ARITHMETIC COMPUTATION. The methods of carrying out the basal operations of arithmetic have been considerably improved since the Fif teenth Century. The old 'galley' method of di vision was replaced by the 'Italian' method, the superiority of which may be seen from the fol lowing examples: Galley.
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3.1416 ) 32.9200 ( 10.48 32.92 ÷ 3.1416 31416 150400 125664 247360 Logarithms, the greatest arithmetical achieve ment of the Seventeenth Century, were introduced by Napier (q.v.) in 1614. Many changes for the better have also been made in the operations for finding the square root and in the algorisms of applied arithmetic.
As to improvements that. may be expected to be introduced in the future, the 'Italian' method of division seems destined to yield to the so called 'Austrian' algorism, which is represented by the following example: Further, proportion, or the old 'rule of three,' will probably be replaced by the equation as such, and the same may be expected for unitary analysis.
Regarding the teaching of arithmetic, the stu dent of pedagogy will look for information to the writers of the Nineteenth Century. The fol lowing may be recommended as valuable works on the history and pedagogy of the subject: Unger, Die Methodik der praktisehen Arithmetik in historischer Entwiekelung (Leipzig, 1888) ; Kehr, Geschichtc tier Methodik (Gotha, 1888, Vol, TIT.) ; Rein. A. Picket, and E. Seheller, Thco•ie and Praxis des Volksschulunterrichts latch llerhartisehea Grundsiitzen (Leipzig, 1898) ; J. A. McLellan and .1. Dewey, Psychology of m her (New York, 1895) ; D. E. Smith, Teaching of Elementary Mathematics (New York, 1900). Notable among higher arithmeties are: Tannery. Loons d'arithme.tique theoriquc et pratique (Paris, 1894) ; and W. W. Roman and D. E. Smith's Higher _Arithmetic (Boston, 1897).