P.Mich.inv. 5663 / Recto

About this Item

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Record Details

Inventory Number

P.Mich.inv. 5663

Processing Number

2527

Section/Side

A (main part and fragments A-C); Recto

Image Side

Recto

Background and Physical Properties

Publ./Side

Recto; Verso is blank

Material

Pap

Size

42 x 21 cm (col. II-XIII); 8 x 5 cm (col. XIV-XV); 15 x 11.5 cm (col. XV-XVII); 4 x 11 cm (col. XVIII); 4.3 x 9 cm (frg. A); 9.2 x 6.6 cm (frg. B); 3.5 x 3.3 cm; 1.7 x 1.7 cm

Items

6 pieces, made of more than 30 fragments, and 2 small fragments

Lines

Main part:

col. II - 13;

col. III - 26;

col. IV - 26;

col. V - 25;

col. VI - 27;

col. VII - 31;

col. VIII - 29;

col. IX - 19;

col. X - 25;

col. XI - 15;

col. XII - 10;

col. XIII - 7;

col. XIV - 2;

col. XV - (2 +) 7;

col. XVI - 8;

col. XVII - 17;

col. XVIII - 18

Fragment A - 14;

Fragment B, col. I - 7;

Fragment B, col. II - 4

Mounted

Yes

Negative

Yes

Conservation Status

Darkened, much damaged papyrus, broken off in many fragments. Incomplete at the beginning and at the end

Status

published

Library

Ann Arbor

Contents

Date

IInd century/IIIrd A.D.

Origin

Unknown place, province of Egypt

Provenance

Karanis, Herakleidou meris, Arsinoite nome, province of Egypt

Acquisition

29-B163*-J

Language

Greek

Genre

Literary: mathematical

Author

Unknown

Type of Text/Title of Work

Tables of Multiplications, Fractions and Multiples

Content

Tables of multiplications (1 to 9, 10 to 90, 100 to 900, 1,000 to 10,000 multiplied by 1 to 10), of fractions (from 1/2 of 3 to 1/9 of 10) and of multiples of fractions (multiples of 1/30)

Subject Headings

Literature

Mathematics

Persons

-

Geographica

-

Translation

(Col. I: lost)

(Col. II: remains of the multiplications of 7 x 2 through 4 x 5)

Col. III:

[5 x 5 = 25]

5 x 6 = 30

5 x 7 = 35

5 x 8 = 40

5 x 9 = 45

5 x 10 = 50

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

6 x 7 = 42

6 x 8 = 48

6 x 9 = 54

6 x 10 = 60

7 x 1 = 7

7 x 2 = 14

7 x 3 = 21

7 x 4 = 28

(traces of the next 8 lines)

Col. IV

[8 x 3 = 24]

