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  Inventory Number

  P.Mich.inv. 4966

  Processing Number

  2357

  Section/Side

  10 parts ("fragments"); Recto

  Background and Physical Properties

  Publ./Side

  Recto; Verso is blank

  Material

  Pap

  Size

  Total size: more than 200 x 23.5 cm.

  Frg. I, a (col. i-ii): 13 x 6 cm;

  frg. I, b (col. ii-iv): 12.5 x 8 cm;

  frg. II: 7.5 x 11 cm;

  frg. III, a (col. i-ii): 10.5 x 14 cm, with a tab about 3 x 2.5 cm at the upper left;

  frg. III, b (col. ii-iii): 14.5 x 15 cm;

  frg. III, c (col. iii-iv): 24 x 15 cm;

  frg. III, d (col. iv-v): 33.5 x 22 cm;

  frg. III, e (col. v): 18 x 20 cm

  frg. III, f (col. v-vi): 18.5 x 23.5 cm;

  frg. III, g (col. vi-vii): 20 x 23.5 cm;

  frg. III, h (col. vii): 8 x 13 cm;

  frg. IIII, i (col. vii): 8 x 22.5 cm;

  frg. IV: 7 x 10.5 cm;

  frg. V: 6 x 5.5 cm;

  frg. VI: 3 x 7 cm;

  frg. VII: 2.5 x 3 cm;

  frg. VIII: 4 x 3.5 cm;

  frg. IX: 3.5 x 7 cm;

  frg. X: 3 x 4 cm

  Items

  19

  Lines

  Frg. I , col. i - 5; col. ii - 6; col. iii - 6; col. iv - 1;

  Frg. II - 11;

  Frg. III, col. i - 11; col. ii - 15; col. iii - 12; col. iv - 18; col. v - 17; col. vi - 21; col. vii - 21;

  Frg. IV = 9;

  Frg. V = 4;

  Frg. VI = 7;

  Frg. VII = 3;

  Frg. VIII = 4;

  Frg. IX = 6;

  Frg. X = 3

  Mounted

  Yes; + 1 folder which has small scraps with no writing.

  Negative

  Yes

  Conservation Status

  Broken off at the left, right, and bottom. Many holes and tears, particularly at the bottom of the fragments; the papyrus was folded, and the pieces which were one on top of the other show the same outline

  Palaeographic Description

  Unusually large, well-formed, but irregular hand, in extremely broad columns; except in the first part of the papyrus (frg. I, i - frg. III, ii), where the hand is not so large and the columns are narrower - the general effect being of greater irregularity and cramping (Robbins)

  Status

  published

  Library

  Ann Arbor

  Contents

  Date

  (Early) IInd century A.D.

  Origin

  Unknown

  Provenance

  Unknown

  Acquisition

  purchased in 1928 through the British Museum

  Language

  Greek

  Genre

  Literary: mathematical

  Author

  Unknown

  Type of Text/Title of Work

  Table of Fractions and Arithmetical Problems

  Content

  Table of fractions with prime denominators, followed by arithmetical problems concerning conversions between silver and copper money and between wheat standards, as well as calculations of carriage charges and of interests

  Subject Headings

  Debt.

  Interest.

  Greek literature.

  Mathematics, Greek.

  Weights and measures, Ancient.

  Mathematics, Ancient--Study and teaching.

  Freight and freightage.

  Translation

  (Frg. I, col. i)

  1/23 = 1/23

  [2/23] = 1/12 + 1/276

  [3/23] = 1/10 + 1/46 + 1/115

  [4/23 = 1/6] + 1/138

  [5/23 = 1/6 + 1/23] + 1/138

  [- - -]

  (Frg. I, col. ii)

  12/29 = 1/4 + 1/8 + 1/29 + 1/232

  13/29 = 1/3 + 1/10 + 1/87 + 1/290

  14/29 = 1//4 + 1/5 + 1/58 + 1/116 + 1/145

  15/29 = 1/2 + 1/58

  16/29 = [1/2] + 1/29 + 1/58

  [17/29 = 1/2 + 1/12] + 1/348

  [- - -]

  (Frg. I, col. III: too fragmentary to be translated: table of 1/31?)

  (Frg. I, col. IV: too fragmentary to be translated)

  (Frg. II: too fragmentary to be translated)

  (Frg. III, i: too fragmentary to be translated)

  (Frg. III, col. ii)

  To what number [may you add] 15, subtract 20, [add 25], and subtract 30; it will be 100 artabai of wheat? As is needful, add together the added artabai, = 400; add together also the subtracted artabai, [= 50]; from these subtract the added artabai, [40, =] 10 artabai; add to the 100 artabai of wheat, = 110; this is the number. Proof: Add 15, = 125, [and] subtract 20; remainder, 105. Add [25] = 130; subtract 30; remainder, the given 100 artabai of wheat.

  [- - -]

  (Frg. III, col. iii)

  (Reduce to silver drachmai:) 43 talents 2000 (drachmai) of copper, on the basis of one stater to 1200 copper (drachmai). As is needful, reduce the 43 talents 2000 (drachmai) to myriads of drachmai; take 1/1200 of these = 216 2/3 staters; multiply [these] by 4 (since the stater contains 4 drachmai), = [866] drachmai 4 obols.

  (Reduce to silver drachmai:) 5800 copper drachmai, on the basis of one stater to 1200 copper drachmai. As is needful, I took 1/1200 of the given 5800 drachmai, = 4 1/2 1/3 staters; multiply these by 4 (since the stater contains 4 drachmai), = 19 drachmai 2 obols.

  (Reduce to copper drachmai:) 3 talents 2000 (drachmai) of silver, on the basis of one stater to 1200 copper drachmai. As is needful, reduce the [3 talents 2000 drachmai to] myriads [of drachmai, = 20,000; of these take 1/4,] because the stater [contains 4 drachmai; = 5000] staters; [multiply these into the] 1200 copper [drachmai, = 6,000,000] copper [drachhmai, = 1000 talents of] copper.

  [- - -]

  (Frg. III, col. iv)

  Of 100 loads, some are at the rate of 10 drachmai, some at 20 drachmai, and some at 20 drachmai, and some at 30 drachmai; the whole price is 2500 drachmai. [As] is needful I multiplied the 100 loads x 30 drachmai = 3000; from this subtract the given 2500 drachmai; remainder, 500 drachmai. And subtract the 10 drachmai from the 30 drachmai; remainder [20]. I took 1/20 of the remainder, 500 drachmai, = 24 with remainder of 20; and subtract the 20 drachmai from the 30 drachmai; remainder 10 of the original. And one operates with 20 because it is necessary to subtract the 10 drachmai from 30; remainder, 20 once = 20; take besides 20 (since I took 1/20 of the 500 drachmai and it was 24 with remainder of 20), = 40; take 1/10 of this (because you have subtracted 20 drachmai from 30 drachmai and 10 were left), = 4; = 1, since [4 x 1] = 4, for [I took 1/4] of [4]; and subtract 1 from 24 (since I took 1/20 of the [remainder], 500 drachmai, and it was [24 with remainder of 20]); 23 is left; so many are the loads at [10] drachmai, = 230 drachmai. Put above the [10 drachmai] the 23 loads and below them the 230 drachmai. I took [10 from the] 20 drachmai, = [10, and] 1/10 of the 40 drachmai, [= 4; and] put [above the 20 drachmai the] 4 loads, [and under the 20 drachmai the] 80 [drachmai;] add 4 [+ 23 = 27]; subtract [230 drachmai from] 2[500 drachmai, = 2270 drachmai; and subtract 80 drachmai from 22]70 drachmai = 21[90 drachmai; and subtract the 27 loads from the 100 loads = 73; add 23 + 4 + 73 = 100, and] add [270 + 80 + 2190 drachmai = 2500 drachmai]

  [- - -]

  (Frg. III, col. v)

  Add 1/2 to 2 = 2 1/2; and [add] the [2/3] represented by the 20 stadia to the 3 schoeni = 3 2/3; reduce the 2 1/2 to halves; it is 5; and the 3 2/3 to halves; it is 7 1/3, [of which] 1/5 = 1 1/5 1/6 1/10; (this multiplied) into 4 1/2 artabai = 6 [1/2 1/10 and] (multiplied) into the 60 artabai = 396, 1/100 of which = 3 1/2 1/4 1/5 1/100. So much they pay for 60 artabai over the distance of 3 schoeni 20 stadia.

