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Ostr. Berlin P. 12609

TEI-XML-File: https://p612399.webspaceconfig.de/xml/elephantine_erc_db_016497.tei.xml



Collection Berlin, Ägyptisches Museum und Papyrussammlung, Staatliche Museen zu Berlin, SPK (P)
Inventory Number Ostr. Berlin P. 12609
Publication Number lit math
Current Location exhibition | Neues Museum, Berlin
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) 105 mm | 91 mm | 11 mm
Dating between -300 and -201
Range of Preservation incomplete

Text Basic Information

Localization of Text on Object convex (outside)
Script, Primary Greek
Language, Primary Greek, Ancient
Comments on Handwriting Zur Handschrift, vgl. F. A. J. Hoogendijk, Twelve Greek Ostraca from Elephantine, in: F. A. J. Hoogendijk - B. P. Muhs (Hgg.), Sixty-Five Papyrological Texts Presented to Klaas A. Worp on the Occasion of his 65th Birthday, Leiden 2008, 287; zu Z. 3 vgl. H. Cadell, Einleitung zu P.Coll.Youtie I 55–62, S. 337, Anm. 13.
Comments on Text Layout 19 lines, other side uninscribed
  recto verso
Quantity of Lines 19


Text Content

Modern Title Geometrische Aufgabe
Text Types
  • scientific | math
Summary of Content geometrical exercise: drawing of a regular icosahedron into a sphere of given diameter (cf. Euclid Stoicheia XIII 16)
Location of Composition Elephantine Upper Egypt, 1st nome Egypt (Certainty: )
Multilingualism Monolingual Script = Language



Transcription Translation Pictures

τῆι ηζἰσόπλευρον ἄρα τὸ ζρη. διὰ δὲ ταῦτα καὶ τὰ ησθ
2θτι ιυκ κφζ. ἴση δὲ καὶ ἡ ρσ τῆ ι ηθ καὶ ἴσας ἑδείξαμεν
3τὰς ρη σθ. ἰσόπλευρον ἄρ' ἑστὶν ἕκαστον τῶν μεταξὺ τριγώνων.
4ἴσας γὰρ καὶ παραλλήλους τῆς χλ τὰς ζμ ην θξ ιο κπ ἐγράψαμεν. ἑξα-
5γώνου ἄρα καὶ ἡ χρ, ἀλλὰ καὶ ἡ ψχδεκαγώνου, ὥστ' εἶναι τὰς ψρ ψσ
6πενταγώνου. ἴση ἄρ' ἡ φρ τῆι ρσ, διὸ ἰσόπλευρά ἐστι τὰ ψφρ ψρσ
7τρίγωνα. διὰ ταῦτα δὲ καὶ ἔκαστον τῶν τὸ ψ ὡς κορυφὴν
8ἐχόντων ἰσόπλευρά ἐστιν. πάλιν ἐκβεβλήσθω
9ἐπ' εὐθείας τῆι λψ ἡ λω, ἴση τῆι τοῦ δεκαγώνου πλευρᾶι.
10ἤχθω δὴ ἀπὸ τοῦ λ κέντρουλζ ἑξαγώνου, δεκαγώνου δ' ἦν ἡ
11λω, πενταγώνου ἄρ' ἡ ζω, διὰ τατα δ' ἰσόπλευρόν ἐστι
12τὰ τρίγωνον τὸ ωζη, διὰ ταὐτ τὸ ζηθικω στερεὸν σχἠμα ἐκ
13πρὸς τῶι ω τὰς κορυφὰς ἐχόντων πέντε
14τριγώνων ἰσοπλεύρων πεποίηται.
15δύο δεκαγώνου πλευραὶ καὶ μία ἑξαγώνου τῆς
16δοθείσης σφαίρας τὴν διάμετρον συμπληροῦσιν. καὶ ἡ τῆς
17δοθείσης σφαρας διάμετρος δυνάμει πενταπλασίων τῆς ἡμι-
18διαμέτρου τοῦ κύκλου ἐστιν τοῦ τὸ πεντάγωνον
19περιλαμβανομένου, ἀφ' οὗ τὸ εἰκοσάεδρον ἀναγέγραπται.
1ΗΖ ... So the triangle ZΡH is equilateral. Thus also the triangles ΗΣΘ,
2ΘΤΙ, ΙΥΚ, ΚΦΖ. But equal is also ΡΣ to the line ΗΘ, and as equal we have shown
3the lines ΡΗ and ΣΘ. So each of the triangles lying between (scil. the circles) is equilateral,
4because we had drawn the perpendiculars ΖΜ, ΗΝ, ΘΞ, ΙΟ, ΚΠ equal and parallel to the line XΛ.
5That is why XP is also (scil. equal to one) hexagonal side. But also ΨΧ was (scil. equal to a) decagonal side, so that ΨΡ and ΨΣ
6 are pentagonal sides. Equal was <also> ΦΡ to side ΡΣ, therefore ΨΦΡ and ΨΡΣ are equilateral
7 triangles. Therefore each of the triangles whose common apex is Ψ is also
8equilateral. Furthermore, let the distance
9ΛΩ be drawn as an extension of the distance ΛΨ, equal to the side of the decagon.
11Let the radius ΛΖ equal to the hexagon side be drawn from the centre of the circle Λ, but (scil. equal) to the decagon side was
12ΛΩ , so ΖΩ is a pentagon side. Therefore equilateral is
13the triangle ΩΖΗ. For the same reason, the spatial figure ΖΗΘΙΚΩ is formed by
14 five equilateral triangles having their apex in Ω.
15Two decagonal sides and one hexagonal side together
16give the diameter of the given sphere 1cf. Euclid El. XIII 16 corollary,
17and the diameter of the given sphere squared is five times
18the radius of the given circle squared,
19drawn around the pentagon on which the icosahedron was built. (after Müller/Mau 1960)

1 cf. Euclid El. XIII 16 corollary

Places (read out from edition)




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




DatasetID 16497
last Change 29.07.2022
Berlpap 16497
Trismegistos 65672
Author BerlPap-Team; Daniel Werning, Philip Schmitz
Dataset License Creative Commons: Attribution-NonCommercial-ShareAlike 4.0 International
Data set citation Data set 16497 (= Ostr. Berlin P. 12609), ERC-Project ELEPHANTINE: BerlPap-Team; Daniel Werning, Philip Schmitz.