8 x 4 = 32

8 x 5 = 40

8 x 6 = 48

8 x 7 = 56

8 x 8 = 64

8 x 9 = 72

8 x 10 = 80

9 x 1 = 9

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

9 x 5 = 45

9 x 6 = 54

9 x 7 = 63

9 x 8 = 72

9 x 9 = 81

9 x 10 = 90

10 x 1 = 10

10 x 2 = 20

10 x 3 = 30

10 x 4 = 40

10 x 5 = 50

10 x 6 = 60

10 x 7 = 70

10 x 8 = 80

Col. V

[10 x 9] = 90

10 x 10 = 100

20 x 1 = 20

20 x 2 = 40

20 x 3 = 60

20 x 4 = 80

20 x 5 = 100

20 x 6 = 120

20 x 7 = 140

20 x 8 = 160

20 x 9 = 180

20 x 10 = 200

30 x 1 = 30

30 x 2 = 60

30 x 3 = 90

30 x 4 = 120

30 x 5 = 150

30 x 6 = 180

30 x 7 = 210

30 x 8 = 240

30 x 9 = 270

30 x 10 = 300

40 x 1 = 40

40 x 2 = 80

40 x 3 = 120

Col. VI

40 x 4 = 160

40 x 5 = 200

40 x 6 = 240

40 x 7 = 280

40 x 8 = 320

40 x 9 = 360

40 x 10 = 400

50 x 1 = 50

50 x 2 = 100

50 x 3 = 150

50 x 4 = 200

50 x 5 = 250

50 x 6 = 300

50 x 7 = 350

50 x 8 = 400

50 x 9 = 450

50 x 10 = 500

60 x 1 = 60

60 x 2 = 120

60 x 3 = 180

60 x 4 = 240

[60 x 5] = 300

60 x 6 = 360

60 x 7 = 420

[60 x 8] = 480

[60 x 9 = 540

60 x 10 = 600]

Col. VII

70 x 1 = 70

70 x 2 = 140

70 x 3 = 210

70 x 4 = 280

70 x 5 = 350

70 x 6 = 420

70 x 7 = 490

70 x 8 = 560

70 x 9 = 630

70 x 10 = 700

80 x 1 = 80

80 x 2 = 160

80 x 3 = 240

80 x 4 = 320

80 x 5 = 400

80 x 6 = 480

80 x 7 = 560

80 x 8 = 640

80 x 9 = 720

80 x 10 = 800

90 x 1 = 90

90 x 2 = 180

90 x 3 = 270

90 x 4 = 360

90 x 5 = 450

90 x 6 = 540

90 x 7 = 630

90 x 8 = 720

90 x 9 = 810

90 x 10 = 900

100 x 1 = 100

Col. VIII

100 x 2 = [200]

100 x 3 = 300

100 x 4 = 400

100 x 5 = 500

100 x 6 = 600

100 x 7 = 700

100 x 8 = 800

100 x 9 = 900

100 x 10 = [1,000]

200 x 1 = 200

200 x 2 = 400

200 x 3 = 600

200 x 4 = 800

200 x 5 = 1,000

200 x 6 = 1,200

200 x 7 = 1,400

200 x 8 = 1,600

200 x 9 = 1,800

200 x 10 = 2,000

300 x 1 = 300

300 x 2 = 600

300 x 3 = 900

300 x 4 = 1,200

300 x 5 = 1,500

300 x 6 = 1,800

300 x 7 = 2,100

300 x 8 = 2,400

300 x 9 = 2,700

300 x 10 = 3,000

Col. IX

[400 x 1 = 400]

[400] x 2 = 800

[400] x 3 = 1,200

[400] x 4 = 1,600

[400] x 5 = 2,000

[8 lines lost]

500 x 4 = 2,000

500 x 5 = 2,500

500 x 6 = 3,000

500 x 7 = 3,500

500 x 8 = 4,000

500 x 9 = 4,500

500 x 10 = 5,000

600 x 1 = 600

600 x 2 = 1,200

600 x 3 = 1,800

600 x 4 = 2,400

600 x 5 = 3,000

600 x 6 = 3,600

600 x 7 = 4,200

600 x 8 = 4,800

Col. X

600 x 9 = 5,400

600 x 10 = 6,000

700 x 1 = 700

700 x 2 = 1,400

700 x 3 = 2,100

700 x 4 = 2,800

700 x 5 = 3,500

700 [x 6] = 4,200

700 x 7 [= 4,900]

700 [x 8 = 5,600]

700 x 9 [= 6,300]

[700 x 10 = 7,000]

800 x 1 = 800

800 x 2 = 1,600

800 x 3 = 2,400

800 x 4 = 3,200

800 x 5 = 4,000

800 x 6 = 4,800

800 x 7 = 5,600

800 x 8 = 6,400

800 x 9 = 7,200

800 x 10 = 8,000

900 x 1 = 900

900 x 2 = 1,800

900 x 3 = 2,700

900 x 4 = 3,600

Col. XI

[1 line missing?]

900 [x . . .]

