section_path: Works/Elements
section_name: Elements
paragraph_text: Elements
  
  Euclid is best known for his thirteen-book treatise, the Elements (Greek: Στοιχεῖα; Stoicheia), considered his magnum opus. Much of its content originates from earlier mathematicians, including Eudoxus, Hippocrates of Chios, Thales and Theaetetus, while other theorems are mentioned by Plato and Aristotle. It is difficult to differentiate the work of Euclid from that of his predecessors, especially because the Elements essentially superseded much earlier and now-lost Greek mathematics. The classicist Markus Asper concludes that "apparently Euclid's achievement consists of assembling accepted mathematical knowledge into a cogent order and adding new proofs to fill in the gaps" and the historian Serafina Cuomo described it as a "reservoir of results". Despite this, Sialaros furthers that "the remarkably tight structure of the Elements reveals authorial control beyond the limits of a mere editor".
  
  The Elements does not exclusively discuss geometry as is sometimes believed. It is traditionally divided into three topics: plane geometry (books 1–6), basic number theory (books 7–10) and solid geometry (books 11–13)—though book 5 (on proportions) and 10 (on irrational lines) do not exactly fit this scheme. The heart of the text is the theorems scattered throughout. Using Aristotle's terminology, these may be generally separated into two categories: "first principles" and "second principles". The first group includes statements labeled as a "definition" (Greek: ὅρος or ὁρισμός), "postulate" (αἴτημα), or a "common notion" (κοινὴ ἔννοια); only the first book includes postulates—later known as axioms —and common notions. The second group consists of propositions, presented alongside mathematical proofs and diagrams. It is unknown if Euclid intended the Elements as a textbook, but its method of presentation makes it a natural fit. As a whole, the authorial voice remains general and impersonal.