  The freight on [100 artabai] for 3 schoeni is 3 1/2 [artabai]; according to schedule there is a freight charge of 60 artabai; how many artabai will be delivered over a distance of 4 schoeni? As is needful I took [1/3] of the 4 schoeni [=] 1 1/3; (this multiplied) into the 3 1/2 artabai = 4 [2/3, (which reduced) to] thirds = 14; and the 60 artabai (reduced) to thirds = 180, 1/14 [of which] = 12 1/2 1/3 1/42; (this multiplied) into 100 artabai = 1285 2/3 1/21; so many (artabai) will be delivered for 60 artabai [over a distance of] 4 schoeni.

  [- - -]

  (Frg. III, col. vi)

  The freight on 100 artabai is [5 artabai]; given a charge of 80 artabai how many artabai in the principal? As is needful, I took [1/5 of] 80 = 16; (multiplied) into 100 = 1600; so many (artabai) in the principal.

  The freight on 100 artabai is 5 artabai; what is the freight on the whole principal amount of 1000 artabai? As is needful I multiplied [5] x 1000 = 5000, of which 1/100 = 50; so many (artabai) are the freight.

  The width of a field is [2 1/2] schoenia; what is the length that there may be 20 arourai? As is needful, reduce the [2 1/2 schoenia to] halves, = 5; and the 20 arourai to halves, = 40; of which 1/5 = 8; this is the length. Proof: Multiply the 2 1/2 schoenia of the width x [the 8] of the length [and it will be] 20.

  [- - -]

  (Frg. III, col. vii)

  The [monthly] interest [on 100 drachmai is 2 drachmai 3 obols]; let 4 months pass, and the whole sum [be ] 1100 drachmai; what is the [principal? Multiply] the 2 drachmai 3 obols into the [4 months,] = 10; into 1100 = 11000, [of which 1/100 =] 110 drachmai; I took 1/110 of 11,000 = 100; this is the interest on 1000 (drachmai); so much is the principal.

  The [monthly] interest [on 100 drachmai] is 2 drachmai 3 obols; let 4 months pass, and the principal be 200 drachmai; what is the interest? [Multiply] the 2 drachmai 3 obols into the [4] months = 10; into 200 = 2000, of which 1/100 = 20; so much is the interest.

  There are artabai of wheat [measured] by the 36-choinix measure; how many will there be by the 40-choinix measure? [Multiply] the 30 artabai of wheat by the 36 [=] 1080, of which 1/40 = 27. [There are so many by the 40-]choinix measure.

  (Frg. IV: too fragmentary to be translated)

  (Frg. V)

  [- - -] the mile contains [8(?)] stadia [- - - the stadium] contains 4 [1/6] geometrical schoenia [- - -] and the mile contains [- - -]

  (Frg. VI-X too fragmentary to be translated)

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  PMich III	Winter JG	1936	145	Winter JG, PMich III, 145, 1936 -- Frg. I, col. i, l. 2: read [ton] 13, 1/3 1/10 1/8[7] 1/290, instead of [ton] 13, 1/3 1/15 [1/29 1/8]7 1/4[35]; - frg. III, col. iv, l. 10: read elabo(n) t[o] 1/20 ton (drachmon) 500, instead of elab[o]n 1/20 ton [loip(on)] (drachmon) 500; - frg. III, col. v, l. 14: perhaps t]as kephal(aiou), instead of ] . u . [k]ephal(ai--); - frg. III, col. vii, l. 4: read toisautai ke[phalaiou], instead of toisautai me[non 4]; - frg. IX, l. 2: read ] . (drachm--) 4 (ob. 4) (ob. 1/2) p[; l. 6: read (drachm--) 4?] (ob. 4) (ob. 1/2) [; - frg. X, l. 1: read ] . (drachm--?) 4 (ob. 4) (ob. 1/2), instead of ] . . de (drachmai) [. (PH)	Frg. I, col. i, l. 2: read [ton] 13, 1/3 1/10 1/8[7] 1/290, instead of [ton] 13, 1/3 1/15 [1/29 1/8]7 1/4[35]; - frg. III, col. iv, l. 10: read elabo(n) t[o] 1/20 ton (drachmon) 500, instead of elab[o]n 1/20 ton [loip(on)] (drachmon) 500; - frg. III, col. v, l. 14: perhaps t]as kephal(aiou), instead of ] . u . [k]ephal(ai--); - frg. III, col. vii, l. 4: read toisautai ke[phalaiou], instead of toisautai me[non 4]; - frg. IX, l. 2: read ] . (drachm--) 4 (ob. 4) (ob. 1/2) p[; l. 6: read (drachm--) 4?] (ob. 4) (ob. 1/2) [; - frg. X, l. 1: read ] . (drachm--?) 4 (ob. 4) (ob. 1/2), instead of ] . . de (drachmai) [. (PH)

  Information on Publications--Bibliography

  Bibliography

  Pack[2] 2309; B. Boyaval, ZPE 23 (1976) p. 196; B. Boyaval, ZPE 31 (1978) p. 121-122; W. Knorr, Historia Mathematica 9 (1982) p. 133-171, with pl. I (frg. I)

  Availability/System Requirements

  Scanner Initials

  CT

  Date Scanned

  7/23/1996

  Institution

  s

  Cataloging

  Cataloger

  PH

  
  
• 

  Get Info

  Check record for portfolio
  View Full Record

  Inventory Number

  P.Mich.inv. 4966

  Processing Number

  2357

  Section/Side

  10 parts ("fragments"); Recto

  Background and Physical Properties

  Publ./Side

  Recto; Verso is blank

  Material

  Pap

  Size

  Total size: more than 200 x 23.5 cm.

  Frg. I, a (col. i-ii): 13 x 6 cm;

  frg. I, b (col. ii-iv): 12.5 x 8 cm;

  frg. II: 7.5 x 11 cm;

  frg. III, a (col. i-ii): 10.5 x 14 cm, with a tab about 3 x 2.5 cm at the upper left;

  frg. III, b (col. ii-iii): 14.5 x 15 cm;

  frg. III, c (col. iii-iv): 24 x 15 cm;

  frg. III, d (col. iv-v): 33.5 x 22 cm;

  frg. III, e (col. v): 18 x 20 cm

  frg. III, f (col. v-vi): 18.5 x 23.5 cm;

  frg. III, g (col. vi-vii): 20 x 23.5 cm;

  frg. III, h (col. vii): 8 x 13 cm;

  frg. IIII, i (col. vii): 8 x 22.5 cm;

  frg. IV: 7 x 10.5 cm;

  frg. V: 6 x 5.5 cm;

  frg. VI: 3 x 7 cm;

  frg. VII: 2.5 x 3 cm;

  frg. VIII: 4 x 3.5 cm;

  frg. IX: 3.5 x 7 cm;

  frg. X: 3 x 4 cm

  Items

  19

  Lines

  Frg. I , col. i - 5; col. ii - 6; col. iii - 6; col. iv - 1;

  Frg. II - 11;

  Frg. III, col. i - 11; col. ii - 15; col. iii - 12; col. iv - 18; col. v - 17; col. vi - 21; col. vii - 21;

  Frg. IV = 9;

  Frg. V = 4;

  Frg. VI = 7;

  Frg. VII = 3;

  Frg. VIII = 4;

  Frg. IX = 6;

  Frg. X = 3

  Mounted

  Yes; + 1 folder which has small scraps with no writing.

  Negative

  Yes

  Conservation Status

  Broken off at the left, right, and bottom. Many holes and tears, particularly at the bottom of the fragments; the papyrus was folded, and the pieces which were one on top of the other show the same outline

  Palaeographic Description

  Unusually large, well-formed, but irregular hand, in extremely broad columns; except in the first part of the papyrus (frg. I, i - frg. III, ii), where the hand is not so large and the columns are narrower - the general effect being of greater irregularity and cramping (Robbins)

  Status

  published

  Library

  Ann Arbor

  Contents

  Date

  (Early) IInd century A.D.

