The Tentamen is built on Bolyai's belief that mathematics consists of arithmetic and geometry with arithmetic as the mathematics of time and geometry as the mathematics of space. He tries to set both disciplines on an axiomatic basis and one his strong beliefs is that the axioms should be independent:
Ang Tentamen ay binuo sa Bolyai ang paniniwala na ang matematika ay binubuo ng arithmetic at geometry sa arithmetic bilang ang matematika ng oras at geometry bilang ang matematika ng space. He tries upang itakda ang parehong disciplines sa isang axiomatic batayan at isa sa kanyang malakas na paniniwala ay ang mga axioms na dapat ay independent: