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

N

220 the sphere of Jupiter. Inside the tetrahedron is inscribed the sphere of Mars. Inside the sphere of Mars is inscribed a dodecahedron, inside of which there is described the sphere of the earth. Inside the sphere of the earth is inscribed an icosahedron, and inside the icosahedron is inscribed the sphere of Venus. Inside the sphere of Venus is inscribed an octahedron, and inside the octahedron is inscribed the sphere of Mercury. N natural number The Latin verb nascor, nasci, natus means to be born, and from the third principal part comes the feminine singular participle natura meaning that which is about to be born and, as a noun, nature. From natura is formed, by the addition of the suffix -alis to the stem, the adjective naturalis with the meaning pertaining to nature. These are the positive integers, the numbers created by God, according to Kronecker. necessary The indeclinable Latin adjective necesse means unavoidable. Allen and Greenough write (New Latin Grammar, §250a): Adjectives meaning belonging to are formed from nouns by means of the suffixes -ārius, -tōrius Thus we get the adjective necessarius, whence was produced necessary. negation The Latin word for denial is negatio, negationis, from whose stem we get the noun negation. Negatio itself is from nego, negare, negavi, negatus, to deny. negative The Latin verb nego, negare, negavi, negatus means to say no. Allen and Greenough write (New Latin Grammar, §251): 221 Adjectives expressing the action of the verb as a quality or tendency are formed from real or apparent verb-stems with the suffixes -āx, -idus, -ulus, -vus (-uus, -īvus, -tīvus) . Thus we get negativus from negatus, and finally negative from negativus. nephroid Aristotle uses the adjective nefroeid»j, shaped like a kidney. It is the juxtaposition of the Greek word for kidney, which is nefrÒj, and eŁdoj, which means shape. It is the name of the curve that is kidney-shaped, the epicycloid of two cusps. If the radius of the fixed circle is a, and the radius of the rolling circle is b with a = 2b, then the parametric equations of the resulting nephroid are x = b(3 cos t – cos 3t) y = b(3 sin t – sin 3t). The length of the nephroid is 24b. The area of the plane region it encloses is 12b2 p. nerve This is the Latin noun nervus, which means a sinew or nerve. It is related to the Greek noun neàron of the same meaning. -ness This English suffix is added to adjectives in order to make nouns. Thus good + ness = goodness. It is wrong to add it to adverbs. Thus, wellness is a low word. It is also wrong to add it to adjectives that themselves are formed from an already existing noun. Thus healthiness is a low word since there is already the adequate noun health. The macaronic addition of this suffix to words of Greek and Latin origin is not recommendable. nilpotent Nil is a short form of nihil, Latin for nothing. Potent is from potens, potentis, the present participle of possum, to be able. The Romans did not add nil as a prefix to adjectives to form new adjectives; nilpotent is thus not a Latin word, but an unlearned modern invention. 222 nodal Nodus is the Latin word for knot. The addition of the adjectival suffix -alis to the stem produces the adjective nodalis, whence we get the English noun upon removal of the case ending -is. node This noun comes from nodus, the Latin word for knot. Noli tangere circulos meos. These are the last words of Archimedes—Get off my circles!—addressed to a Roman soldier who was trampling on a mathematical diagram that he had just drawn with a stick in the sand. The scene is the subject of a famous mosaic preserved in the Städelsches Kunstinstitut und Städtische Galerie in Frankfurt am Main. non- The Latin adverb non means not. The English habit of forming one word by adding non- to adjectives (for example, non-singular) instead of using two words (for example, not singular) is a habit not in conformity with the best style. The use of the connecting hyphen is recommendable to prevent an unseemly concatenation. nonagon This is an absurd word used by the unlearned for enneagon, q.v. It is the same sort of concoction as septagon, q.v. non-homogeneity See the entries non...