Metadata
Text
Text: Dates
Literature

Persons & Deities

Ostr. Berlin P. 12002

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

Metadata

Collection

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] Certainty:
Ancient Provenance District	Upper Egypt, 1st nome (Ombites) [Trismegistos]
Type of Discovery	archaeological excavation Certainty:
Finder (= First Purchaser)	Rubensohn, Otto (excavation director) Certainty:
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

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

Text

Transcription

Translation

Pictures

convex

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

¹ marg.:

convex

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

¹ marg.:

Places (read out from edition)

Dates

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

Literature

Dorandi, T., La tradizione papiracea degli „Elementi“ di Euclide (1992). (311)
Fowler, D., The Mathematics of Plato’s Academy. A New Reconstruction (1999). (209-211)
Horak, u., Illuminierte Papyri, Pergamente und Papiere I (1992). (253)
Müller, W. & Mau, J., Mathematische Ostraka aus der Berliner Sammlung (1960). (1-10 no. 2)

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 (CC BY-NC-SA)
Data set citation	Data set 16498 (= Ostr. Berlin P. 12002), ERC-Project ELEPHANTINE: BerlPap-Team; Daniel Werning, Philip Schmitz.