  Origin

  Unknown

  Provenance

  Unknown

  Acquisition

  purchased in 1928 through the British Museum

  Language

  Greek

  Genre

  Literary: mathematical

  Author

  Unknown

  Type of Text/Title of Work

  Table of Fractions and Arithmetical Problems

  Content

  Table of fractions with prime denominators, followed by arithmetical problems concerning conversions between silver and copper money and between wheat standards, as well as calculations of carriage charges and of interests

  Subject Headings

  Debt.

  Interest.

  Greek literature.

  Mathematics, Greek.

  Weights and measures, Ancient.

  Mathematics, Ancient--Study and teaching.

  Freight and freightage.

  Translation

  (Frg. I, col. i)

  1/23 = 1/23

  [2/23] = 1/12 + 1/276

  [3/23] = 1/10 + 1/46 + 1/115

  [4/23 = 1/6] + 1/138

  [5/23 = 1/6 + 1/23] + 1/138

  [- - -]

  (Frg. I, col. ii)

  12/29 = 1/4 + 1/8 + 1/29 + 1/232

  13/29 = 1/3 + 1/10 + 1/87 + 1/290

  14/29 = 1//4 + 1/5 + 1/58 + 1/116 + 1/145

  15/29 = 1/2 + 1/58

  16/29 = [1/2] + 1/29 + 1/58

  [17/29 = 1/2 + 1/12] + 1/348

  [- - -]

  (Frg. I, col. III: too fragmentary to be translated: table of 1/31?)

  (Frg. I, col. IV: too fragmentary to be translated)

  (Frg. II: too fragmentary to be translated)

  (Frg. III, i: too fragmentary to be translated)

  (Frg. III, col. ii)

  To what number [may you add] 15, subtract 20, [add 25], and subtract 30; it will be 100 artabai of wheat? As is needful, add together the added artabai, = 400; add together also the subtracted artabai, [= 50]; from these subtract the added artabai, [40, =] 10 artabai; add to the 100 artabai of wheat, = 110; this is the number. Proof: Add 15, = 125, [and] subtract 20; remainder, 105. Add [25] = 130; subtract 30; remainder, the given 100 artabai of wheat.

  [- - -]

  (Frg. III, col. iii)

  (Reduce to silver drachmai:) 43 talents 2000 (drachmai) of copper, on the basis of one stater to 1200 copper (drachmai). As is needful, reduce the 43 talents 2000 (drachmai) to myriads of drachmai; take 1/1200 of these = 216 2/3 staters; multiply [these] by 4 (since the stater contains 4 drachmai), = [866] drachmai 4 obols.

  (Reduce to silver drachmai:) 5800 copper drachmai, on the basis of one stater to 1200 copper drachmai. As is needful, I took 1/1200 of the given 5800 drachmai, = 4 1/2 1/3 staters; multiply these by 4 (since the stater contains 4 drachmai), = 19 drachmai 2 obols.

  (Reduce to copper drachmai:) 3 talents 2000 (drachmai) of silver, on the basis of one stater to 1200 copper drachmai. As is needful, reduce the [3 talents 2000 drachmai to] myriads [of drachmai, = 20,000; of these take 1/4,] because the stater [contains 4 drachmai; = 5000] staters; [multiply these into the] 1200 copper [drachmai, = 6,000,000] copper [drachhmai, = 1000 talents of] copper.

  [- - -]

  (Frg. III, col. iv)

  Of 100 loads, some are at the rate of 10 drachmai, some at 20 drachmai, and some at 20 drachmai, and some at 30 drachmai; the whole price is 2500 drachmai. [As] is needful I multiplied the 100 loads x 30 drachmai = 3000; from this subtract the given 2500 drachmai; remainder, 500 drachmai. And subtract the 10 drachmai from the 30 drachmai; remainder [20]. I took 1/20 of the remainder, 500 drachmai, = 24 with remainder of 20; and subtract the 20 drachmai from the 30 drachmai; remainder 10 of the original. And one operates with 20 because it is necessary to subtract the 10 drachmai from 30; remainder, 20 once = 20; take besides 20 (since I took 1/20 of the 500 drachmai and it was 24 with remainder of 20), = 40; take 1/10 of this (because you have subtracted 20 drachmai from 30 drachmai and 10 were left), = 4; = 1, since [4 x 1] = 4, for [I took 1/4] of [4]; and subtract 1 from 24 (since I took 1/20 of the [remainder], 500 drachmai, and it was [24 with remainder of 20]); 23 is left; so many are the loads at [10] drachmai, = 230 drachmai. Put above the [10 drachmai] the 23 loads and below them the 230 drachmai. I took [10 from the] 20 drachmai, = [10, and] 1/10 of the 40 drachmai, [= 4; and] put [above the 20 drachmai the] 4 loads, [and under the 20 drachmai the] 80 [drachmai;] add 4 [+ 23 = 27]; subtract [230 drachmai from] 2[500 drachmai, = 2270 drachmai; and subtract 80 drachmai from 22]70 drachmai = 21[90 drachmai; and subtract the 27 loads from the 100 loads = 73; add 23 + 4 + 73 = 100, and] add [270 + 80 + 2190 drachmai = 2500 drachmai]

  [- - -]

  (Frg. III, col. v)

  Add 1/2 to 2 = 2 1/2; and [add] the [2/3] represented by the 20 stadia to the 3 schoeni = 3 2/3; reduce the 2 1/2 to halves; it is 5; and the 3 2/3 to halves; it is 7 1/3, [of which] 1/5 = 1 1/5 1/6 1/10; (this multiplied) into 4 1/2 artabai = 6 [1/2 1/10 and] (multiplied) into the 60 artabai = 396, 1/100 of which = 3 1/2 1/4 1/5 1/100. So much they pay for 60 artabai over the distance of 3 schoeni 20 stadia.

  The freight on [100 artabai] for 3 schoeni is 3 1/2 [artabai]; according to schedule there is a freight charge of 60 artabai; how many artabai will be delivered over a distance of 4 schoeni? As is needful I took [1/3] of the 4 schoeni [=] 1 1/3; (this multiplied) into the 3 1/2 artabai = 4 [2/3, (which reduced) to] thirds = 14; and the 60 artabai (reduced) to thirds = 180, 1/14 [of which] = 12 1/2 1/3 1/42; (this multiplied) into 100 artabai = 1285 2/3 1/21; so many (artabai) will be delivered for 60 artabai [over a distance of] 4 schoeni.

  [- - -]

  (Frg. III, col. vi)

  The freight on 100 artabai is [5 artabai]; given a charge of 80 artabai how many artabai in the principal? As is needful, I took [1/5 of] 80 = 16; (multiplied) into 100 = 1600; so many (artabai) in the principal.

  The freight on 100 artabai is 5 artabai; what is the freight on the whole principal amount of 1000 artabai? As is needful I multiplied [5] x 1000 = 5000, of which 1/100 = 50; so many (artabai) are the freight.

  The width of a field is [2 1/2] schoenia; what is the length that there may be 20 arourai? As is needful, reduce the [2 1/2 schoenia to] halves, = 5; and the 20 arourai to halves, = 40; of which 1/5 = 8; this is the length. Proof: Multiply the 2 1/2 schoenia of the width x [the 8] of the length [and it will be] 20.

  [- - -]

  (Frg. III, col. vii)

  The [monthly] interest [on 100 drachmai is 2 drachmai 3 obols]; let 4 months pass, and the whole sum [be ] 1100 drachmai; what is the [principal? Multiply] the 2 drachmai 3 obols into the [4 months,] = 10; into 1100 = 11000, [of which 1/100 =] 110 drachmai; I took 1/110 of 11,000 = 100; this is the interest on 1000 (drachmai); so much is the principal.

  The [monthly] interest [on 100 drachmai] is 2 drachmai 3 obols; let 4 months pass, and the principal be 200 drachmai; what is the interest? [Multiply] the 2 drachmai 3 obols into the [4] months = 10; into 200 = 2000, of which 1/100 = 20; so much is the interest.

  There are artabai of wheat [measured] by the 36-choinix measure; how many will there be by the 40-choinix measure? [Multiply] the 30 artabai of wheat by the 36 [=] 1080, of which 1/40 = 27. [There are so many by the 40-]choinix measure.

