Ostr. Berlin P. 12002
Verena M. Lepper
Artefact metadata
BerlPap-Team; Daniel Werning, Philip Schmitz
TEI encoding
Daniel A. Werning
Sandro Schwarz
Ägyptisches Museum und Papyrussammlung, Berlin
Berlin
v2.1
Licence for this TEI document: Creative Commons, Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
Germany
Berlin
Berlin, Ägyptisches Museum und Papyrussammlung, Staatliche Museen zu Berlin, SPK (P)
Berlin, Ägyptisches Museum und Papyrussammlung, Staatliche Museen zu Berlin, SPK (P)
Papyrussammlung
Ostr. Berlin P. 12002
Ostr. Berlin P. 12002
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
convex (outside)
Geometrische Aufgaben
clay | fired
ostracon
palaeography
- object's condition:
- text's condition: incomplete
12002: 14 Zeilen; P. 12007: 12 Zeilen; P. 12008: mind. 8 lines, other side uninscribed
Egypt
Upper Egypt, 1st nome
Elephantine
Rubensohn, Otto (excavation director)
Egypt
Upper Egypt, 1st nome
Elephantine
partage
excavation of O. Rubensohn in Elephantine, winter 1906/07 (26.12.1906)
(unknown)
magazine | papyrus depository
-
1-10 no. 2
209-211
253
311
[http://www.trismegistos.org/tm/detail.php?quick=65672]
[http://smb.museum/berlpap/index.php/16498]
Amulet charm
documentary
account
horizontal format
vertical format
administrative document
bill
commentary
contract
horizontal format
documentary | contract | promissory note
vertical format
dedication
dept instrument
diary
foundation charter
hypomnema
horizontal format
vertical format
indictment
Documentary | Jar Label
legal document
letter
"Urkundenformat"
horizontal format
letter address
private
transversa carta
vertical format
list
name list
onomasticon
product list
marriage contract
names
note
oath
vertical format
offer
documentary | official
documentary | official letter
Order for payment or delivery
documentary | order to arrest
petition to the king (enteuxis, mkmk)
proskynema
act of worhsip wšt.t
name
Documentary | Ration List
receipt
tax receipt
tombstone
will/testament
Documentary | Wooden Label
drawing
commentary
vigniette
literary
biography
commentary
eulogy
historic
lamentation
narrative
prose
verse
poetry
wisdom
instruction
proverb(s)
(no inscription)
(other)
petition to the emperor
Prescription
religious
Christian
commentary
dedication
divination
litany
magical
oracular inquiry
Gnostic
Islamic
religious | Islamic | amulet
dedication
divination
litany
magical
oracular inquiry
ritual
Jewish
dedication
divination
litany
magical
oracular inquiry
ritual
Manichaic
Mesopotamian
polytheistic Aramaian
polytheistic Egyptian
dedication
divination
litany
love charm
magical
oracular inquiry
ritual
unclear religion
dedication
divination
litany
magical
oracular inquiry
religious-literary
Christian
Biblical
New Testament
Old Testament
commentary
eulogy
hymn
lithurgical
monastical
myth
patristic
prayer
Gnostic
commentary
eulogy
hymn
prayer
Islamic
commentary
eulogy
hymn
myth
prayer
Qurʾānic
Jewish
commentary
eulogy
Hebrew Bible
hymn
myth
prayer
Manichaic
commentary
eulogy
