Elements, Book I, Proposition 4.
Latin translation: Quod erat demonstrandum (often abbreviated Q.E.D.).
Euclid’s Elements
Quotes from bookElements
EuclidOriginal title Στοιχεῖα
The Elements is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions , and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.
“And the whole [is] greater than the part.”
Καὶ τὸ ὅλον τοῦ μέρους μεῖζον
ἐστιν
Elements, Book I, Common Notion 8 (5 in certain editions)
Cf. Aristotle, Metaphysics, Book Η 1045a 8–10: "… the totality is not, as it were, a mere heap, but the whole is something besides the parts … [πάντων γὰρ ὅσα πλείω μέρη ἔχει καὶ μὴ ἔστιν οἷον σωρὸς τὸ πᾶν]"
Euclid’s Elements
“A prime number is one (which is) measured by a unit alone.”
Elements, Book 7, Definition 11 (12 in certain editions)
Euclid’s Elements
