For example, Archimedes of Syracuse and Apollonius of Perga, the greatest mathematicians of their time, received their training from Euclid's students and his Elements and were able to solve many open problems at the time of Euclid. It is a prime example of how to write a text in pure mathematics, featuring simple and logical axioms, precise definitions, clearly stated theorems, and logical deductive proofs. The Elements consists of thirteen books dealing with geometry (including the geometry of three-dimensional objects such as polyhedra), number theory, and the theory of proportions.