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Ostr. Berlin P. 12002

TEI-XML-File: https://p612399.webspaceconfig.de/xml/elephantine_erc_db_016498.tei.xml



Collection Berlin, Ägyptisches Museum und Papyrussammlung, Staatliche Museen zu Berlin, SPK (P)
Inventory Number Ostr. Berlin P. 12002
Publication Number lit. math
Current Location magazine | papyrus depository
Publication Permission Status (unknown)
Publication Status published

Origin / Provenance

Ancient Provenance Site Elephantine (Ꜣbw; Yb; YbꜢ; YbꜤ; Ἐλεφαντίνη, יב , ⲉⲓⲏⲃ) [Trismegistos]
Ancient Provenance District Upper Egypt, 1st nome (Ombites) [Trismegistos]
Type of Discovery archaeological excavation
Finder (= First Purchaser) Rubensohn, Otto (excavation director)
District of Find / Purchase in Egypt Upper Egypt, 1st nome (Ombites) [Trismegistos]
Type of Acquisition for the Intitution partage
Date of Acquisition for the Intitution between 1906 and 1906


Object Type ostracon
Color pottery, yellow brown
Size (Height | Width | Thickness) 99 mm | 62 mm | 11 mm
Dating between -300 and -201
Criteria for Dating palaeography

Text Basic Information

Localization of Text on Object convex (outside)
Range of Preservation (Text) incomplete
Script, Primary Greek
Language, Primary Greek, Ancient
Comments on Text Layout 12002: 14 Zeilen; P. 12007: 12 Zeilen; P. 12008: mind. 8 lines, other side uninscribed
  recto verso
Quantity of Lines 14


Text Content

Modern Title Geometrische Aufgaben
Text Types
  • scientific | math
Summary of Content geometrical exercise: mathematical proof of the equality and ratio of the squares over the sides of various polygons (pentagons, hexagons, decagons) in a circle (cf. Euclid Stoicheia XIII 10); corrections in lines 12 and 14
Location of Composition Elephantine Upper Egypt, 1st nome Egypt (Certainty: )
Multilingualism Monolingual Script = Language



Transcription Translation Pictures
1 . .
2ἀποδείκνυται ἡ πρότασις, ὅτι ἡ τοῦ
3πενταγώνου πλευρδύναται
4τήν τε τοῦ ἑξα-
5γώνου το γ κύκλωι τῶι αβ
6καὶ τὴν τοῦ δεκαγώνου. ἔστωσαν αἱ αγ βγ 1marg.:ἰσοπλεύρου
7πλευραὶ δεκαγνου. ἀλλ'δεκα
8γώνου ἡ γβ περιφέρεια δ1ίχα τετμήσθω.
9δῆλον, ὅτι ἡ ὑπὸ τῶν λγβ γωνία τῆι
10ὑπὸ τῶν γβλ, κοινῆι τοῦ τε αβγ καὶ τοῦ βκλ
11τριγώνου ἐστὶν ἴση. ἔστιν ρ'ς ἡ αβ
12πρὸς βγ, οὕτως βγ πρὸς βλ. τὸ ἄρ'ὑπὸ τἠς ῶν αβ βλ
13ἴσον τῶι ἀπὸ τῆς βγ. πάλιν ἡ α . .
14 λωι. αιδὲ γη βη εἰκοσαγώνοθ

1 marg.:
2The theorem is proved, that the square over the side of the
3pentagon is equal to the sum of the squares
4over the sides of the hexa-
5gon in the circle AB
6and of the decagon. Let ΑΓ and ΒΓ be sides of the 1marg.:equilateral
7decagon. Let the arc over the decagon side
8ΓB be bisected.
9It is clear, since the angle ΛΓΒ is equal to
10the angle ΓΒΛ common to the triangles ΑΒΓ and ΒΚ (read Γ)Λ.
11Thus the ratio ΑΒ
12 to ΒΓ is equal to the ratio ΒΓ to ΒΛ. Thus the rectangle formed by the sides ΑΒ ΒΛ
13is equal in area to the square over the side ΒΓ ...
14but the stretches ΓΗ and ΒΗ are sides of an icosagon ... (after Müller/Mau 1960)

1 marg.:
Places (read out from edition)




RulerID Regnal Year MonthID Day Date of the Text Gregorian Date dating_comment
-299 BCE -200 BCE ;




DatasetID 16498
last Change 29.07.2022
Berlpap 16498
Trismegistos 65672
Author BerlPap-Team; Daniel Werning, Philip Schmitz
Dataset License Creative Commons: Attribution-NonCommercial-ShareAlike 4.0 International
Data set citation Data set 16498 (= Ostr. Berlin P. 12002), ERC-Project ELEPHANTINE: BerlPap-Team; Daniel Werning, Philip Schmitz.