  (Frg. IV: too fragmentary to be translated)

  (Frg. V)

  [- - -] the mile contains [8(?)] stadia [- - - the stadium] contains 4 [1/6] geometrical schoenia [- - -] and the mile contains [- - -]

  (Frg. VI-X too fragmentary to be translated)

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  PMich III	Winter JG	1936	145	Winter JG, PMich III, 145, 1936 -- Frg. I, col. i, l. 2: read [ton] 13, 1/3 1/10 1/8[7] 1/290, instead of [ton] 13, 1/3 1/15 [1/29 1/8]7 1/4[35]; - frg. III, col. iv, l. 10: read elabo(n) t[o] 1/20 ton (drachmon) 500, instead of elab[o]n 1/20 ton [loip(on)] (drachmon) 500; - frg. III, col. v, l. 14: perhaps t]as kephal(aiou), instead of ] . u . [k]ephal(ai--); - frg. III, col. vii, l. 4: read toisautai ke[phalaiou], instead of toisautai me[non 4]; - frg. IX, l. 2: read ] . (drachm--) 4 (ob. 4) (ob. 1/2) p[; l. 6: read (drachm--) 4?] (ob. 4) (ob. 1/2) [; - frg. X, l. 1: read ] . (drachm--?) 4 (ob. 4) (ob. 1/2), instead of ] . . de (drachmai) [. (PH)	Frg. I, col. i, l. 2: read [ton] 13, 1/3 1/10 1/8[7] 1/290, instead of [ton] 13, 1/3 1/15 [1/29 1/8]7 1/4[35]; - frg. III, col. iv, l. 10: read elabo(n) t[o] 1/20 ton (drachmon) 500, instead of elab[o]n 1/20 ton [loip(on)] (drachmon) 500; - frg. III, col. v, l. 14: perhaps t]as kephal(aiou), instead of ] . u . [k]ephal(ai--); - frg. III, col. vii, l. 4: read toisautai ke[phalaiou], instead of toisautai me[non 4]; - frg. IX, l. 2: read ] . (drachm--) 4 (ob. 4) (ob. 1/2) p[; l. 6: read (drachm--) 4?] (ob. 4) (ob. 1/2) [; - frg. X, l. 1: read ] . (drachm--?) 4 (ob. 4) (ob. 1/2), instead of ] . . de (drachmai) [. (PH)

  Information on Publications--Bibliography

  Bibliography

  Pack[2] 2309; B. Boyaval, ZPE 23 (1976) p. 196; B. Boyaval, ZPE 31 (1978) p. 121-122; W. Knorr, Historia Mathematica 9 (1982) p. 133-171, with pl. I (frg. I)

  Availability/System Requirements

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  CT

  Date Scanned

  7/23/1996

  Institution

  s

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  Inventory Number

  P.Mich.inv. 693

  Processing Number

  3031

  Section/Side

  Recto

  Background and Physical Properties

  Publ./Side

  Recto; Verso is blank

  Connections

  Archive of Kronion son of Apion, nomographos of the grapheion of Tebtynis

  Material

  Pap

  Size

  31 x 27.5 cm

  Items

  1

  Lines

  Col. I - 53 (+ marginal notes: 7 and 2 lines);

  col. II - 53;

  col. III - 16

  Mounted

  Yes

  Negative

  No

  Conservation Status

  A rectangular piece (14 x 4 cm) has been broken off from the lower left corner; several small holes scattered through the sheet; top of col. II badly defaced

  Palaeographic Description

  In the handwriting of Kronion, son of Apion (Boak)

  Status

  published

  Library

  Ann Arbor

  Contents

  Date

  (After) January 17, 46 A.D.

  Origin

  Tebtynis, Polemonos meris, Arsinoite nome, province of Egypt

  Provenance

  Tebtynis, Polemonos meris, Arsinoite nome, province of Egypt

  Acquisition

  1921, Acquired by Kelsey from Nahman in Cairo

  Language

  Greek

  Genre

  Documentary

  Author

  Kronion son of Apion

  Type of Text/Title of Work

  Account of Expenditures

  Content

  Account of the private expenditures of Kronion, the official of the record-office (grapheion) of Tebtynis for the first five months of the 6th year of the emperor Claudius (from Sept. 1, 45 A.D. to Jan. 17, 46 A.D.; compare his official disbursements for the same period in P.Mich. II, 123, Recto, col. I, and Verso, col. I-II)

  Subject Headings

  Accounts--Egypt--Tebtunis (Extinct city)

  Talei (Extinct city)

  Religious institutions--Egypt--Tebtunis (Extinct city)

  Cadastres--Egypt--Tebtunis (Extinct city)

  Wool--Egypt--Tebtunis (Extinct city)

  Food--Prices--Egypt--Tebtunis (Extinct city)

  Granaries--Egypt--Tebtunis (Extinct city)

  Wood--Egypt--Tebtunis (Extinct cit)

  Drachma.

  Priests--Egypt--Tebtunis (Extinct city)

  Prices--Egypt--Tebtunis (Extinct city)

  Crops--Egypt--Tebtunis (Extinct city)

  Slaves--Egypt--Tebtunis (Extinct city)

  Clothing and dress--Egypt--Tebtunis (Extinct city)

  Artisans--Egypt--Tebtunis (Extinct city)

  Home economics--Egypt--Tebtunis (Extinct city)

  Food.

  Notaries--Egypt--Tebtunis (Extinct city)

  Freight and freightage--Egypt--Tebtunis (Extinct city)

  Persons

  Claudius, Emperor;

  Heronas (Heron), nomographos (see P.Mich. II, p. 96);

  Marsisouchos, heiaireus (hiereus);

  Chrates;

  Eutychos son of Takolleeinis (see P.Mich. II, p. 216);

  Eutychos son of Chrates (see also P.Mich. II, 123, Recto, col. VIII, l. 40; V, 343);

  Orsenouphis son of Phombos;

  Onnophris thesaurophylax (see P.Mich. II, p. 224);

  Aphrodisios (son of) Teris <Or: Aphrodisios (also called) Teris>

  Kronion (son of Apion) (grapheion official);

  (unnamed) sitokapeloi;

  Herodion son of Kephalas;

  Papontos son of Marames;

  (another?) Eutychos;

  Patron, hegoumenos synodou theou (= Patron son of Tyrannos?);

  Posis, Theogonites;

  Mommous, wife (of Chrates son of Harpaesis?);

  (unnamed) pediske (paidiske) of Chrates son of Harpaesis;

  Chrates son of Harpeesis (Harpaesis) (see also P.Mich. V, 340);

  Onnophris, pteraphoros (see P.Mich. II, p. 224);

  Harmaeis, gerdios;

  P[- - -];

  Kanariates;

  [- - -] (Kronias?), ho tous katalochismous <ascholoumenos>

  (another?) Aphrodisios;

  Eutychas (grapheion official);

  (another?) Eutychas

  Apias;

  Synesios;

  Eutychas son of Eutychos;

  Orsenouphis son of Belphis (see also P.Mich. II, p. 224; V, p. 389);

  (another?) Orsenouphis(?);

  Orsenouphis son of Tabas;

  Hatres;

  Patron son of Tyrannos (= Patron, hegoumenos synodou theou?);

  Kastoras;

  Satyros;

  Orsenouphis, rhabdistes;

  Maron;

  Soterichos son of Kronides (see also P.Mich. II, 121, Recto, col. IV, viii, 1);

  (unnamed) ergatai;

  Lysas son of Kephalas;

  Horos son of Plesis;

  Herakleides son of Plesis;

  Tabas rhabdistes;

  Tenesrois daughter of Apias;

  Tateeus;

  Pnesis;

  Herakles;

  Didymas;

  Sagatos (son of Apetes?);

  Horos, son of Apetes;

  Apetes, father of Horos (and Sagatos?);

  Gaius;

  Apollonies <read: Apollonides?>;

  Tabos;

  (another?) Kastoras (& unnamed brothers);

  Helenos;

  Kronion son of Belles grandson of Kalas

  Geographica

  Theogonites; Tali (Talei); (Arsinoiton) polis

  Translation

  (Col. I)

  Account of (my) private expenditures of the 6th year of Tiberius Claudius Caesar Augustus Germanicus the Emperor, month of Sebastos.

