The book is an epistemological distinction betwen Leibniz and Descartes in how they varied with proofs and eternal truths. It seeks to draw similarities and differences of their doctrines by comparison and contrast. Hacking's focus throughout is philosophy of mathematics and prehistory in the context of content and form. As the title asserts topics include proofs- finite and infinite. Eternal truth through geometrical and algebraic dialogue, in the first time in history according to Hacking, offers evidence of proofs. A short yet dense read of two great philosophers.