hymn
prayer
Mesopotamian
commentary
eulogy
hymn
myth
prayer
polytheistic Aramaian
commentary
eulogy
hymn
myth
prayer
polytheistic Egyptian
Book of the Dead
Coffin Text
commentary
eulogy
hymn
myth
prayer
Pyramid Text
unclear religion
commentary
eulogy
hymn
myth
prayer
scientific
astronomy
Book of Dream
commentary/gloss
math
calculation
essay
geometry
medicine
essay
prescription
scientific | Alchemical presciption
scientific | astrology
horoscop
writing exercise
(unclear)
Akkadian
Arabic
Aramaic, Imperial
Carian
Egyptian
Coptic
Akhmimic
Bohairic
Fayumic
Middle Egyptian / Oxyrhynkhitic
Old Coptic
Sahidic
Sub-Akhmimic
Demotic
Early Demotic
Early Demotic - Ptolemaic Demotic
Ptolemaic - Roman Demotic
Ptolemaic Demotic
Roman Demotic
Late Egyptian
Later Egyptian
Middle Egyptian
Middle Egyptian, Classical
Middle Egyptian, Late
Neo-Middle Egyptian
Old Egyptian
pre-Coptic Egyptian
pre-Coptic Egyptian / Greek
Ptolemaic
Egyptian languages
English
German
Greek, Ancient
Greek, Ancient or Coptic
Hebrew
Hebrew, Ancient
Late Aramaic
Latin
Libyan
Mandaic
Meroitic
Nabataean
(none)
(not identified)
Nubian
Old Nubian
Old Persian
Pahlavi
Phoenician
Semitic language
Syriac
Uninscribed
Late Aramaic
Arabic
Aramaic, Imperial
Carian
Coptic
Coptic Cursive
Coptic Half-uncial
Coptic Uncial
Egyptian
Cursive Hieroglyphs
Demotic
Early Demotic
Early to Middle Demotic
Late Demotic
Middle Demotic
Middle to Late Demotic
Hieratic
Abnormal Hieratic
Archaic Hieratic
Late Hieratic
"Späthieratische Buchschrift"
Middle Hieratic
"Mittelhieratische Buchschrift"
"Mittelhieratische Kanzleischrift"
New Kingdom Hieratic
"Neuhieratische Buchschrift"
"Neuhieratische Kanzleischrift"
Old Hieratic
Hieroglyphs
Cryptography
Hieroglyphs | Late Period
Ptolemaic
Greek
Greek or Coptic
Hebrew
Latin
Meroitic Cursive
Meroitic Hieroglyphs
(none)
(not identified)
Pahlavi
Phoenician
Syriac
uninscribed
Mathematik
Geometrie
Euklid
Elementa
. .
ἀποδείκνυται ἡ πρότασις, ὅτι ἡ τοῦ
πενταγώνου πλευρὰ δύναται
τήν τε τοῦ ἑξα-
γώνου το
ἐγ κύκλωι τῶι αβ
καὶ τὴν τοῦ δεκαγώνου. ἔστωσαν
αἱ αγ βγ marg.:ἰσοπλεύρου
πλευραὶ δεκαγώνου. ἀλλ'ἡ δεκα
γώνου ἡ γβ περιφέρεια δ1ίχα τετμήσθω.
δῆλον, ὅτι ἡ ὑπὸ
τῶν λγβ γωνία τῆι
ὑπὸ τῶν γβλ, κοινῆι
τοῦ τε αβγ καὶ τοῦ βκλ
τριγώνου ἐστὶν ἴση. ἔστιν ἄρ'ὡς ἡ αβ
πρὸς βγ, οὕτως βγ πρὸς βλ. τὸ ἄρ'ὑπὸ τἠς ῶν αβ βλ
ἴσον τῶι ἀπὸ τῆς βγ. πάλιν ἡ α . .
λωι. ἡαιδὲ γη
βη εἰκοσαγώνοθ
...
The theorem is proved, that the square over the side of the
pentagon is equal to the sum of the squares
over the sides of the hexa-
gon in the circle AB
and of the decagon. Let ΑΓ and ΒΓ be sides of the marg.:equilateral
decagon. Let the arc over the decagon side
ΓB be bisected.
It is clear, since the angle ΛΓΒ is equal to
the angle ΓΒΛ common to the triangles ΑΒΓ and ΒΚ (read Γ)Λ.
Thus the ratio ΑΒ
to ΒΓ is equal to the ratio ΒΓ to ΒΛ. Thus the rectangle formed by the sides ΑΒ ΒΛ
is equal in area to the square over the side ΒΓ ...
but the stretches ΓΗ and ΒΗ are sides of an icosagon ... (after Müller/Mau 1960)