[5 or 6 lines missing]

[1,000] x 4 = 4,000

[1,000] x 5 = 5,000

1,000 x 6 = 6,000

1,000 x 7 = [7,000]

1,000 x 8 = 8,000

1,000 x 9 = 9,000

1,000 x 10 = 10,000

2,000 x 1 = [2,000]

2,000 x 2 = 4,000

2,000 x 3 = 6,000

2,000 x 4 = 8,000

2,000 x 5 = 10,000

Col. XII

[6 lines missing]

3,000 x 2 = 6,000

[3,000] x 3 = [9,000]

[4 lines missing]

[3,000 x 8] = 24,000

[3,000] x 9 = 27,000

[3,000] x 10 = 30,000

[4,000] x 1 = 4,000

[4,000] x 2 = 8,000

4,000 x 3 = 12,000

4,000 x 4 = 16,000

4,000 x 5 = [20,000]

Col. XIII

[10 lines missing]

[5,000] x 6 = 30,000

5,000 x 7 = 35,000

5,000 x 8 = 40,000

5,000 x 9 = 45,000

5,000 x 10 = 50,000

[2(?) lines missing]

Col. XIV

[8 lines missing]

7,000 x 1 = 7,000

7,000 x 2 = 14,000

[some lines missing]

Col. XV

[8,000 x 1] = 8,000

[8,000 x 2] = 16,000

[8,000 x 3] = 24,000

8,000 x 4 = 32,000

8,000 x 5 = 40,000

8,000 x 6 = 48,000

[8,000 x 7] = 56,000

Col. XVI

[9,000 x 7] = 63,000

9,000 x 8 = 72,000

9,000 x 9 = 81,000

9,000 x 10 = 90,000

10,000 x 1 = 10,000

10,000 x 2 = 20,000

[10,000 x 3] = 30,000

[10,000 x 4] = 40,000

Col. XVII (= Fragment C, col. I)

5 (x 1/30) = 1/6

5 1/2 (x 1/30) = 1/6 + 1/60

6 (x 1/30) = 1/5

6 1/2 (x 1/30) = 1/5 + 1/60

7 (x 1/30) = 1/5 + 1/30

7 1/2 (x 1/30) = 1/5 [+ 1/20]

8 (x 1/30) = [1/5 + 1/15]

8 1/2 (x 1/30) = 1/5 [+ 1/15 + 1/60]

9 (x 1/30) = 1/5 [+ 1/10]

9 1/2 (x 1/30) = 1/5 [+ 1/10 + 1/60]

10 (x 1/30) = 1/3

10 1/2 (x 1/30) = 1/3 + 1/60

11 (x 1/30) = 1/3 + 1/30

11 1/2 (x 1/30) = 1/3 [+ 1/20]

12 (x 1/30) = 1/3 1/15

12 1/2 (x 1/30) = 1/3 + 1/15 [+ 1/60]

13 (x 1/30) = 1/3 [+ 1/10]

Col. XVIII (= Fragment C, col. II)

[11 lines missing]

19 (x 1/30) = [1/2 + 1/10 + 1/30]

19 1/2 (x 1/30) = 1/2 + 1/10 + 1/20

20 (x 1/30) = 2/3

20 1/2 (x 1/30) = 2/3 + 1/60

21 (x 1/30) = 2/3 + 1/30

21 1/2 (x 1/30) = 2/3 + 1/20

22 (x 1/30) = 2/3 + 1/15

22 1/2 (x 1/30) = 2/3 + 1/12

23 (x 1/30) = 2/3 + 1/10

23 1/2 (x 1/30) = 2/3 + 1/10 + 1/60

24 (x 1/30) = 2/3 + 1/10 + 1/30

24 1/2 (x 1/30) = [2/3 + 1/10 + 1/20]

25 (x 1/30) = [2/3 + 1/6]

25 1/2 (x 1/30) = [2/3 + 1/6 +1/60]

26 (x 1/30) = 2/3 [+ 1/5]

26 1/2 (x 1/30) = 2/3 [+ 1/5 + 1/60]

[- - -]

Fragment A

1/[1 of 2 = 2]

1/[2 of 3 = 1 1/2]