  On the 4th. For the price(?) for the sake of 5 stathmia of wool: 8 silver drachmai.

  On the 10th. For the price of 1 keramion of wine for Heronas the notary: 17 obols;

  for petty expenses: 2 drachmai;

  similarly, for us, for expenses: 4 drachmai.

  For Marsisouchos the priest, for the price of 1 5/6 artaba of wheat: 8 drachmai.

  On the 14th. For the price of 1 1/3 artaba of lentils, for Chrates: 4 drachmai.

  On the 16th. For Eutychos the son of Takolleeinos, for 1 artaba: 4 drachmai.

  On the 19th. For Eutychos, son of Chrates, for 1 3/10 artaba: 4 drachmai.

  On the 24th. For Orsenouphis, son of Phombos, for the price of 3 1/2 artabai of wheat: 20 drachmai.

  On the 27th. For Onnophris the granary guard, for the price of 2 artabai of wheat: 16 drachmai.

  For Aphrodisios, (son of) Teris <Or: Aphrodisios (also called) Teris>, for the price of 1 artaba of wheat: 8 drachmai.

  Similarly, through me, Kronion, for the dealers in corn, in the granaries, for 3 artabai of wheat: 24 drachmai.

  On the 29th. For Herodion, son of Kephalas, for the price of 1 1/10 artaba of wheat: 8 drachmai.

  For the price of 2 stathmia of wool, for Papontos, son of Marames: 4 drachmai.

  On the 30th. For the price of 1 keramion of wine and 1 keramion of oil, for Eutychos: 4 drachmai.

  For Patron, president of the association of the god for the 5th year: 4 drachmai.

  For Posis, of Theogonis, for the price of 1 keramion of wine: 4 drachmai.

  In the city for the wife, Mommous, and the maidservant of Chrates, son of Harpeesis, as travel money: 4 drachmai.

  On Phaophi 1. Through Onnophris the pteraphoros and Harmaeis the weaver and another, to (be paid to) P[- - -], for what he sent to Kanariates: 8 drachmai.

  On the 4th. For the price of 1 keramion of wine: 18 obols; for a made dish: 4 obols; for oil: 3 obols.

  Similarly, for [- - -], the <administrator> of the (catoecic) registers, for 1 keramion of wine: 18 obols;

  for the price of . . .: 10 obols;

  [- - -]: 3 obols.

  For the association of Harpochrates, for 2 keramia: 36 obols.

  [For the price of oil] and a made dish: 5 obols.

  [For the price of oil(?)]: 3 obols.

  [For the price] of oil and a made dish: 5 obols.

  [For the price] of oil(?): 3 obols.

  [For - - -] and oil and a made dish: 9 obols.

  [For - - -] and oil: 6 obols.

  [- - - for(?)] Aphrodisios, for the price of 2 1/10 artabai of wheat: 16 drachmai.

  For the price of 1 1/2 artaba of wheat: 12 drachmai.

  [For the price of oil] and a made dish: 6 obols.

  [For the price of oil] and a made dish: 6 obols. Similarly 3 obols.

  [For(?)] Tabas, for his son:

  [for the price] of 1 keramion of wine: 18 obols;

  [for the price] of eggs: 1 obol;

  [for the price of oil]: 3 obols.

  For petty expenses: 19 obol.

  On Neos Sebastos 1. For the price of a made dish and oil: 3 obols.

  [- - -]: 3 obols.

  [For the price] of a made dish: 1 obol. For the price of oil: 3 obols.

  For Eutychas, for the price of breads baked in a pan and of a made dish: 3 obols.

  For the same, for the price of breads baked in a pan: 1 obol.

  [- - -] for the price of breads: 4 obols.

  [- - - for] a made dish: [. .] obols.

  [For - - -], for the price of [- - - and] oil(?): 4 obols.

  (In the left margin, opposite l. 14-20)

  . . . and the robes of Apias for 32 drachmai, on the 7th of Phaophi.

  (In the left margin, opposite l. 25-27)

  On the 21. For us . . . Synesios.

  (Coll. II)

  For Eutychas, son of Eutychos, for the price of 12 measures of barley: 4 drachmai.

  [For the price] of 4 1/2 stathmia of [wool], for Orsenouphis, son of Belphis: 8 drachmai.

  . . . of 4 stathmia of wool . . .: 7 obols.

  For Orsenouphis(?), as salary for a half-stathmion of thread: 10 obols.

  On the 10th. [For the price] of oil: 3 obols.

  On the 13th. [For the price] of oil and a made dish: 5 obols.

  [For the price] of oil: 3 obols; for a made dish: 2 obols.

  [For the price] of 1 keramion [of wine]: 14 obols.

  [- - -] and (for) beer: 10 obols.

  On the 17th. For the price [- - -]: 2 obols.

  On the 18th. Through Orsenouphis, son of Tabas, (who works) in the workshop of Hatres, for the price of wool: 4 drachmai.

  On the 19h. [- - -]: 2 obols.

  On the 20th. For Patron, son of Tyrannos: 10 obols.

  For the price of 1 keramion of wine from Talei, (for) entertaining Eutychas: 22 obols.

  On the . . For the price of a half-artaba of turnips: 6 obols.

  For the price of a made dish and of oil: 6 obols.

  On the . . For the price of oil: 3 obols.

  On the 28th. For the price of oil and of a made dish: 5 obols.

  On the 29th. For the price of oil: 3 obols.

  Entertaining Kastoras: 10 obols.

  For the price of the thread to complete the outer garment and of the tunics: 4 drachmai.

  On Choiak 2. [- - -] of the robe and of the tunics: 16 obols;

  for the price of purple dye: 3 1/2 obols.

  For the price of oil: 3 obols.

  On the 4th. For the price of oil and a made dish: 5 obols.

  For the price of oil: 3 obols.

  On the 7th. For the price of oil: 3 obols.

  For the price of 10 artabai and 8 measures of dates: 28 drachmai.

  For the fare of one donkey and for expenses: 19 1/2 obols.

  For Satyros, for the price of 3 measures of dates: 8 obols.

  For Orsenouphis the (cloth-)beater, for the price of fishes (salachia): 4 drachmai.

  On the . . For Patron, son of Tyrannos, for contributions for the 6th year: 4 drachmai.

  On the 9th(?). For the price of oil and of a made dish: 5 obols.

  On the 13th. Entertaining Maron and Soterichos, son of Kronides: a contribution of 4 drachmai.

  On the 14th. For the workers cutting the wood, and for the freight charges in the same matter, for 6 loads of wood: 34 obols.

  For a made dish and for oil: 5 obols.

  For Lysas, son of Kephalas, what I deducted (from his account) as a loan for the scribe's fee for Horos and Herakleides, both sons of Plesis: 8 drachmai.

  On the 16th. Through Tabas the (cloth-)beater, for the price of oil: 4 drachmai.

  To Tenesrois, daughter(?) of Apias, for the price of 1 keramion of wine: 20 obols.

  On the 17th. For the price of a made dish: 2 obols.

  For Tateeus, for the price of 2 artabai of barley: 8 silver drachmai.

  On the 19th. For the price of a made dish: 1 obol.

  For Pnesis, for the price of 4 stathmia of wool: 8 drachmai.

  On the 20th. For the price of a made dish: 2 obols.

  On the . . For the price of a made dish: 2 obols.

  On the . . For the price of a made dish and vegetables: 3 obols.

  Entertaining Herakles and Didymas with Pnesis: for each, a keramion of wine: 20 obols; and a made dish: 3 obols.

  On the . . Entertaining Sagatos and Horos and Apetes, (his/their?) father: 10 obols.

  [- - -] and eggs: 10 obols.

  (Col. III)

  And for the receipt that Gaius made for Onnophris the granary guard: 14 obols;

  and for (Eutychos) the son of Chrates and (Eutychos) the son of Takolleeinis, for payments: 2 obols.

  On the 30th. Entertaining Onnophris the granary guard: for 2 keramia of wine, 42 obols.

  On Tybi 1. For the price of a made dish and oil: 5 obols.

  On the 3rd. For the price of a made dish and oil: 6 obols.

  On the 5th. For the price of a made dish and oil: 5 obols.

