Euclid was probably born in Athens and later moved to the center of culture of his age, Alexandria of Egypt. He is associated foremost with the Elements, a single treatise in which propositions are derived from principles labeled as “deﬁnitions,” “postulates,” and “common notions” (or axioms).The work is a compilation based on several sources. Books I to VI of the Elements deal with Plane geometry, books VII to X with Arithmetic and theory of numbers and books XI-XIII with solid geometry. Two more books dealing with the regular solids were added to the Elements, Book XIV was composed by Hypsicles of Alexandria at the beginning of the second century BCE and is a work of outstanding merit; Book XV is of a much later time and inferior in quality; it was written by a pupil of Isidores of Miletos (the architect of Hagia Sophia, c. 532).The strictly axiomatic structure of the book and its rigorous use of logic served for centuries as the model for scientific enquiry.

The first Latin translation from Arabic by Campanus was published in 1482 in Venice, the first from the original Greek by Zamberti also in Venice, in 1505, and republished in 1537 in our edition by Johannes Hervagius (Herwagen), (1497- 1558), with a preface by the great Lutheran scholar Philip Melanchthon (1497-1560).

The page shows an image of the famous Pythagoras’ theorem, showing that a square drawn on one side of a triangle with a right (90 degrees) angle is equal to the squares drawn on the other two sides. Pythagoras of Samos (died 497/6 BCE), founded a sort of religious brotherhood, which attached great importance to mathematics and raised it to the rank of a science. Many geometrical discoveries are ascribed to them, most famously this one. The text of the theorem (proposition 47 from Book I) is attributed to Euclid, the explanation is by the later Alexandrian mathematician Theon (CE 335-CE 405). Theon’s explanation, translated by Zamberti, is followed by further comments taken from Campanus’ translation.

**Sources**

- Paul T Keyser and Georgia Irby-Massie (eds), The encyclopedia of ancient natural scientists : the Greek tradition and its many heirs, Milton Park, Abingdon, Oxon ; New York, NY : Routledge, 2008.
- George Sarton, Introduction to the history of science, Baltimore: Williams & Wilkins Co., 1927-1948, vol. 1, pp. 73-75 (on Pythagoras and his theorem) and pp. 153-6 (on Euclid).
- George Sarton, Ancient science and modern civilization, [Lincoln, Neb.] : University of Nebraska Press, 1954. pp. 20-22.
- Ludovico Geymonat (ed.) Storia del pensiero filosofico e scientifico. Milano, Garzanti, 1970-1972, vol. 2, p. 77.