ANALYTICAL GEOMETRYCHAPTER I.PRELIMINARY OBSERVATIONS.1. Algebra is that branch of Mathematics in which quantities are represented by letters, and the operations to be performed upon them indicated by signs. It serves to express generally the relations which must exist between the known and unknown parts of a problem, in order that the conditions required by this problem may be fulfilled. These parts may be numbers, as in Arithmetic, or lines, surfaces, or solids, as in Geometry.2. Before we can apply Algebra to the resolution of Geometrical problems, we must conceive of a magnitude of known value, which may serve as a term of comparison with other magnitudes of the same kind. A magnitude which is thus used, to compare magnitudes with each other, is called a unit of measure, and must always be of the same dimension with the magnitudes compared.3. In Linear Geometry the unit of measure is a line, as a foot, a yard,