  Entertaining Apollonies <read: Apollonides?> 'with Eutychas and Tabos': a contribution of 12 obols.

  On the 9th. For the price of a made dish and oil: 6 obols.

  On the 11th. For the price of oil: 5 obols.

  On the 14th. For the price of oil and of a made dish: 6 obols.

  Entertaining Kastoras and his brothers as a favor to Helenos: a participation of 5 drachmai.

  On the 19th. For the price of vegetables and oil and a made dish: 6 1/2 obols.

  On the 21st. For the price of oil: 4 obols.

  On the 22nd. For Kronion, son of Belles grandson of Kalas, for the price of wool: 4 drachmai.

  For the price of vegetables in the city: 6 1/2 obols.

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  PMich II	Boak AER	1933	127	Boak AER, PMich II, 127, 1933

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  Inventory Number

  P.Mich.inv. 3218

  Processing Number

  1882

  Section/Side

  Recto + Verso

  Background and Physical Properties

  Publ./Side

  Recto + Verso

  Connections

  Zenon archive

  Material

  Pap

  Size

  17.5 x 33 cm

  Items

  1

  Lines

  Recto - 29;

  Verso - 3

  Mounted

  No

  Negative

  No

  Conservation Status

  middle part quite damaged

  Palaeographic Description

  L. 27-29 in Zenon's hand

  Status

  published

  Library

  Ann Arbor

  Contents

  Date

  248 or 247 B.C.

  Origin

  Unknown place, Egypt

  Provenance

  Philadelpheia, Herakleidou meris, Arsinoite nome, Egypt

  Acquisition

  November 1925; Acquired from Brummer

  Language

  Greek

  Genre

  Documentary

  Author

  Unknown; Zenon

  Type of Text/Title of Work

  Money account

  Content

  Money account, perhaps a commercial agent on board a Nile boat, concerning 1,000 copper drachmai that the writer has received, and of which 701 have been repaid in various transactions

  Subject Headings

  Accounts--Egypt.

  Arsinoë (Fayy¯um : Extinct city)

  Alexandria.

  Receipts (Acknowledgments)--Egypt.

  Freight and freightage--Egypt.

  Business--Egypt.

  Drachma.

  Wool--Transportation--Egypt.

  Persons

  Theogenes (see Pap.Lugd.Bat. XXI, p. 339);

  Dromon (see Pap.Lugd.Bat. XXI, p. 321);

  Asklepiades;

  Epharmostos (son of Agreophon) (see Pros.Ptol. IV 11382; VI 16381);

  Mikion (see Pros.Ptol. V 14223);

  Hieron (see Pap.Lugd.Bat. XXI, p. 346)

  Geographica

  Alexandria; Kanopos; Krokodilon polis (Arsinoiton polis); Ptolemais; Kerke

  Translation

  (Recto)

  We have received what you paid to Theogenes in Alexandria, 1,000 copper drachmai.

  Towards this you have received what Dromon in Kanopos (paid), 180 silver drachmai, and in Alexandria, what Epharmostos . . ., 140 silver drachmai; [- - -] choai at 1 drachme 1 1/2 obol each, equal 320 silver drachmai; [- - -] from Krokodilon polis [- - -]; 'for those who transferred (the freight) from the mouth (of the river) to the boat [- - -]'; and transport fare to Ptolemais [- - -]; and from Ptolemais to Kerke [- - -], equal 645 silver drachmai, which equal [- - -] at the four drachmai, 695 (copper) drachmai 4 1/2 obols; (and) 6 copper drachmai 1 obol; giving a total of: 701 copper drachmai 5 1/2 obols; remain: 298 drachmai 1/2 obol.

  (2nd hand) And Mikion took 20 minas of wax, 16 (drachmai) 2 obols; and in the 38th year, he has received for '15' minas of wool, 30 drachmai; and what we have guaranteed from Hieron for '15' other minas, 30 drachmai.

  (Verso: vestiges of title or docket)

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  PMich I	Edgar CC	1931	61	Edgar CC, PMich I, 61, 1931 -- BL IV, 55 (lines 17-18). Line 26: read 16 (drachmai) 2 obols, rather than 16 (drachmai). (PH)	BL IV, 55 (lines 17-18). Line 26: read 16 (drachmai) 2 obols, rather than 16 (drachmai). (PH)

  Information on Publications--Bibliography

  Bibliography

  T. Reekmans, CE 30 (1955) p. 373.

  Availability/System Requirements

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  sc

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  PH

  
  
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  Inventory Number

  P.Mich.inv. 3218

  Processing Number

  1882

  Section/Side

  Recto + Verso

  Background and Physical Properties

  Publ./Side

  Recto + Verso

  Connections

  Zenon archive

  Material

  Pap

  Size

  17.5 x 33 cm

  Items

  1

  Lines

  Recto - 29;

  Verso - 3

  Mounted

  No

  Negative

  No

  Conservation Status

  middle part quite damaged

  Palaeographic Description

  L. 27-29 in Zenon's hand

  Status

  published

  Library

  Ann Arbor

  Contents

  Date

  248 or 247 B.C.

  Origin

  Unknown place, Egypt

  Provenance

  Philadelpheia, Herakleidou meris, Arsinoite nome, Egypt

  Acquisition

  November 1925; Acquired from Brummer

  Language

  Greek

  Genre

  Documentary

  Author

  Unknown; Zenon

  Type of Text/Title of Work

  Money account

  Content

  Money account, perhaps a commercial agent on board a Nile boat, concerning 1,000 copper drachmai that the writer has received, and of which 701 have been repaid in various transactions

  Subject Headings

  Accounts--Egypt.

  Arsinoë (Fayy¯um : Extinct city)

  Alexandria.

  Receipts (Acknowledgments)--Egypt.

  Freight and freightage--Egypt.

  Business--Egypt.

  Drachma.

  Wool--Transportation--Egypt.

  Persons

  Theogenes (see Pap.Lugd.Bat. XXI, p. 339);

  Dromon (see Pap.Lugd.Bat. XXI, p. 321);

  Asklepiades;

  Epharmostos (son of Agreophon) (see Pros.Ptol. IV 11382; VI 16381);

  Mikion (see Pros.Ptol. V 14223);

  Hieron (see Pap.Lugd.Bat. XXI, p. 346)

  Geographica

  Alexandria; Kanopos; Krokodilon polis (Arsinoiton polis); Ptolemais; Kerke

  Translation

  (Recto)

  We have received what you paid to Theogenes in Alexandria, 1,000 copper drachmai.

  Towards this you have received what Dromon in Kanopos (paid), 180 silver drachmai, and in Alexandria, what Epharmostos . . ., 140 silver drachmai; [- - -] choai at 1 drachme 1 1/2 obol each, equal 320 silver drachmai; [- - -] from Krokodilon polis [- - -]; 'for those who transferred (the freight) from the mouth (of the river) to the boat [- - -]'; and transport fare to Ptolemais [- - -]; and from Ptolemais to Kerke [- - -], equal 645 silver drachmai, which equal [- - -] at the four drachmai, 695 (copper) drachmai 4 1/2 obols; (and) 6 copper drachmai 1 obol; giving a total of: 701 copper drachmai 5 1/2 obols; remain: 298 drachmai 1/2 obol.

  (2nd hand) And Mikion took 20 minas of wax, 16 (drachmai) 2 obols; and in the 38th year, he has received for '15' minas of wool, 30 drachmai; and what we have guaranteed from Hieron for '15' other minas, 30 drachmai.

  (Verso: vestiges of title or docket)

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  PMich I	Edgar CC	1931	61	Edgar CC, PMich I, 61, 1931 -- BL IV, 55 (lines 17-18). Line 26: read 16 (drachmai) 2 obols, rather than 16 (drachmai). (PH)	BL IV, 55 (lines 17-18). Line 26: read 16 (drachmai) 2 obols, rather than 16 (drachmai). (PH)

  Information on Publications--Bibliography

  Bibliography

  T. Reekmans, CE 30 (1955) p. 373.

  Availability/System Requirements

  Institution

  sc

  Cataloging

  Cataloger

  PH

  
  
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  Inventory Number

  P.Mich.inv. 3219

  Processing Number

  1883

  Section/Side

  Recto

  Background and Physical Properties

  Publ./Side

  Recto

  Connections

  Zenon archive

  Material

  Pap

  Size

  22.5 x 13.5 cm

  Items

  1

  Lines

  Recto - 12;

  Verso - 1

  Mounted

  No

  Negative

  No

  Conservation Status

  broken off on the left and right sides; badly mutilated

  Status

  published

  Library

  Ann Arbor

  Contents

  Date

  August, 249 B.C.

