Scholarship on List or table: T-S Ar.39.380
List or table T-S Ar.39.380- Bibliographic citation
- Jacques Sesiano, "Koptisches Zahlensystem und (griechisch-)koptische Multiplikationstafeln nach einem arabischen Bericht," Centaurus 32 (n.p., 1989).
- Relation to document
- Discussion
- Bibliographic citation
- Bernard R. Goldstein and David Pingree, "More Horoscopes from the Cairo Geniza,"Proceedings of the American Philosophical Society 125, no. 3 (n.p., 1981), 155–89.
- Relation to document
- Discussion
- Bibliographic citation
- Marina Rustow's digital edition and digital translation, available online through the Princeton Geniza Project at https://geniza.princeton.edu/documents/20917/.
- Relation to document
- Digital Edition
- Digital Translation
Editor: Rustow, Marina
Translator: Rustow, Marina
T-S Ar.39.380 1r
p. 2 (multiplication, 70, 80, and 90)
_Column 1_
(top lost: 70 × 1, 2, and 3)
1 [𐋰 𐋤 𐋴]𐋱
2 [𐋰 𐋭] ͵𐋢[𐋺]
3 𐋰 𐋶 𐋢̈ ͵𐋨
4 𐋰 ͵𐋤 𐋫̈ 𐋨̈
——
5 𐋰 𐋥 𐋵𐋮
6 𐋰 𐋮 ͵𐋣𐋷
7 [𐋰] 𐋷 𐋣̈ ͵𐋥
(bottom lost: 70 × 5000)
_Column 2_
(top lost: 70 × 6, 7, 8)
1 [𐋰 𐋩 𐋸]𐋬
2 [𐋰] 𐋲 ͵𐋦𐋵
3 𐋰 𐋻 𐋦̈ ͵𐋣
4 𐋰 ͵𐋩 𐋯̈ 𐋣̈
——
5 𐋰 𐋡̈ 𐋰̈
_Column 3_
(top lost: 80 × 1)
1 [𐋱 𐋢 𐋳]𐋯
2 [𐋱 𐋫] ͵𐋡𐋸
3 [𐋱 𐋴] 𐋡̈ ͵𐋦
4 [𐋱] ͵𐋢 𐋪̈ 𐋦̈
——
5 [𐋱 𐋣 𐋴]𐋭
6 [𐋱 𐋬] ͵𐋢𐋶
7 [𐋱] 𐋵 𐋢̈ ͵𐋤
8 [𐋱 ͵𐋣] 𐋫̈ 𐋤̈
——
9 𐋱 𐋤 𐋵[𐋫]
10 𐋱 𐋭 ͵𐋣𐋴
11 𐋱 𐋶 𐋣̈ ͵𐋢
12 𐋱 ͵𐋤 𐋬̈ 𐋢̈
——
13 𐋱 𐋥 𐋶
14 𐋱 𐋮 ͵𐋤
15 𐋱 𐋷 𐋤̈
16 [𐋱] ͵𐋥 𐋭̈
——
_Column 4_
1 [𐋱 𐋸] 𐋤̈ ͵𐋨
2 [𐋱 ͵𐋦] 𐋭̈ 𐋨̈
——
3 𐋱 𐋧 𐋷[𐋯]
4 𐋱 𐋰 ͵𐋥𐋸
5 𐋱 𐋹 𐋥̈ [͵𐋦]
6 𐋱 ͵𐋧 𐋮̈ [𐋦̈]
——
7 𐋱 𐋨 𐋸𐋭
8 𐋱 𐋱 ͵𐋦𐋶
9 𐋱 𐋺 𐋦̈ ͵𐋤
10 𐋱 ͵𐋨 𐋯̈ 𐋤̈
——
11 𐋱 𐋩 𐋹𐋫
12 𐋱 𐋲 ͵𐋧𐋴
13 𐋱 𐋻 𐋧̈ ͵𐋢
14 𐋱 ͵𐋩 𐋰̈ 𐋢̈
——
15 𐋱 𐋡̈ 𐋱 (should be 𐋱̈)
——
_Column 5_
1 𐋲 𐋳 [͵𐋩]
2 𐋲 ͵𐋡 𐋩̈
——
3 𐋲 𐋢 𐋳𐋱
4 𐋲 𐋫 ͵𐋡𐋺
5 𐋲 𐋴 𐋡̈ ͵𐋨
6 𐋲 ͵𐋢 𐋪̈ 𐋨̈
——
7 𐋲 𐋣 𐋴𐋰
8 𐋲 𐋬 ͵𐋢𐋹
9 𐋲 𐋵 𐋢̈ ͵𐋧
10 𐋲 ͵𐋣 𐋫̈ 𐋧̈
——
11 𐋲 𐋤 𐋵𐋯
12 𐋲 𐋭 ͵𐋣𐋸
13 𐋲 𐋶 𐋣̈ [͵𐋦]
14 𐋲 ͵𐋤 𐋬̈ 𐋦̈
——
15 𐋲 𐋥 𐋶𐋮
16 𐋲 𐋮 ͵𐋤𐋷
17 𐋲 𐋷 𐋤̈ ͵𐋥
18 [𐋲 ͵𐋥] 𐋭̈ [𐋥̈]
p. 3 (division by 12, 24, 48)
_Column 1 (÷ 12)_
(top lost: 1–4 ÷ 12)
1 𐋥 𐋣ʹ 𐋪𐋢ʹ
2 𐋦 𐅵
3 𐋧 𐅵 𐋪𐋢ʹ
4 [𐋨 𐅷]
