This paper consists of a translation of Andre Tacquet's discussion of the question of sizes of stars in a heliocentric universe, as published in his posthumous Opera Mathematica of 1668, along with introductory material and analysis. While Robert Hooke mentions Tacquet as one of the "great Anti-copernicans", who argued the question of star sizes against the heliocentric theory with "great vehemency and insulting", Tacquet's discussion has received only scant attention... The kernel of Tacquet's argument is that the absence of any detectable parallax in the stars, combined with the measured apparent sizes of the stars, means that, in a heliocentric universe, the sizes of stars compare to the size of Earth's orbit via the same proportion that they compare to the size of the Earth in a geocentric universe. The translated material presents this argument in a straightforward manner, insulting absent. (read more)