  Origin

  probably Philadelpheia, Herakleidou meris, Arsinoite nome, Egypt

  Provenance

  Philadelpheia, Herakleidou meris, Arsinoite nome, Egypt

  Acquisition

  November 1925; Acquired from Brummer

  Language

  Greek

  Genre

  Documentary

  Author

  [- - -]

  Type of Text/Title of Work

  Business Letter

  Content

  Report to Zenon from one of his agents about quantities of barley, poppy seed and sesame, from which certain amounts are deducted as payment for transport, sifting, winnowing, and measuring

  Subject Headings

  Commercial correspondence--Egypt.

  Farm produce--Transportation--Egypt.

  Agricultural laborers--Egypt.

  Freight and freightage--Egypt.

  Persons

  Zenon (son of Agreophon) (see Pros.Ptol. I 80 + add.);

  Glaukias (see Pros.Ptol. IV 10175);

  Harbichis;

  [- - -], sitometres;

  Haren[- - -] (see also below);

  Nika[- - -];

  Maron (see also Pros.Ptol. IV 10289);

  (unnamed) koskineutai;

  (unnamed) brastai;

  (unnamed) sitometrai;

  Harentotes sitologos(?) (see Pros.Ptol. I 1342 + add.)

  Geographica

  Philadelpheia(?)

  Translation

  (Text too fragmentary to be translated).

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  PMich I	Edgar CC	1931	53	Edgar CC, PMich I, 53, 1931

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  Inventory Number

  P.Mich.inv. 3219

  Processing Number

  1883

  Section/Side

  Recto

  Background and Physical Properties

  Publ./Side

  Recto

  Connections

  Zenon archive

  Material

  Pap

  Size

  22.5 x 13.5 cm

  Items

  1

  Lines

  Recto - 12;

  Verso - 1

  Mounted

  No

  Negative

  No

  Conservation Status

  broken off on the left and right sides; badly mutilated

  Status

  published

  Library

  Ann Arbor

  Contents

  Date

  August, 249 B.C.

  Origin

  probably Philadelpheia, Herakleidou meris, Arsinoite nome, Egypt

  Provenance

  Philadelpheia, Herakleidou meris, Arsinoite nome, Egypt

  Acquisition

  November 1925; Acquired from Brummer

  Language

  Greek

  Genre

  Documentary

  Author

  [- - -]

  Type of Text/Title of Work

  Business Letter

  Content

  Report to Zenon from one of his agents about quantities of barley, poppy seed and sesame, from which certain amounts are deducted as payment for transport, sifting, winnowing, and measuring

  Subject Headings

  Commercial correspondence--Egypt.

  Farm produce--Transportation--Egypt.

  Agricultural laborers--Egypt.

  Freight and freightage--Egypt.

  Persons

  Zenon (son of Agreophon) (see Pros.Ptol. I 80 + add.);

  Glaukias (see Pros.Ptol. IV 10175);

  Harbichis;

  [- - -], sitometres;

  Haren[- - -] (see also below);

  Nika[- - -];

  Maron (see also Pros.Ptol. IV 10289);

  (unnamed) koskineutai;

  (unnamed) brastai;

  (unnamed) sitometrai;

  Harentotes sitologos(?) (see Pros.Ptol. I 1342 + add.)

  Geographica

  Philadelpheia(?)

  Translation

  (Text too fragmentary to be translated).

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  PMich I	Edgar CC	1931	53	Edgar CC, PMich I, 53, 1931

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  Inventory Number

  P.Corn. Inv. II 2

  Processing Number

  1246

  Section/Side

  Recto

  Background and Physical Properties

  Publ./Side

  Recto; traces of an adress on the Verso

  Connections

  P. L. Bat 20, 54, cf. P. L. Bat 21 A, p.129.

  Material

  Pap

  Size

  9.4 x 31 cm.

  Items

  1

  Lines

  Recto: 1-31

  Verso: 1-2

  Mounted

  No

  Negative

  No

  Conservation Status

  Light-brown papyrus which is rather regularly torn off at the left and the right sides. Cut off at the bottom. Three vertical folds still visible (TC).

  Palaeographic Description

  Careless Ptolemaic hand. Some marginhas been left: at the left side 2.2 cm., at the bottom 2.7 cm. and at the right side only 0.7 cm. Text on recto has been divided in three sections separated by some empty space of aprroximately 1 cm and the bottom section (ll. 27-31) is washed out.

  Status

  published

  Library

  Ann Arbor

  Contents

  Date

  Middle third century B.C.

  Origin

  Philadelpheia, Herakleidou meris, Arsinoite nome, Egypt

  Provenance

  Philadelpheia, Herakleidou meris, Arsinoite nome, Egypt

  Acquisition

  In 1922 through the agency of the British Museum for Cornell University; handed over to the University of Michigan in 1972.

  Language

  Greek

  Genre

  Documentary

  Author

  Unknown

  Type of Text/Title of Work

  Estimate of freight charges

  Content

  List of estimated expenses connected to the transportation by boat of unknown objects.

  Subject Headings

  Drachma.

  Taxation--Egypt.

  Measures and weights, Ancient.

  Currency convertibility (Egypt)

  Cargo ships--Handling--Egypt.

  Freight and freightage--Egypt.

  Fees, Administrative--Egypt.

  Persons

  -

  Geographica

  -

  Translation

  Ll. 4-26. "Freightage, reckoned in copper, 45 drachmas (?). Inspection tax at Memphis, silver, 4 drachmas. Thus there are added to the charges per 100 (artabas), 49 drachmas, 2 1/4 obols (?). Also in Memphis the . . . toll, at 1 chalkous per artaba, (total) silver, 2 drachmas 1/2 obol. Discount, 1 1/4 obols. Clerical charges on the boat,silver, 2 (drachmas) 4 obols. Distributed per 100 (artabas), with discount, 3 obols. Labor charge, 1 (drachma) 4 obols. Added for temple dues per 100 (artabas), tranposed into copper, 2 (drachmas) 3 obols. For commision agent, who will receive and measure, per 100, 1 drachma. Total charges per 100 artabas, in copper, 57 drachmas 2 obols. Figuring the total as 56 drachmas 2 obols, the charge per artaba is 3 1/2 obols, not including interest, lodging, food, police protection (?)." Verso: "T . . . to Phormio."

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  PCorn	Westermann WL - Kraemer CJ	1926	3	Pl p37	Westermann WL - Kraemer CJ, PCorn, 3, 1926, Pl p37 -- For all the corrections until January 1978, see P.L.Bat. 21A, pp. 33 and 129	For all the corrections until January 1978, see P.L.Bat. 21A, pp. 33 and 129

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  Inventory Number

  P.Mich.inv. 6831

  Processing Number

  2950

  Section/Side

  Recto

  Background and Physical Properties

  Publ./Side

  Recto; Verso is blank

  Material

  Pap

  Size

  18.2 X 10.3 cm

  Items

  3

  Lines

  20

  Mounted

  No

  Negative

  Yes

  Conservation Status

  broken off at the bottom; surface badly abraded, especially down the center

  Palaeographic Description

  See electronic version of PMich IX, 560

  Status

  published

  Library

  Ann Arbor

  Contents

  Date

  October 31, 46 A.D.

  Origin

  Karanis, Herakleidou meris, Arsinoite nome, province of Egypt

  Provenance

  Karanis, Herakleidou meris, Arsinoite nome, province of Egypt

  Acquisition

  35-288-A

  Language

  Greek

  Genre

  Documentary

  Author

  Horion son of Papontos

  Type of Text/Title of Work

  Contract of Lease of Land

  Content

  Contract by which Horion son of Papontos leases from Tithoes son Nepheros some tax-exempted land in the ousia of Livia

  Subject Headings

  Farmers--Egypt--Karanis (Extinct city)

  Ethnic groups--Egypt--Karanis (Extinct city)

  Land tenure--Egypt--Karanis (Extinct city)

  Leases--Egypt--Karanis (Extinct city)

  Iranians--Egypt

  Tax exemption--Egypt--Karanis (Extinct city)

  Contracts--Egypt--Karanis (Extinct city)

  Scars--Egypt--Karanis (Extinct city)

  Weights and measures, Ancient.

