arithmancy

[Gr. ἀριθμός (arithmos) = a number, and μαντεία ( manteia ) = prophesying, divination; μάντις (mantis) = a diviner, a prophet.] Pretended divination of future events by means of numbers. a-rith-mět-ic, * a-rith-mět-ick, * rith'-mět-icke, *ars'-mět-rike, *ars'mět-rýk, s . [In Ger. arithmetik; Fr. arith métique; Port. arithmetic a; Sp. & Ital. a rit metic a; Lat. arithmetic a ; Gr. ἀριθμητική (arith mētikē ) [supply τέχνη (techne) = art), the fem. Οἱ ἀριθμητικός ( arithmētikos ) = of or for numbering; ἀριθμός (arithmos) = number.] In its broadest sense the science and art which treat of the properties of numbers. This definition, however, would include Algebra, which is considered a distinct branch. Algebra deals with certain letters of the alphabet, such as x, y, z, a, b, c, ., standing as symbols for numbers; arithmetic operates on numbers themselves, as 1, 2, 3, 4, . Viewed as a science, arithmetic is a branch of mathematics; looked on as an art, its object is to carry out for practical purposes certain rules regarding numbers, without troubling itself to investigate the foundation on which those rules are based. 303 ratios. In such cases the sum of the extremes is that of the means. [PROPORTION.] arithmetical proportionals. The numbers so related to each other. (The term is opposed to geometric proportionals.) (PROPORTIONAL.] arithmetical relation. The comparison of numbers in an arithmetical progre ion with the view of ascertaining how much they differ from each other. arithmetical ratio. The difference between any two numbers constituting part of a series in arithmetical progre ion. metic, treating, as the name implies, of decimals. There are also Logarithmic Arithmetic for computation by logarithms, and Instrumental Arithmetic for calculation by means of instruments or machines. Another division is into Theoretical Arithmetic, treating of the science of numbers, and Practical Arithmetic , which points out the best method of practically working questions or sums. Political Arithmetic is arithmetic applied to political economy, as is done in the statistical returns so continually presented to Parliament. Finally, Universal Arithmetic is a name sometimes applied to Algebra. The chief subjects generally treated under the science or art of Arithmetic are (1) Numeration and Notation; (2) Addition; (3) Subtraction; (4) Multiplication; (5) Division; (6) Reduction; (7) Compound Addition; (8) Compound Subtraction; (9) Compound Multiplication; (10) Compound Division; (11) Simple Proportion (Rule of Three); (12) Compound Proportion; (13) Vulgar Fractions; (14) Decimal Fractions; (15) Duodecimals; (16) Involution; (17) Evolution; (18) Ratios, Proportions, and Progre ions; (19) Fellowship or Partnership; (20) Simple Interest; (21) Compound Interest; and (22) Position. ( Hutton , .) Of these, the most important are the simple proce es of Addition, Subtraction, Multiplication, and Division, the judicious use of which, singly or in combination, will solve the most complex arithmetical questions. "At the same time one of the founders of the Society, Sir William William Petty, created the science of political arithmetic, the humble but indispensable handmaid of political philosophy."-Macaulay: Hist. Eng ., ch. iii. Arithmetic of Infinites : The summing up of an infinite series of numbers.