P.Mich.inv. 621 / Recto

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About this Item

front | summary (1 items)

front | detail (13 items)

unspecified | detail (4 items)

Record Details

Inventory Number
P.Mich.inv. 621
Processing Number
2701
Section/Side
Recto
Image Side
Recto

Background and Physical Properties

Publ./Side
Recto; Verso is blank
Material
Pap
Size
About 106.75 x 9.2 cm
Items
1
Lines
Col. I - 12;
col. II - 15;
col. III - 15;
col. IV - 14;
col. V - 14;
col. VI - 14;
col. VII - 15;
col. VIII - 15;
col. IX - 12;
col. X - 13;
col. XI - 14;
col. XII - 15;
col. XIII - 16;
col. XIV - 16;
col. XV - 16;
col. XVI - 15;
col. XVII - 14;
col. XVIII - 13;
col. XIX - 1
Mounted
Yes
Negative
Yes
Conservation Status
Broken (or cut) off on the left
Palaeographic Description
Clear, uniform hand (Robbins)
Status
published
Library
Ann Arbor

Contents

Date
IVth century A.D.
Origin
Unknown
Provenance
Unknown (Fayum?)
Acquisition
Brought from Egypt by Sir E. Wallis Budge of the British Museum (early 1921), and allotted to the University of Michigan by Sir Frederic Kenyon (letter of Sept. 21, 1921)
Language
Greek
Genre
Literary: Mathematical
Author
Unknown
Type of Text/Title of Work
Table of Fractions
Content
Table of fractions, beginning with the last part of the sevenths and ending with the eighteenths (a heading "nineteenths" follows, but the table was never filled in). Accents distinguishing fractions from integers were added afterwards, with a few mistakes.
Translation
(Col. I)
[Of 1000, the 1/7th =] 142 1/2 1/3 1/42
[Of 2000 =] 285 2/3 1/21
[Of 3000 =] 428 1/2 1/14
[Of 4000 =] 571 1/3 1/15 1/35
[Of 5000 =] 714 1/4 1/28
[Of 6000 =] 827 1/7
[Of 7000 =] 1000
[Of 8000 =] 1142 1/2 1/3 1/42
[Of 9000 =] 1285 2/3 1/21
[Of 10000 =] 1428 1/2 1/14
Eighths:
[Of 1, the 1/8th=] 1/8
[the 1/8th (of 6000) =] 750
(Col. II)
Of 2 =1/4
Of 3 = 1/4 1/8
Of 4 = 1/2
Of 5 = 1/2 1/8
Of 6 = 1/2 1/4
Of 7 = 1/2 1/4 1/8
Of 8 = 1
Of 9 = 1 1/8
Of 10 = 1 1/4
Of 20 = 2 1/2
Of 30 = 3 1/2 1/4
Of 40 = 5
Of 50 = 6 1/4
Of 60 = 7 1/2
Of 70 = 8 1/2 1/4
(Col. III)
Of 80 = 10
Of 90 = 11 1/4
Of 100 = 12 1/2
Of 200 = 25
Of 300 = 37 1/2
Of 400 = 50
Of 500 = 62 1/2
Of 600 = 75
Of 700 = 87 1/2
Of 800 = 100
Of 900 = 112 <1/2>
Of 1000 = 125
Of 2000 = 250
Of 3000 = 375
Of 4000 = 500
(Col. IV)
Of 5000 = 625
Of 6000 = 750
Of 7000 = 875
Of 8000 = 1000
Of 9000 = 1125
Of 10000 = 1250
Ninths:
Of 1, the 1/9th = 1/9
The 1/9th (of 6000) = 666 2/3
Of 2 =1/6 1/18
Of 3 = 1/3
Of 4 = 1/3 1/9
Of 5 = 1/2 1/18
Of 6 = 2/3
(Col. V)
Of 7 = 2/3 1/9
Of 8 = 1/2 1/3 1/18
Of 9 = 1
Of 10 = 1 1/9
Of 20 = 2 1/6 1/18
Of 30 = 3 1/3
Of 40 = 4 1/3 1/9
Of 50 = 5 1/2 1/18
Of 60 = 6 2/3
Of 70 = 7 2/3 1/9
Of 80 = 8 1/2 1/3 1/18
Of 90 = 10
Of 100 = 11 1/9
Of 200 = 22 1/6 1/18
(Col. VI)
Of 300 = 33 1/3
Of 400 = 44 1/3 1/9
Of 500 = 55 1/2 1/18
Of 600 = 66 2/3
Of 700 = 77 2/3 1/9
Of 800 = 88 1/2 1/3 1/18
Of 900 = 100
Of 1000 = 111 1/9
Of 2000 = 222 1/6 1/18
Of 3000 = 333 1/3
Of 4000 = 444 1/3 1/9
Of 5000 = 555 1/2 1/18
Of 6000 = 666 2/3
Of 7000 = 777 2/3 1/9
(Col. VII)
Of 8000 = 888 1/2 1/31/18
Of 9000 =1000
Of 10000 = 1111 1/9
Tenths:
Of 1, the 1/10th = 1/10
The 1/10th (of 6000) = 600
Of 2 =1/5
Of 3 = 1/5 1/10
Of 4 = 1/3 1/15
Of 5 = 1/2
Of 6 = 1/2 1/10
