Lines are made up of points, and have extension only in one direction. Surfaces have length and breadth, and are distinguished as triangles, quadrilaterals, polygons, etc., according to the number of lines that circumscribe them. Solids have length, breadth, and thickness. From a few elementary facts, much geometrical science has been deduced, by very simple, logical processes. It is intimately related to other sciences, and of much practical importance; but, if there were no other advantage derived, as a discipline of the reasoning faculty there can be nothing better. To pursue the study profitably there is little need of an instructor. Class recitations are helpful, but let any one intent on personal culture, and having only a little time for the work, get a good elementary treatise on plane and solid geometry, and study it. The exercise will become a delight, will give strength and grip to the faculties, and furnish protection against the mental dissipation caused by spending much time in the hasty, careless reading of what is fitly called light literature. Analytical geometry is that branch which examines, discusses and develops the properties of geometrical magnitudes by the use of algebraic symbols. The questions or problems are solved, not, as in plane geometry, by diagrams or figures drawn to show certain relations of magnitudes, but by making algebraic symbols represent them, and thus solving the problems. Analysis is much used in simple algebraic processes, but more in analytical geometry, and in differential and integral calculus, which has been called the transcendental analysis. It is useful as a higher branch of the science, and without it the best achievements of the greatest mathematicians would scarcely have been possible. These last named branches are generally best pursued in our higher academies and colleges. A college course would be sadly deficient without them, but only for exceptional cases would it be advisable to put them in a course of study to be pursued privately. If this brief mention of the higher mathematics kindles desire for further knowledge, and you hesitate to grapple with them alone, by all means go to college, and after a proper introduction, wherein the chief embarrassment is felt, even calculus will be found an agreeable acquaintance.