In this article, the author proposes a methodology for the rhetorical analysis of scientific, technical, mathematical, and engineering (STEM) discourse based on the common topics (topoi) of this discourse. Beginning with work by Miller, Prelli, and other rhetoricians of STEM discourse--but factoring in related studies in cognitive linguistics--she argues for a reimagining of topoi as basic schema that interrelate texts, objects, and writers in STEM communities. Then, she proposes a topical method as a stable, broadly applicable heuristic that may help fit the rhetorical dynamics of the much-studied research article (RA) into the wider context of written technical discourse--exactly the type of improvement that Gross, Fahnestock, and others have proposed. Finally, as an illustration of this argument, the author performs a pilot topical survey of 18 RAs representing six STEM disciplines. This survey yields a set of 30 topoi used samplewide that can form a starting point for future surveys. She answers challenges to the significance and relevance of a topical method and finishes by sketching some future applications of the method that can move rhetoric of science beyond the RA. (Contains 3 tables, 2 figures, and 7 notes.)