The objective of this book is to elucidate the shape of Greek mathematical contemplating. It might be study on three ranges: as an overview of the practices of Greek arithmetic; as a precept of the emergence of the deductive method; and as a case-analysis for a primary view on the historic previous of science. The begin line for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the event and lettering of their diagrams, and the persevering with interaction between textual content material and diagram in their proofs, to light up the underlying cognitive processes. A shut examination of the mathematical use of language follows, notably mathematicians' use of repeated formulae. Two important chapters acquired right down to current how mathematical proofs are structured and make clear why Greek mathematical comply with manages to be so satisfactory. A final chapter appears into the broader historic setting of Greek mathematical apply.