Legend
All the scripts (including the diagrams) are flipped to be read left to right.
Column numbers are according to [Struve 1930].
tp-ḥsb
Rubrum. Written in red.
m[j ḫpr]
j ḫpr
restored from being partially or almost entirely damaged.
<1/>10
The scribe omitted the glyph.
ḫpr-ḫr
The scribe wrote an extra glyph.
|3|
Line number.
Problem 1 [ edit ]
Problem 2 [ edit ]
Problem 3 [ edit ]
Problem 4 [ edit ]
Column 5
(triangle partially damaged; not likely a right triangle)
•
\
Problem 5 [ edit ]
Column 7
8
9
10
11
12
13
14
Problem 6 [ edit ]
|1| tp n jr.t ꜥ.t[1]
|2| mj ḏd n=k ꜥ.t[1] nt sṯꜣt 1/2 1/4 n ꜣw n wsḫ
|3| jrj.ḫr=k jr=k 1/2 1/4 r gm.t wꜥ(1) ḫpr.ḫr [m] 1 1/3
|4| [jrj 12] pn ntj m sṯꜣt 1 1/3 ḫpr.[ḫr] 16
|5| jrj.ḫr=k jr=k qnb.t=f ḫpr.ḫr 4 n ꜣw 1/2 1/4 m 3 n |6| wsḫ jr.t mj ḫpr
4
+----+
| 12 | 3
+----+
\1 4
\2 8
↑ 1.0 1.1 1.2 1.3 ꜥ.t
is reading of [Gunn & Peet 1929]. [Imhausen 2002] doesn't agree that is present in line 1, but agrees with them in line 2. [Struve 1930] reads it as pr
.
Problem 7 [ edit ]
Problem 8 [ edit ]
↑ For , [Struve 1930] reads .
↑ For , [Peet 1931] suggests thta it is the scribe's typographic error of .
↑ For , [Peet 1931][Peet 1931] reads .
Problem 9 [ edit ]
Problem 10 [ edit ]
Column 18
1
2
3
4
5
6
[1]
|1| tp n jr.t nb.t
|2| mj ḏd n=k nb.t m tp rꜣ |3| r 4 1/2 m ꜥḏ
ḥꜣ |4| dj=k rḫ=j ꜣḥ.t=s
jrj.ḫr=k |5| jrj=k 1/9 n 9 ḥr-ntt jr nb.t
|6| 1/2 pw n j[...][1]
ḫpr.ḫr 1
|7| jrj.ḫr=k jrj=k ḏꜣ.t m 8
|8| jrj.ḫr=k jrj=k 1/9 n 8
|9| ḫpr.ḫr 2/3 1/6 1/18
jrj.ḫr=k |10| jrj=k ḏꜣ.t n.t pꜣ 8 r sꜣ |11| pꜣ 2/3 1/6 1/18
ḫpr.[ḫr] 7 1/9
|12| jrj.ḫr=k jrj=k 7 1/9 zp 4 1/2
|13| ḫpr.ḫr 32
mk ꜣḥ.t=s pw
|14| gmj=k nfr
↑ 1.0 1.1 For the damaged word, [Struve 1930] reads jnr
. [Peet 1931b] denies the possibility and suggests jpt
.
Problem 11 [ edit ]
Column 22
7
8
9
10
[1]
11
Problem 12 [ edit ]
Column 23
1
2
3
4
5
6
7
8
Problem 13 [ edit ]
Problem 14 [ edit ]
|1| tp n jr.t ⏢
|2| mj ḏd n=k ⏢ n 6 n sttj
|3| [r] 4 ḥr ẖr.y r 2 ḥr ḥr.w
|4| [jrj].ḫr=k jrj=k 4 pn m znn
ḫpr.ḫr 16
|5| jrj.ḫr=k qꜣb=k 4
ḫpr.ḫr 8
|6| jrj.ḫr=k jrj=k 2 pn m znn
ḫpr.ḫr 4
|7| jrj.ḫr=k dmḏ=k pꜣ 16 |8| ḥnꜥ pꜣ 8 ḥnꜥ pꜣ 4
|9| ḫpr.ḫr 28
jrj.ḫr=k jrj=k |10| 1/3 n 6
ḫpr.ḫr 2
jrj.ḫr=k |11| jrj=k 28 zp 2
ḫpr.ḫr 56
|12| mk nj-sw 56
gmj=k nfr
Problem 15 [ edit ]
Problem 16 [ edit ]
Column 31
1
2
3
4
[2]
5
6
7
↑ 1.0 1.1 1.2 is per [Imhausen 2002], reading as a ligature according to [Möller 1909]. [Struve 1930] reads , and [Peet 1931] reads .
↑ is according to Imhausen. [Struve 1930] reads , and [Peet 1931] reads .
Problem 17 [ edit ]
Column 34
7
8
9
\
Problem 18 [ edit ]
|1| tp n jr.t rꜣ n [...] 5 [...] m sttj
|2| mj ḏd n=k rꜣ n [...] 5 [...] jrj m sttj
|3| ḥꜣ dj=k rḫ=j sttj=f
jrj.ḫ<r>=k jrj=k |4| pꜣ 5 [...]
ḫpr.ḫr 53 m pꜣ 5
|5| ḫpr.ḫr 10 m pꜣ rꜣ
jrj.ḫr=k jrj=k 51 [...][1] zp
↑ [Struve 1930] reads it as m 80 , [Miatello 2013] reads it as ntf mnḫ.t .
Problem 19 [ edit ]
Problem 20 [ edit ]
Problem 21 [ edit ]
Problem 22 [ edit ]
Problem 23 [ edit ]
Problem 24 [ edit ]
Problem 25 [ edit ]
References [ edit ]
Imhausen, A. (2002). Ägyptische Algorithmen: eine Untersuchung zu den mittelägyptischen mathematischen Aufgabentexten (Vol. 65). Otto Harrassowitz Verlag.
Miatello, Luca. "A Longstanding Enigma: Problem 18 of the Moscow Mathematical Papyrus ", Journal of the American Research Center in Egypt , 2012.
Miatello, Luca. "Problem 10 of the Moscow Mathematical Papyrus: Corrupted Part or Technicality? ", Göttinger Miszellen , 2013.
Miatello, Luca. "Inferring the Construction Process of Two Geometric Algorithms , Göttinger Miszellen, 2018.
Peet, T. Eric. "A problem in Egyptian geometry." The Journal of Egyptian Archaeology , Vol. 17. pp. 100-106. 1931.
Peet, T. Eric. "Notices on Recent Publications: Mathematischer Papyrus des Staatlichen Museums der Schönen Künste in Moskau ." The Journal of Egyptian Archaeology , Vol. 17. pp. 154-160. 1931.
Struve, W. W. Mathematischer Papyrus des Staatlichen Museums der Schönen Künste in Moskau . Quellen und Studien zur Geschichte der Mathematik; Abteilung A: Quellen. 1. Band. 1930.
Moscow Papyrus Problem 10