By the above question, I mean how would one effectively study synthetic geometry (geometry that makes no reference to explicit formulas or coordinate systems, like described in Euclid's Elements)? Do you just read through the propositions, try to reconstruct them later and perhaps more or are there some practice problems? Analytic geometry, for example, uses algebra to determine numerical aspects of geometrical figures. It was developed by Rene Descartes and Pierre de Fermat independently of one another. Studying and practicing analytic geometry seems, to me, a bit more straightforward at the moment. For example, you probably first learn about points, lines, line segments, and rays, how to label them, how to use the Cartesian coordinate system and so on. Perhaps this statement is naive but studying synthetic geometry seems completely different from analytic geometry. Anyway, if anyone has any advice, thank you.