MATERIALISM. 182 MATHEMATICS. philosophers (see Ioxian School) were by im- plication materialists; Demoeritus, Leucippus, Epicurus, and Lucretius (see articles on them) worked out a quite elaborate materialistic sys- tem. There is a materialistic vein running through the thought of many of the Italian philosophers of the Renaissance. Gassendi, like- wise, makes consciousness, at least in the form of feeling, an inseparable attribute of matter. The eighteenth century was especially marked by its materialistic philosophy. Priestley in Eng- land and La ilattrie, Diderot, and llolliach in France were outspoken in their materialism of the attributive kind. The latter part of the eigh- teenth century and the early part of the nine- teenth century were characterized by a strong anti-materialistic reaction, to be followed again in the middle of the latter century by a strong outburst of materialistic thought. Carl Vogt, Jacob Jloleschotl. Louis Biichncr. and Heinrich Czolbe carried on a vigorous propagandism in favor of materialism, but the results of the scientific study of psychology were too patent, and the nineteenth century went out with a strong dislike for the view that made nuitter tlie one essential reality. For an e.cellent history of materialism, see F. A. Lange, Ocschichte des Matcriulisinun (Iser- lohn, 1866; 5th ed. 1806; Eng. trans, by K. C. Thomas. London. 1870-81). The best work to commend to the reader who wishes to know what recent materialism has to say for itself is BUchner, Kraft iind Stoff (Frankfort, 1857; Eng. trans., Force and Matter, 4th ed., London, 1884). MATERIALS, Stbength of. See Strength OF M.VTEKIALS. MATE'RIA MED'ICA (Lat., medical ma- terial). That dciiartriicnt of the .science of medi- cine which treats of the materials employed for the alleviation and cure of disease: (1) Their physical properties; (2) various modes of prep- aration; (3) chemical composition and rela- tions, including the tests for purity, and the means of detecting prtibable adulterations; (4) physiological action on man and animals in large and small doses; (5) therapeutic actions ami uses, and the average doses in which they shimld be prescribed; and (6) the oHicial prep- arations containing the substances in question, and their uses. Strict classification of drugs into groups according to their physiological ac- tion is impossible, as their action is so-complex that one wouhl often be found in several classes. It is, however, eustomarv to group them accord- ing to their most marked or inq)ortant charac- teristic for convenience of descrii)tion and ease in recalling those having a common action. See TiiKRArKirrrs ; Pharmacopiicia. MATERIEL, ma'tA'rf'61' (Lat. malerialiti. re- lating to matter). This term in its military sense includes evcrj-thing in the military or naval services used by, or necessary to, the i)ersonnel ; such as nnns, ammunition, baggage, provisions, stores, tools, horses, wagons, tents, etc. MATERNA, matcr'na, .-^fAI.IE (1847—) . .
.■ siiiiiii iipciu singer, born in Saint Georgen, Styria. She maile her first stage appearance in fJralz. 1861, and in the same year married Karl Frieilricli. n well known actor, and with him was engaged at the ( 'arlTlieater. Vienna. Tier il.'liul ;is a prima-donna occurred in HUM, when she sang at the Imperial Opera as Selika in L'Africahw. In 1876 she created the part of Briinnhilde in Vagner"s Xibelungen trilogj- at Bayreuth. She became one of the greatest so- pranos of the early Wagnerian opera, and a great favorite in the United States. MAT GRASS. S,v Aiimoi-hila; Nardus. MATHEMATICAL SOCIETY, Tuf. Ameri- can. An association for the advancement of niatlie- matical science. It was reorganized in .July, 1804, luider its present name. The society has a meniborsliip of about 400. A meeting is held an- nually at Columbia University, and .section meet- ings take place at Chicago and San Francisco. It publishes two periodicals, the liulliliii of the American MalluiiKitical l^ocicty, and the Truns- actiiiii.i of llic A)iiirirnn Mnlhrmalirol Society. MATHEMATICAL SOCIETY, The Lonuo.. An association founded in I8lj.") by a number of English mathematicians, and incorporated in 1804. It was instituted for the promotion of mathematical knowledge. The society owns an excellent library of books and periodicals on sci- entific subjects. The socict,v began in 186.") tin- publication of the Procccdin<is of the I.iindun Mathematical Society, and has now thirty-five volumes of essays upon advanced mathematical to])ics, MATHEMATICS (Lat. mathematica, from Ok. iitttliifiariKij, iiKillicmalikt; mathenmtics, from ItuBiifi-a, madhiina, learning, science, from imv- davvtv, manlhanein, to learn). The technical meaning of the word is due to the Pj-thagorcans, who distinguished four branches: "There are four degrees of mathematics: arithmetic, music, geometry, spherics." In modern times attempts have frequently been made to frame a satisfac- tory definition of the scope of the science. Des- cartes asserts that "all sciences which have for their object the search after order and measure belong to mathematics." D'Alembert in the Enc;iclo]>cdie defines it as the science which con- siders the properties of magnitude in so far as this is ealeulalde or measurable. Comte, in his Philosophic poxitive, s])eaks of it as the sciiiicc which proposes to determine certain magnitudes from certain others from the exact relations that exist between them. Sagnet has proposed the following: "Mathematics have for their object the study of exact and necessary relations con- cerning the magnitude, the form, and the relative position of various objects, nutterial or imma- terial, which a]ipeal to our senses." With re- gard to these definitions it may be observed that they are all based on concepts such as 'magni- tude.' 'order,' 'measure.' that are themselves ex- tremely ditlicult to define. lIisTouY. Mathematics as a science makes its first definite appearance among the Egyptians. There are evidences of its antiquit.v among the Chinese. Hindus, and Babylonians, but tlie earliest written records of considerable mathe- matical progress are found in Iv.'vpt, and give nn interesting view of the stale of the science as earlv as the latter part of the third millenniuni before Christ. .i that time arithmetic was suf- ficientl.v developed to include a fair niimerical system, a cumbersome but elaborate treatment of conmion fractions, and some work in finite series. . limited and imperfect system of mensuration was known, a be<.'inning was made in algeliraic .symbolism, and the simple equation was solved.