1/[3 of 4 = 1 1/3]

1/4 [of 5 = 1 1/4]

1/5 [of 6 = 1 1/5]

1/6 [of 7 = 1 1/6]

1/7 [of 8 = 1 1/7]

1/8 [of 9 = 1 1/8]

1/9 of [10 = 1 1/9]

1/9 of [8 = 1/2 + 1/3 + 1/18]

1/9 of [7 = 2/3 + 1/9]

1/9 of [6 = 2/3]

1/9 of [5 = 1/2 + 1/18]

1/9 of [4 = 1/3 + 1/9]

Fragment B, col. I

1/40 of 50 = 1 1/4

1/50 of 60 = 1 1/5

1/60 of 70 = 1 1/6

1/70 of 80 = 1 1/7

1/80 of 90 = 1 1/8

1/90 of 100 = 1 1/9

1/100 of 110 = 1 1/10

Fragment B, col. II

(Text too fragmentary to be read).

Information on Publications

Publications

Series and Volume	Editor	Year	Pg/Nr	Photo	SB	Preferred Citation	Corrections
PMich XV	Sijpesteijn PJ	1982	686	Pl. I	Sijpesteijn PJ, PMich XV, 686, 1982, Pl. I -- The bottom of col. IX (8 lines, multiplication of 600 by 1 to 8) has been omitted in the edition between lines 186 and 187. - Small fragments composing the top of col. X (11 lines, from 600 x 9 to 700 x 9) were found back among fragments kept under the same inventory number. - Line 200 (900 x 4) is preserved at the end of col. X, not missing at the top of col. XI, as indicated in the edition. - Lines 205-206 are missing. - The fragment bearing col. XIV bears also the beginning of two lines of co. XV, which cannot be identified (8,000 multiplied by ?). - The fragments bearing col. XV and what was called Fragment C, col. I, in the editio princeps are certainly joining, so that col. I-II of Fragment C are now col. XVI-XVII. - The bottom of col. XVI (6 lines, multiplication of 1/30 by 10 1/2 to 13) has been omitted in the edition between lines 286 and 287. - Fragment B, col. II, doesn't bear the multiplication of 1/30 by 3 to 4 1/2, which was in the missing top of col. XVI; no certain reading can be offered. - Some minor fragments added or moved. (PH)	The bottom of col. IX (8 lines, multiplication of 600 by 1 to 8) has been omitted in the edition between lines 186 and 187. - Small fragments composing the top of col. X (11 lines, from 600 x 9 to 700 x 9) were found back among fragments kept under the same inventory number. - Line 200 (900 x 4) is preserved at the end of col. X, not missing at the top of col. XI, as indicated in the edition. - Lines 205-206 are missing. - The fragment bearing col. XIV bears also the beginning of two lines of co. XV, which cannot be identified (8,000 multiplied by ?). - The fragments bearing col. XV and what was called Fragment C, col. I, in the editio princeps are certainly joining, so that col. I-II of Fragment C are now col. XVI-XVII. - The bottom of col. XVI (6 lines, multiplication of 1/30 by 10 1/2 to 13) has been omitted in the edition between lines 286 and 287. - Fragment B, col. II, doesn't bear the multiplication of 1/30 by 3 to 4 1/2, which was in the missing top of col. XVI; no certain reading can be offered. - Some minor fragments added or moved. (PH)
SCIAMVS 21	Sesiano, Jacques	2020	83-140	Sesiano, Jacques, SCIAMVS 21, 83-140, 2020

Availability/System Requirements

Institution

sc

Cataloging

Cataloger

PH

Year Begin

100

Year End

199

Technical Details

Collection

Advanced Papyrological Information System (APIS UM)

Image Size

3072 x 2320

File Size

948 KB

Record

2527

Link to this Item

https://quod.lib.umich.edu/a/apis/x-2527/5663ar2.tif content_copy

Related Links

IIIF

Manifest

https://quod.lib.umich.edu/cgi/i/image/api/manifest/apis:2527 content_copy