The logic and experimental data are described with which chemists originally deduced the formulas of the fundamental compounds such as H[subscript 2], H[subscript 2]O, Cl[subscript 2], NH[subscript 3], CH[subscript 4], and HCl. This information is never provided in current texts at any level and the formulas of such simple compounds are taken as axiomatic. It is argued that fourth-year high school and first-year undergraduate students studying chemistry would gain substantially from exposure to the fascinatingly simple but very powerful logic with which these molecular formulas and structures were deduced. The article provides an ample number of examples from which an instructor can choose to complement the standard topics in an introductory course. Further explanations, questions, and worked answers are provided in the Supplemental Material to assist students and also to help the instructor place the topic in the chemistry syllabus. (Contains 5 tables and 14 notes.)