did you read the article you posted or this one?

from yours With Cato’s recipe, which Vitruvius was attempting to
explain, the limestone is now known as calcium carbonate
and varying hydrates thereof: Ca(CO 3) x H 2O, where “x” is
one to four. When kilned, this substance loses water and car-
bon dioxide. The two-thirds that remain are CaO, calcium
oxide. This com pound, synonymously named burnt lime,
caustic lime, quicklime, and in Latin, calx, slakes violently
in water—as Vitruvius knew—and produces slaked lime,
Ca(OH) 2, or calcium hydroxide. Now add two parts of sand
to this and you have Cato’s mix.

they had thought it was the after product, slacked lime and not quicklime that was the key ingredient.