  Farm produce--Egypt--Karanis (Extinct city)

  Field crops--Seeds--Egypt--Karanis (Extinct city)

  Real property--Egypt--Karanis (Extinct city)

  Transportation--Cost--Egypt--Karanis (Extinct city)

  Freight and freightage--Egypt--Karanis (Extinct city)

  Persons

  Claudius, Emperor;

  Horion son of Papontos;

  Tithoes son of Nepheros, Perses tes epigones;

  Livia (see geographica)

  Geographica

  Karanis, Herakleidou meris of the Arsinoite nome; ousia (former estate) of Livia; Perses

  Translation

  The seventh year of Tiberius Claudius Caesar Augustus Germanicus the Emperor, the 4th of the month Neos Sebastos, in Karanis in the Herakleides division of the Arsinoite nome. Horion, son of Papontos, about fifty years old, with a scar on the little finger of his left hand, has leased to Tithoes, son of Nepheros, a Persian of the epigone, about sixty years old, with a scar in the middle of his forehead, the aroura and one-half and one-eighth, or as many as may be, that he himself is cultivating near Karanis, part of the estate of Livia, which is tax-exempted, for the seventh year of Tiberius Claudius Caesar Augustus Germanicus the Emperor for planting with vegetable seed. All the resulting produce and . . . [are to be brought] to the threshing floor, from which two shares will belong to Horion and one share to Tithoes. All the transportation charges to the threshing floor [shall be charged to Horion], the [work] of cultivation [to Tithoes] . . .

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  PMich IX	Husselman EM	1971	560	Husselman EM, PMich IX, 560, 1971 -- BL VII, 113 (on lines 8, 8-9); IX 162 (on line 13).	BL VII, 113 (on lines 8, 8-9); IX 162 (on line 13).

  Information on Publications--Bibliography

  Bibliography

  P.J. Parsons, CR 24 (1974) p. 148; G.M. Parassoglou, Imperial Estates in Egypt (Amsterdam, 1978) p. 57, n. 45; p. 101.

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  Inventory Number

  O.Mich.inv. 9311

  Processing Number

  751

  Section/Side

  Recto

  Background and Physical Properties

  Publ./Side

  Recto; Verso is blank

  Material

  Ost

  Size

  8.5 X 7.4 cm

  Items

  1

  Lines

  4

  Mounted

  No

  Negative

  No

  Conservation Status

  complete

  Status

  published

  Library

  Cairo

  Contents

  Date

  9/8 B.C.[?]

  Origin

  Bacchias, Herakleidou meris, Arsinoite nome, province of Egypt

  Provenance

  Karanis, Herakleidou meris, Arsinoite nome, province of Egypt

  Acquisition

  29-B166*-C

  Language

  Greek

  Genre

  Documentary

  Author

  Simon

  Type of Text/Title of Work

  Account of Deliveries in Kind

  Content

  Account of the amount of wheat transported from Bacchias in several shipments(?)

  Subject Headings

  Measures and weights, Ancient.

  Tax collection--Egypt--Bachias (Extinct city)

  Bacchias (Extinct city)

  Drachma.

  Signatures (Writing)

  Wheat--Transportation--Egypt.

  Wheat--Registers--Egypt.

  Freight and freightage--Egypt.

  Taxation--Egypt--Bachias (Extinct city)

  Persons

  Simon

  Geographica

  Bacchias

  Translation

  Year 22, of the village of Bacchias:

  1st (shipment?), 75 artabai of wheat; 2nd (shipment?), 73 (artabai of wheat); 3rd (shipment?), 88 (artabai of wheat); 4th (shipment?), 64 (artabai of wheat); tranportation charges of these: 1050 (drachmai).

  (2nd hand) I, Simon, have sealed.

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  OMich IV	Youtie HC	1975	1119	SB XIV 11506	Youtie HC, OMich IV, 1119, 1975 -- SB XIV 11506

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  Inventory Number

  O.Mich.inv. 4258

  Processing Number

  106

  Background and Physical Properties

  Publ./Side

  Recto; Verso is blank

  Material

  Ost

  Size

  9.3 x 4.8 cm

  Items

  1

  Lines

  6

  Mounted

  No

  Negative

  No

  Conservation Status

  Complete

  Status

  published

  Library

  Kelsey Museum

  Contents

  Date

  April 5, 297 A.D.

  Origin

  Thraso, Themistou meris, Arsinoite nome, province of Egypt

  Provenance

  probably Thraso, Themistou meris, Arsinoite nome, province of Egypt

  Acquisition

  purchased by Dr. D.L. Askren; acquired from him in July, 1925

  Language

  Greek

  Genre

  Documentary

  Author

  Unknown

  Type of Text/Title of Work

  Receipt for Delivery in Kind

  Content

  Receipt for delivery of chaff

  Subject Headings

  Taxation--Egypt--Karanis (Extinct city)

  Tax collection--Egypt--Arsinoite Nome.

  Crop residues--Transportation--Egypt--Arsinoite Nome.

  Freight and freightage--Rates--Egypt--Arsinoite Nome.

  Receipts (Acknowledgments)--Egypt--Arsinoite Nome.

  Persons

  Ptoleminos, archo . . . <or son of Archon?>;

  Agathodoros

  Geographica

  Thraso

  Translation

  6th. Ptoleminos, . . ., has delivered for the account of Thraso one basket (sargane) of chaff and 130 pounds of chaff for the freight charges; he paid(?) through Agathodoros. In the 13th, 12th, and 5th year, Pharmouthi 10th.

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  OMich I	Amundsen L	1935	52	Amundsen L, OMich I, 52, 1935
  PSakaon	Parassoglou GM	1978	83	Parassoglou GM, PSakaon, 83, 1978

  Information on Publications--Bibliography

  Bibliography

  H.C. Youtie, TAPA 76 (1945) p. 148, n. 54 [= H.C. Youtie, Scriptiunculae I (Amsterdam, 1973) p. 161, n. 54.]

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  Inventory Number

  O.Mich.inv. 9808

  Processing Number

  1069

  Background and Physical Properties

  Publ./Side

  Recto; Verso is blank

  Connections

  -

  Material

  Ost

  Size

  8.1 X 5.3 cm

  Items

  1

  Lines

  7

  Mounted

  No

  Negative

  No

  Conservation Status

  complete; lines 1-2 badly faded

  Palaeographic Description

  see electronic version of OMich III, 1029

  Status

  published

  Library

  Cairo

  Contents

  Date

  November 20, 296 A.D.

  Origin

  Karanis, Herakleidou meris, Arsinoite nome, province of Egypt

  Provenance

  Karanis, Herakleidou meris, Arsinoite nome, province of Egypt

  Acquisition

  32-234*-T

  Language

  Greek

  Genre

  Documentary

  Author

  Dioskoros

  Type of Text/Title of Work

  Receipt of tax payment in kind

  Content

  Tax receipt for wine paid by Serenus for the annona

  Subject Headings

  Veterans--Rome.

  Tax collection--Egypt--Karanis (Extinct city)

  Wine--Egypt--Karanis (Extinct city)

  Measures and weights, Ancient.

  Freight and freightage--Egypt--Karanis (Extinct city)

  Persons

  Domitius Domitianus, Emperor;

  Serenus, veteran (see also O. Mich. I, 548);

  Kallonios;

  Dioskoros (see also O. Mich. II, 802)

  Geographica

  horiodeiktia of Karanis

  Translation

  In the 2nd year of our lord Lucius Domittius Domittianus Augustus, Hathyr 24, has paid Serenus, veteran, through Kallonios, for the annona as fixed by decree of the new epigraphe of the horiodeiktia of Karanis, four sextarii of wine, = 4 sextarii. I, Dioskoros, have signed. And transportation charges on these.

  Information on Publications

  Publications

  Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
  OMich III	Youtie HC	1951	1029	Youtie HC, OMich III, 1029, 1951

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