P.Mich.inv. 621
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Record Details
- Inventory Number
- P.Mich.inv. 621
- Processing Number
- 2701
- Section/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.
- Subject Headings
- Greek literature.
- Mathematics, Greek.
- Mathematics, Ancient--Study and teaching.
- Fractions.
- 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)
- Papyri.info Link
- https://papyri.info/apis/michigan.apis.2701
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
- Record
- 2701
- Link to this Item
-
https://quod.lib.umich.edu/a/apis/x-2701/621r_4_neg.tif
Rights and Permissions
The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain. If you have questions about the collection, please contact APIS Help. If you would like to request high-resolution images, please contact the Papyrology Collection. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology.
No Copyright. This work has been identified as being free of known restrictions under copyright law, including all related and neighboring rights. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
Cite this Item
View the Help Guide for more information.
- Full citation
-
"P.Mich.inv. 621." In the digital collection Advanced Papyrological Information System (APIS UM). https://quod.lib.umich.edu/a/apis/x-2701/621r_4_neg.tif. University of Michigan Library Digital Collections. Accessed May 23, 2024.