An Introduction to Algebra: Being the First Part of a Course of Mathematics (Classic Reprint)

But motum though a quantity, is not, strictly speaking, a magnitude. It has neither length, breadth, nor thickness. 6. Trigonometry and Conic Sections are branches of the mathematics, in which the principles of geometry are applied to triangles, and the sections of a cone. 7. Mathematics are either pure or mixed. In pure mathematics, quantities are considered, independently of any substances actually existing. But, in mixed mathematics, the relations of quantities are investigated, in connection with some of the properties of matter, or with reference to the common transactions of business. Thus, inS urveying, mathematical principles are applied to the measuring of land; in Optics, to the properties of light; and in A stronomy, to the motions of the heavenly bodies. 8. The science of the pure mathematics has long been distinguished, for the clearness and distinctness of it principles ;and the irresistible conviction, which they carry to the mind of every one who is once made acquainted with them. This is to be ascribed, partly to the nature of the subjects, and partly to the exactness of the definitions, the axioms, and the demonstrations. 9. The foundation of all mathematical knowledge must be laid in definitions. A definition is an explanation of what is meant, by any word or phrase. Thus, an equilateral triangle is defined, by saying, that it is a figure bounded by three equal sides. It is essential to a complete definition, that it perfectly distinguish the thing defined, from every thing else. On many subjects it is difllicult to give such precision to language, that it shall convey, to every hearer or reader exactly the same ideas. But, in the mathematics, the piincipal terms may be BO defined, as not to leave room for the least difierence of apprehension, respecting their meaning. All must be agieed, as to the nature of a circle, a square, and a trian
(Typographical errors above are due to OCR software and don't occur in the book.)