During the years 1873-1879, J. Willard Gibbs published his now-famous set of articles that form the basis of the current perspective on chemical thermodynamics. The second article of this series, "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces," published in 1873, is particularly notable for two reasons. First, it establishes what is now referred to "Gibbs energy" as the quantity that must be minimized at equilibrium under the conditions of constant temperature and pressure. Second, it introduces a completely geometrical (and nowadays essentially lost) analysis of thermodynamics. A full 26 years later, in unpublished lecture notes from 1899 that can be found only in the collection at Yale University, Gibbs describes a novel way to use this geometrical analysis to depict Gibbs energy. These lecture notes have been summarized in detail previously by Edwin B. Wilson. The goal of this short article is to show just how useful such a geometrical analysis can be. The author notes in advance that this approach is significantly different from previous graphical analyses involving Gibbs energy, including, in this "Journal," discussions of graphing Gibbs energy versus temperature or Gibbs energy versus reaction extent. In particular, the author will show how a remarkably simple extension of Gibbs' original concept allows for the description of eight thermodynamic quantities (P, V, T, S, U, H, G, and A) on the same graph, emphasizing the relatedness of these functions. The author extends this graphic idea to consider chemical, not just thermal, equilibrium. (Contains 4 figures.)