1533, from M.Fr. invertir, from L. invertere "turn upside down, turn about," from in- "in, on" + vertere "to turn" see versus). Inversion is from 1551.
In*verse"\, a. [L. inversus, p. p. of invertere: cf. F. inverse. See Invert.]1. Opposite in order, relation, or effect; reversed; inverted; reciprocal; -- opposed to direct. 2. (Bot.) Inverted; having a position or mode of attachment the reverse of that which is usual. 3. (Math.) Opposite in nature and effect; -- said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity; as, multiplication is the inverse operation to division. The symbol of an inverse operation is the symbol of the direct operation with -1 as an index. Thus sin-1 x means the arc whose sine is x. Inverse figures (Geom.), two figures, such that each point of either figure is inverse to a corresponding point in the order figure. Inverse points (Geom.), two points lying on a line drawn from the center of a fixed circle or sphere, and so related that the product of their distances from the center of the circle or sphere is equal to the square of the radius. Inverse, or Reciprocal, ratio (Math.), the ratio of the reciprocals of two quantities. Inverse, or Reciprocal, {proportion, an equality between a direct ratio and a reciprocal ratio; thus, 4 : 2 : : 1/3 : 1/6, or 4 : 2 : : 3 : 6, inversely.
In*ver"sion\, n. [L. inversio: cf. F. inversion. See Invert.]1. The act of inverting, or turning over or backward, or the state of being inverted. 2. A change by inverted order; a reversed position or arrangement of things; transposition. It is just the inversion of an act of Parliament; your lordship first signed it, and then it was passed among the Lords and Commons. --Dryden. 3. (Mil.) A movement in tactics by which the order of companies in line is inverted, the right being on the left, the left on the right, and so on. 4. (Math.) A change in the order of the terms of a proportion, so that the second takes the place of the first, and the fourth of the third. 5. (Geom.) A peculiar method of transformation, in which a figure is replaced by its inverse figure. Propositions that are true for the original figure thus furnish new propositions that are true in the inverse figure. See Inverse figures, under Inverse. 6. (Gram.) A change of the usual order of words or phrases; as, "of all vices, impurity is one of the most detestable," instead of, "impurity is one of the most detestable of all vices." 7. (Rhet.) A method of reasoning in which the orator shows that arguments advanced by his adversary in opposition to him are really favorable to his cause. 8. (Mus.) (a) Said of intervals, when the lower tone is placed an octave higher, so that fifths become fourths, thirds sixths, etc. (b) Said of a chord, when one of its notes, other than its root, is made the bass. (c) Said of a subject, or phrase, when the intervals of which it consists are repeated in the contrary direction, rising instead of falling, or vice versa. (d) Said of double counterpoint, when an upper and a lower part change places. 9. (Geol.) The folding back of strata upon themselves, as by upheaval, in such a manner that the order of succession appears to be reversed. 10. (Chem.) The act or process by which cane sugar (sucrose), under the action of heat and acids or ferments (as diastase), is broken or split up into grape sugar (dextrose), and fruit sugar (levulose); also, less properly, the process by which starch is converted into grape sugar (dextrose). Note: The terms invert and inversion, in this sense, owe their meaning to the fact that the plane of polarization of light, which is rotated to the right by cane sugar, is turned toward the left by levulose.
In*vert"\, v. t. [imp. & p. p. Inverted; p. pr. & vb. n. Inverting.] [L. invertere, inversum; pref. in- in + vertere to turn. See Verse.]1. To turn over; to put upside down; to upset; to place in a contrary order or direction; to reverse; as, to invert a cup, the order of words, rules of justice, etc. That doth invert the attest of eyes and ears, As if these organs had deceptious functions. --Shak. Such reasoning falls like an inverted cone, Wanting its proper base to stand upon. --Cowper. 2. (Mus.) To change the position of; -- said of tones which form a chord, or parts which compose harmony. 3. To divert; to convert to a wrong use. [Obs.] --Knolles. 4. (Chem.) To convert; to reverse; to decompose by, or subject to, inversion. See Inversion, n., 10.
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