Abstract
When one has studied analytic geometry, calculus and kindred branches of mathematics which depend to a certain extent upon the construction of loci he is confronted with the difficulty of determining a fairly accurate representation of specific functions. Such a problem bears considerable thought. In an attempt to find a satisfactory method of analysis, the author has grouped several devices which are quite helpful in the construction of various curves. Although there are apparently no rules or laws set down in this field, the following Procedures will be found to be useful in the majority of cases. Nevertheless, these developments should not be considered as mechanical formulae into which data is inserted and from which the required information issues. It is better to think of them as tools which, if used properly, will produce logical conclusions, the importance of this viewpoint lies in the fact that on some occasions certain developments are of no avail. Hence it is the ability to understand and manipulate the various formulae that, is of greatest, significance.