Of 7 = 1/2 1/5
Of 8 = 2/3 1/10 1/30
Of 9 = 1/2 1/3 1/15
Of 10 = 1
(Col. VIII)
Of 20 = 2
Of 30 = 3
Of 40 = 4
Of 50 = 5
Of 60 = 6
Of 70 = 7
Of 80 = 8
Of 90 = 9
Of 100 = 10
Of 200 = 20
Of 300 = 30
Of 400 = 40
Of 500 = 50
Of 600 = 60
Of 700 = 70
(Col. IX)
Of 800 = 80
Of 900 = 90
Of 1000 = 100
Of 2000 = 200
Of 3000 = 300
Of 4000 = 400
Of 5000 = 500
Of 6000 = 600
Of 7000 = 700
Of 8000 = 800
Of 9000 =900
Of 10000 = 1000
(Col. X)
Elevenths:
Of 1, the1/11th = 1/11
The 1/11th (of 6000) = 545 1/3 1/11 1/33
Of 2 =1/6 1/66
Of 3 = 1/4 1/44
Of 4 = 1/3 1/33
Of 5 = 1/3 1/11 1/33
Of 6 = 1/2 1/22
Of 7 = 1/2 1/11 1/22
Of 8 = 2/3 1/22 1/66
Of 9 = 1/2 1/22 1/44
Of 10 = 1/2 1/3 1/22 1/33
Of 11 = 1
(Col. XI)
Twelfths:
Of 1, the 1/12thj = 1/12
The 1/12th (of 6000) = 500
Of 2 =1/6
Of 3 = 1/4
Of 4 = 1/3
Of 5 = 1/3 1/12
Of 6 = 1/2
Of 7 = 1/2 1/12
Of 8 = 2/3
Of 9 = 2/3 1/12
Of 10 = 1/2 1/3
Of 11 = 1/2 1/3 1/12
Of 12 = 1
(Col. XII)
Thirteenths:
Of 1, the 1/13th = 1/13
The 1/13th (of 6000) = 461 1/2 1/26
Of 2 =1/7 1/91
Of 3 = 1/6 1/26 1/39
Of 4 = 1/4 1/26 1/52
Of 5 = 1/3 1/26 1/78
Of 6 = 1/3 1/13 1/26 1/78
Of 7 = 1/2 1/26
Of 8 = 1/2 1/13 1/26 {1/78}
Of 9 = 2/3 1/39
Of 10 = 2/3 1/13 1/39
Of 11 = 1/2 1/3 1/78
Of 12 = 1/2 1/3 1/13 {1/26} 1/78
Of 13 = 1
(Col. XIII)
Fourteenths:
Of 1, the 1/14th = 1/14
The 1/14thj (of 6000) = 428 1/2 1/14
Of 2 =1/7
Of 3 = 1/7 1/14
Of 4 = 1/4 1/28
Of 5 = 1/4 1/14 1/28
Of 6 = 1/3 1/15 1/35
Of 7 = 1/2
Of 8 = 1/2 1/14
Of 9 = 1/2 1/7
Of 10 = 2/3 1/21
Of 11 = 2/3 1/14 1/28 <Should be: 1/2 1/4 1/28>
Of 12 = 1/2 1/3 1/142
Of 13 = 1/2 1/3 1/14 1/42
Of 14 = 1
(Col. XIV)
Fifteenths:
Of 1, the 1/15th = 1/15
The 1/15th (of 6000) = 400
Of 2 = 1/10 1/30
Of 3 = 1/5
Of 4 = 1/5 1/15
Of 5 = 1/3
Of 6 = 1/3 1/15
Of 7 = 1/3 1/10 1/30
Of 8 = 1/3 1/5
Of 9 = 1/2 1/10
Of 10 = 1/2 1/3 <Should be: 2/3>
Of 11 = 1/2 1/3 1/15 <Should be: 2/3 1/15>
Of 12 = 2/3 1/10 1/30
Of 13 = 1/2 1/3 1/30
Of 14 = 1/2 1/3 1/10
(Col. XV)
Of 15 = 1
Sixteenths:
Of 1, the 1/16th = 1/16
The 1/16th (of 6000) = 375
Of 2 = 1/8
Of 3 = 1/8 1/16
Of 4 = 1/4
Of 5 = 1/4 1/16
Of 6 = 1/4 1/8
Of 7 = 1/4 1/8 1/16
Of 8 = 1/2
Of 9 = 1/2 1/16
Of 10 = 1/2 1/8
Of 11 = 1/2 1/8 1/16
Of 12 = 2/3 1/14
Of 13 = 1/2 1/4 1/16
(Col. XVI)
Of 14 = 1/2 1/4 1/8
Of 15 = 1/2 1/4 1/8 1/16
Of 16 = 1
Seventeenths:
Of 1, the 1/17th = 1/17
The 1/17th (of 6000) = 352 1/2 1/3 1/17 1/34 1/51
Of 2 = 1/12 1/51 1/68
Of 3 = 1/12 1/17 151 1/68
Of 4 = 1/12 1/15 1/17 1/34 1/51 <Should be: 1/12 1/15 1/17 1/68 1/85>
Of 5 = 1/4 1/34 1/68
Of 6 = 1/3 1/51
Of 7 = 1/3 1/17 1/51
Of 8 = 1/3 1/15 1/17 1/85
Of 9 = 1/2 1/34
Of 10 = 1/2 1/17 1/34
(Col. XVII)
Of 11 = 1/2 1/12 1/17 1/34 1/51 <Should be: 1/2 1/12 1/34 1/51 1/68>
Of 12 = 1/2 1/12 1/17 1/34 1/51 1/78
Of 13 = 1/2 1/4 1/68
Of 14 = 1/2 1/4 1/17 1/68
Of 15 = 1/2 1/17 1/34 1/68 <Should be: 1/2 1/3 1/34 1/51>
Of 16 = 1/2 1/3 1/17 1/34 1/51
Of 17 = 1
Eighteenths:
Of 1, the 1/18th = 1/18
The1/18th (of 6000) = 333 1/3
Of 2 = 1/9
Of 3 = 1/9 1/18
Of 4 = 1/6 1/18
Of 5 = 1/6 1/9
(Col. XVIII)
Of 6 = 1/3
Of 7 = 1/3 1/18
Of 8 = 1/3 1/9
Of 9 = 1/2
Of 10 = 1/2 1/18
Of 11 = 1/2 1/9
Of 12 = 2/3
Of 13 = 2/3 1/18
Of 14 = 2/3 1/9
Of 15 = 1/2 1/3
Of 16 = 1/2 1/3 1/18
Of 17 = 1/2 1/3 1/9
Of 18 = 1
(Col. XIX)
Nineteenths:
(The rest of the column is left blank)

