MATERIA MEDICA 



MATHEMATICS 



MATE'RIA MED '1C A, a Latin phrase mean- 

 ing the materials of medicine, is the division of 

 medical science which relates to the materials 

 used in the cure, alleviation or prevention of 

 disease. The materials are classified according 

 to physical properties, method of preparation, 

 composition, their action as curative agents, 

 etc. See MEDICINE AND DRUGS. 



MATHEMATICS, math e mat' iks. To the 

 child in the elementary school mathematics 

 means arithmetic, processes of addition and 

 subtraction; to the high school pupil the con- 

 ception widens and takes in algebra and, later, 

 geometry ; while to the student who pursues the 

 subject further the term takes on an even 

 broader meaning. But in all these branches, 

 no matter how they may differ in subject- 

 matter and in methods, there is a similarity 

 they are all sciences which deal with magni- 

 tude, quantities and numbers, and their rela- 

 tions. That is about as good a definition as 

 can be given of mathematics, for while some 

 of the greatest scientists and philosophers have 

 attempted to define the term, no one has ever 

 succeeded to the satisfaction of all. 



All mathematical conceptions that is, all 

 conceptions or ideas which can be definitely 

 described in terms of numbers are within the 

 scope of mathematics; and even the person 

 who could not define a mathematical concep- 

 tion, or perhaps has never even heard the 

 name, can tell whether or not any notion does 

 come within the range of mathematics. It is 

 clear, for instance, that sugar, regarded as the 

 chief ingredient of candy, is not a mathematical 

 conception; when only its bulk, its weight 

 and its price are considered it is such a notion. 

 A book may contain the wisdom of the ages, 

 or all the beauties of poetry, and thus lie quite 

 outside the scope of mathematics, but in so 

 far as it is a rectangular solid with a definite 

 length, breadth and thickness, it is a mathe- 

 matical conception. 



The Great Branches. Mathematics is not 

 just one science, but a great group, joined 

 together by similarity in subject matter and 

 treatment. As generally considered, it is di- 

 vided into three great departments, but these 

 are so closely related, so interwoven with each 

 other, that no hard and fast distinctions are 

 possible. The departments are: 



(1) Arithmetic, which deals with the nature 

 and properties of numbers, and with operations 

 performed by means of them. This branch 

 also includes algebra in so far as the latter 

 science is but generalized arithmetic, express- 



ing the same facts in symbols instead of fig- 

 ures; 



(2) Analysis, which includes some of the 

 more abstruse and theoretical phases of alge- 

 bra, as differential equations, but has as its 

 main branch calculus; 



(3) Geometry, which treats of the measure- 

 ment and properties of lines, angles, surfaces 

 and solids. One branch of this subject, ana- 

 lytical geometry, is included by some authori- 

 ties under analysis. Trigonometry is a higher 

 phase of geometry. 



Pure and Applied Mathematics. Anyone who 

 has studied geography or physics or astronomy 

 knows that from time to time he has much use 

 for mathematics. He knows, too, that he uses 

 numbers not as abstract things with no especial 

 connection with the concrete affairs of life, but 

 as a means of finding out certain very definite 

 facts. This phase of mathematics, which con- 

 siders theories and principles only as they are 

 related to the material world, is known as 

 applied mathematics, and it is opposed to pure 

 mathematics, which treats of theories and prin- 

 ciples for their own sake. The student who 

 masters the multiplication table is studying 

 pure mathematics; it makes no difference to 

 him whether grains of sand or solar systems 

 are under consideration two times six makes 

 twelve in either case. 



Pure mathematics lies at the basis of applied 

 mathematics, but this does not mean that the 

 latter is of minor importance. In studying 

 such practical subjects as heat and optics and 

 electricity, app'lied mathematics is of the 

 greatest service, and many of the discoveries 

 of science could never have been made with- 

 out its help. An illustration of this fact 

 will be interesting. The planet Uranus, over 

 a billion and a half miles from the sun, 

 was believed by astronomers to be the outer- 

 most member of the solar system, and all its 

 movements were carefully charted. But ob- 

 servation showed that at times it behaved very 

 strangely, apparently wandering out of its 

 path, and astronomers decided that only the 

 attraction of another planet, far beyond it, 

 could thus pull it from its course. Accordingly 

 they set to work, and by means of mathe- 

 matical formulas figured out where the new 

 planet ought to be. Then when all was ready, 

 they examined the heavens through their 

 strongest lenses, and there was the planet just 

 where they had calculated it must be, and 

 they named it Neptune. The telescope alone 

 might never have discovered this planet. 



