Bringing the meta-mathematics of Hero of Alexandria and Claudius Ptolemy into conversation for the first time, I argue that they employ identical rhetorical strategies in the introductions to Hero's Belopoeica, Pneumatica, Metrica and Ptolemy's Almagest. They each adopt a paradigmatic argument, in which they criticize the discourses of philosophers and declare epistemological supremacy for mathematics by asserting that geometrical demonstration is indisputable. The rarity of this claim---in conjunction with the paradigmatic argument---indicates that Hero and Ptolemy participated in a single meta-mathematical tradition, which made available to them rhetoric designed to introduce, justify, and bolster the value of mathematics.
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