Information on Publications

Publications
Series and Volume Editor Year Pg/Nr Photo SB Preferred Citation Corrections
CP 18 Robbins FE 1923 328-333 Robbins FE, CP 18, 328-333, 1923
PMich III Robbins FE 1936 146 Robbins FE, PMich III, 146, 1936

Information on Publications--Bibliography

Bibliography
L.C. Karpinski, Isis 5 (1922) p. 20-25; Q. Vetter, CP 20 (1925) p. 309-312; Pack[2] 2310; W. Knorr, Historia Mathematica 9 (1982) p. 133-171, with Pl. II

Availability/System Requirements

Scanner Initials
CT
Date Scanned
7/23/1996
Institution
sr

Cataloging

Cataloger
PH
Year Begin
300
Year End
399

Technical Details

Image Size
18440 x 2440
File Size
3 MB
Record
2701
Link to this Item
https://quod.lib.umich.edu/a/apis/x-2701/621r.tif

Rights and Permissions

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Manifest
https://quod.lib.umich.edu/cgi/i/image/api/manifest/apis:2701:621R.TIF

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Full citation
"P.Mich.inv. 621; Recto." In the digital collection Advanced Papyrological Information System (APIS UM). https://quod.lib.umich.edu/a/apis/x-2701/621r.tif. University of Michigan Library Digital Collections. Accessed March 28, 2024.
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