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Funding for this project generously provided by Overdeck Family Foundation

around 75–125 CE

Euclid Diagram Papyrus

Oldest known complete diagram from Euclid's Elements

This fragment of a papyrus contains one of the oldest known complete diagrams from Euclid's Elements. It was discovered in Oxyrhynchus, Egypt, by an expedition of Grenfell and Hunt in 1896–1897.

Euclid Diagram Papyrus

The fragment contains an unlabeled diagram and a statement of the fifth proposition in Book 2 of the Elements: if a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half. The statement can be interpreted as a geometric formulation of the algebraic identity (x + y)(x - y) + y² = x².

Artifact dimensions

8.5 cm × 15.2 cm

Original artifact location

Oxyrhynchus (historical name), Menia, Egypt (current name)

Current artifact location

Penn Museum, Philadelphia

Catalog number

E2748 (current), ES 2748 (historical)


Geometry timeline Babylonian Nested Triangle Tablet Babylonian Geometrical Problem Tablet Babylonian Sippar Recombination Text Moscow Mathematical Papyrus Euclid's Elements Euclid Diagram Papyrus Moche Net Balance Scale Al-Tusi's Commentary on the Elements

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Computational Explanation

Other Resources

Additional Reading

  • Fowler, D. The Mathematics of Plato's Academy, 2nd ed. Oxford, England: Clarendon Press, 1999.
  • Euclid. Euclid's Elements. Green Lion Press, 2002.
  • Grenfell, B. P. and Hunt, A. S. Plate 58 in Oxyrhynchus Papyri I, Vol. IV. London: Egypt Exploration Fund, 1898.
  • Heath, T. L. Euclid's Elements, Vol. 1 (Books I and II). New York: Dover, 1956.

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