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Euclid's Elements
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The Elements is a mathematical treatise written c. 300 BC by the Ancient Greek mathematician Euclid.
Papyrus Oxyrhynchus 29, a fragment of Euclid's Elements dated to c. 3rd–4th century AD. Found at Oxyrhynchus, the diagram accompanies Book II, Proposi
Papyrus Oxyrhynchus 29, a fragment of Euclid's Elements dated to c. 3rd–4th century AD. Found at Oxyrhynchus, the diagram accompanies Book II, Proposition 5.
Euclid's subdivision of line segment AB into the golden ratio from Book II Proposition 11, with an arc added to the traditional diagram. The construct
Euclid's subdivision of line segment AB into the golden ratio from Book II Proposition 11, with an arc added to the traditional diagram. The construction finds the midpoint E of side AC of square ABCD, intersects line AC at F with a circle of radius EB, and constructs a second square AFGH, whose vertex H is the subdivision point.
The Pythagorean theorem in MS. Vat.gr.190
The Pythagorean theorem in MS. Vat.gr.190
A woman teaching geometry, from a manuscript (c. 1309–1316) of Adelard of Bath's 12th century translation of the Elements from Arabic into Latin
A woman teaching geometry, from a manuscript (c. 1309–1316) of Adelard of Bath's 12th century translation of the Elements from Arabic into Latin
Parallel postulate
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In geometry, the parallel postulate is the fifth postulate in Euclid's Elements and a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
Euclid's Elements
…without interpreting these magnitudes as numbers. While the first four postulates are relatively straightforward, the fifth is not. It is known as the parallel postulate, and the question of its independence from the other four postulates became the focus of a long line of research leading to the development of non-Euclidean…
The page containing the Parallel Postulate from the 1747 Latin edition of Euclid’s Elements, originally Euclid’s 5th Postulate, here reclassified and
The page containing the Parallel Postulate from the 1747 Latin edition of Euclid’s Elements, originally Euclid’s 5th Postulate, here reclassified and presented as Axiom XII by the editor.