P.Mich.inv. 620 / Recto
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Record Details
- Inventory Number
- P.Mich.inv. 620
- Processing Number
- 2698
- Section/Side
- Recto
- Image Side
- Recto
Background and Physical Properties
- Publ./Side
- Recto; Verso unpublished (part of a list of names? - in a later, coarser hand)
- Material
- Pap
- Size
- 21 x 12.5 cm
- Items
- 1
- Lines
- Recto, col. i-10;
- col. ii-17
- Mounted
- Yes
- Negative
- Yes
- Conservation Status
- Broken off at the left, right and bottom
- Palaeographic Description
- very irregular, literary hand (Robbins)
- Status
- published
- Library
- Ann Arbor
Contents
- Date
- (Early) IInd century A.D.
- Origin
- Unknown
- Provenance
- Unknown
- 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
- Algebraic Problems
- Content
- Three mathematical problems, the solutions of which are found by algebraic methods. Each of the problems apparently fell into four parts: the statement or hypothesis, the solution, the check, and a table recapitulating the calculations. In the tables, a special symbol is used for the unknown quantity, X
- Subject Headings
- Algebra|vProblems, exercises, etc.
- Mathematics, Egyptian--Study and teaching.
- Mathematics, Greek--Study and teaching.
- Translation
- [Given 9900 drachmai, let it be divided into four parts; let the second be greater than the first by 1/7 of the first; let the third exceed the sum of the first two by 300 drachmai, and let the fourth exceed the sum of the first three by 300 drachmai; find the numbers.]
- (Col. I)
- . . . again multiply the 150 drachmai into the 30 numbers of the fourth term; it gives 4500; plus the 900 drachmai in its assigned value = 5100; this is the fourth term. Then add the four terms 1050 + 1200 + 2550 + 5100 = 9900.
- Check: since he says, "Let the second exceed the first by 1/7", take 1/7 of the first term, 1050, = 150; add this to 1050 = 1200, which is the second term. Again, since he says, "Let the third exceed the two by 300 drachmai", add the first and the second = 2250, and add the 300 drachmai of the excess = 2550, which is the third term. And since he says, "Let the fourth exceed the three by 300 drachmai," add the three = 4800; and add the 300 drachmai of the excess = 5100, which is the fourth; the sum is 9900 in all.
- (Table:)
- 1/7 300 dr. 300 dr. 9900 dr.
- 7X 8X 15X 300 dr. 30X 600 dr.
- = 60X [900 dr.]
- 150 [. . . .]
- 1050 = 1200 2550 5100 [9900]
- 150 [- - -]
- [- - -]
- (Col. II)
- [Since] the second is four times the first, multiply 4 x 42 = 168 and add the 12 of the excess = 180; this is the second number.
- Check: take 1/6 of the second number = 30; but ad 12 = 42, which is the first; and multiply 42 by 4 = 168; moreover add 12 = 180, which is the second.
- 1/6 12 units(?) 4 times 12 units(?)
- 1X 4X 12 units(?)
- 2/3 2 units(?) = 2/3 + [14] units(?)
- 1/3 14 units(?)
- 1 42 168 + 12 = 180
- -----
- There are three numbers; the sum of the three is 5300; and let the first and the second be 24 times the third, and the second and third be 5 times the first. Let the three numbers thus be found.
- Since the first and the second are 24 times the third, therefore the three together are 25 times the third. Divide 5300 by 25; it gives 216; this is [the third number - - -]
- Papyri.info Link
- https://papyri.info/apis/michigan.apis.2698
Information on Publications
- Publications
-
Series and Volume Editor Year Pg/Nr Photo SB Preferred Citation Corrections CP 24 Robbins FE 1929 321-329 Robbins FE, CP 24, 321-329, 1929 PMich III Robbins FE 1936 144 Pl. III Robbins FE, PMich III, 144, 1936, Pl. III
Information on Publications--Bibliography
- Bibliography
- L.C. Karpinski - F.E. Robbins, Science 70 (1929) p. 311-314; K. Vogel, CP 25 (1930) p. 373-375; Pack [2] 2324
Availability/System Requirements
- Scanner Initials
- CT
- Date Scanned
- 6/6/1996
- Institution
- sr
Cataloging
- Cataloger
- PH
- Year Begin
- 100
- Year End
- 199
Technical Details
- Image Size
- 2940 x 2056
- File Size
- 804 KB
- Record
- 2698
- Link to this Item
-
https://quod.lib.umich.edu/a/apis/x-2698/620r.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.
Related Links
IIIF
- Manifest
-
https://quod.lib.umich.edu/cgi/i/image/api/manifest/apis:2698:620R.TIF
Cite this Item
View the Help Guide for more information.
- Full citation
-
"P.Mich.inv. 620; Recto." In the digital collection Advanced Papyrological Information System (APIS UM). https://quod.lib.umich.edu/a/apis/x-2698/620r.tif. University of Michigan Library Digital Collections. Accessed April 24, 2024.