mistake. The participle potens, potentis of possum, to be able, means, capable, powerful. identity From the Latin adjective idem, which means the same, there arose in the fifth century the late Latin noun identitas, identitatis with the meaning sameness. - -ikÒj, -ik», -ikÒn The Greeks added this suffix to the stem of a noun to create an adjective denoting relation, fitness, or ability. Hence when such words came into Latin, the ending was modified to -icus, -ica, -icum. The ending -ic on an English adjective is a give-away that it has this origin. When forming adjectives, it is incorrect to superimpose this suffix on a root that is not Greek. For example, with a Latin root one uses the corresponding suffix -alis, -ale. image The Latin word imago, imaginis means a likeness. It entered French and then English as image. Words of Latin origin that are the same in French and English entered the English language as a result of the Norman invasion of 1066. imaginary The Latin adjective imaginarius was formed by adding the adjectival suffix -arius to the stem of the noun imago, imaginis, which 172 means likeness. The English adjective is the Latin word without the case ending -us, the i having been changed, per bellezza as the Italians say, to y. The dreary names imaginary and complex were applied to the set of numbers of the form a + b(–1)1/2 which, if b ≠0, had no place on the number line; such entities, it was thought, were like phantoms and quite beyond comprehension. implication The Latin noun implicatio, implicationis means an entangling, an entanglement. It is formed from the fourth...