The equation of the hyperbola usually presents itself to the student in the form in the elements of graphs, before the canonical form is reached in Analytical Geometry. Some of the properties of the curve are easily obtained from the above equation by the methods of elementary geometry; the object of this note is to illustrate the process. We shall use the equation in the form xy = c2, and it will be convenient to arrange the discussion in numbered Theorems. The axes may be rectangular or oblique.