IX. DEPARTMENT: 



MATHEMATICS. 



THE department of Mathematics, includes the study of numbers 

 and magnitudes ; and hence it is sometimes termed, the science of 

 quantity. The name is from the Greek juov0av, I learn : and was 

 applied to it, because the ancients considered this department, in 

 reference to its various uses, as the basis of all learning. As it finds 

 its highest applications in the investigation of the laws of nature, we 

 have here considered it as chiefly introductory to their study ; and as 

 belonging to the same province of human knowledge. As the 

 science of quantity, it is applicable to all quantities which can be 

 measured by a standard unit, and thus expressed by numbers or mag- 

 nitudes. There are objects, such as feeling or thought, which may 

 vary in intensity, but which we have not the means of measuring. 

 We cannot say that we love one person exactly twice as much as 

 another ; or that one man is four times as wise as another ; since love 

 and wisdom aie not mathematical quantities. But we can measure 

 time, by seconds, days, or years ; space, by inches, yards, or miles ; 

 and motion, by the space passed over in a given unit of time. Such 

 quantities, therefore, may be expressed by numbers, and subjected to 

 Mathematical calculations. 



Mathematics, as a general science, is often subdivided into Pure, and 

 Mixed. Pure Mathematics, relates to numbers, figures, or magnitudes 

 abstractly, and without any necessary reference to material or tangible 

 objects : but Mixed Mathematics, is the application of the former to 

 natural objects ; as matter, space, time, motion, and the like, which, 

 though subject to mathematical relations, involve other principles, 

 depending on the laws of nature. Thus, Mechanics, Astronomy, 

 Navigation, Music, and other sciences, are sometimes included under 

 the name of Mathematics : but we would here restrict the term to 

 the Pure Mathematics, with some occasional applications ; as being 

 sufficiently extensive and important to constitute one department of 

 human knowledge. It should not be forgotten that new mathemati- 

 cal principles and problems have led to new discoveries in nature, or 

 inventions in the arts ; and these, in their turn, have led to other new 

 principles and problems in Mathematics. 



The question may here arise, into how many branches this depart- 

 ment should be divided. The branches of Arithmetic, Algebra, and 

 Geometry, are generally recognized as distinct and elementary ; while 

 Trigonometry is sometimes connected with the latter, and sometimes 

 regarded as a distinct branch. Considering, however, that Trigo- 

 nometry is an application of Algebra to certain Geometrical figures, 

 we have no hesitation in associating it with Conic Sections, in the 

 branch of Analytic Geometry. The study of Descriptive Geometry, 

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