5 𐋩 𐅵 𐋤ʹ
6 𐋪 𐅵 𐋣ʹ
7 𐋫 𐋡 𐅷
8 𐋬 𐋢 𐅵
9 𐋭 𐋣 𐋣ʹ
10 𐋮 𐋤 𐋦ʹ
11 [𐋯] 𐋥
12 𐋰 𐋥 𐅵 [𐋣ʹ]
13 𐋱 𐋦 𐅷
14 𐋲 𐋧 𐅵
15 𐋳 𐋨 𐋣ʹ
_Column 2 (÷ 12)_
(top lost: 200–800 ÷ 12)
1 𐋻 [𐋰𐋥]
2 ͵𐋡 𐋱[𐋣 𐋣ʹ]
3 ͵𐋢 [𐋳𐋯𐋦 𐅷]
4 ͵𐋣 𐋴𐋮
5 ͵𐋤 𐋵𐋬𐋣 [𐋣ʹ]
6 ͵𐋥 𐋶𐋪𐋦 [𐅷]
7 ͵𐋦 𐋷
8 ͵𐋧 𐋷𐋱𐋣 [𐋣ʹ]
9 ͵𐋨 𐋸𐋯𐋦 𐅷
10 ͵𐋩 𐋹𐋮
11 𐋡̈ 𐋺𐋬𐋣 [𐋣ʹ]
(Arabic note after column)
القيرطين
_Column 3 (÷ 24)_
(top lost: 1–20 ÷ 24)
1 𐋬 𐋡 [𐋤ʹ]
2 𐋭 𐋡 𐅷
3 𐋮 𐋢 𐋪[𐋢ʹ]
4 𐋯 𐋢 𐅵
5 𐋰 𐋢 𐅵 [𐋣ʹ 𐋪𐋢ʹ]
6 𐋱 𐋣 𐋣ʹ
7 𐋲 𐋣 𐅵 𐋤ʹ
8 𐋳 𐋤 𐋦ʹ
_Column 4 (÷ 24)_
(top lost: 200–2000 ÷ 24)
1 ͵𐋣 𐋳[𐋫𐋥]
2 ͵𐋤 𐋳𐋯𐋦 𐅷
3 ͵𐋥 𐋴𐋨 [𐋣ʹ] (?)
4 ͵𐋦 𐋴𐋮
5 ͵𐋧 𐋴𐋲𐋡 𐅷
6 ͵𐋨 𐋵𐋬𐋣 𐋣ʹ
7 ͵𐋩 𐋵𐋰𐋥
8 𐋡̈ 𐋶𐋪𐋦 𐅷
(Arabic note after column)
صور القيراط
_Column 5 (÷ 48)_
(top lost: 1–10 ÷ 48)
1 𐋫 [𐋤ʹ 𐋦ʹ]
2 𐋬 𐅵 𐋨ʹ
3 𐋭 [𐅵 𐋣ʹ]
4 𐋮 𐋡 [𐋫𐋤ʹ]
5 [𐋯] 𐋡 [𐋤ʹ]
6 𐋰 𐋡 [𐋣ʹ 𐋨ʹ]
7 𐋱 𐋡 𐅷
8 𐋲 𐋡 𐅵 [𐋣ʹ 𐋫𐋤ʹ]
(bottom lost: 100 ÷ 48)
p. 2 (multiplication, 70, 80, and 90)
Column 1_
(top lost: 70 × 1, 2, and 3)
1 [70 × 4 = 2]80
2 [70 × 40] = 2,[8]00
3 70 × 400 = 28,000
4 70 × 4,000 = 280,000
——
5 70 × 5 = 350
6 70 × 50 = 3,500
7 [70] × 500 = 35,000
(bottom lost: 70 × 5000)
_Column 2_
(top lost: 70 × 6, 7, 8)
1 [70 × 9 = 6]30
2 [70] × 90 = 6,300
3 70 × 900 = 63,000
4 70 × 9,000 = 630,000
——
5 70 × 10,000 = 700,000
_Column 3_
(top lost: 80 × 1)
1 [80 × 2 = 1]60
2 [80 × 20] = 1,600
3 [80 × 200] = 16,000
4 [80] × 2,000 = 160,000
——
5 [80 × 3 = 2]40
6 [80 × 30] = 2,400
7 [80] × 300 = 24,000
8 [80 × 3,000] = 240,000
——
9 80 × 4 = 3[2]0
10 80 × 40 = 3,200
11 80 × 400 = 32,000
12 80 × 4,000 = 320,000
——
13 80 × 5 = 400
14 80 × 50 = 4,000
15 80 × 500 = 40,000
16 [80] × 5,000 = 400,000
——
_Column 4_
1 [80 × 600] = 48,000
2 [80 × 6,000] = 480,000
——
3 80 × 7 = 5[6]0
4 80 × 70 = 5,600
5 80 × 700 = 5[6],000
6 80 × 7,000 = 5[6]0,000
——
7 80 × 8 = 640
8 80 × 80 = 6,400
9 80 × 800 = 64,000
10 80 × 8,000 = 640,000
——
11 80 × 9 = 720
12 80 × 90 = 7,200
13 80 × 900 = 72,000
14 80 × 9,000 = 720,000
——
15 80 × 10,000 = 80 (should be 800,000)
——
_Column 5_
1 90 × 100 = [9,000]
2 90 × 1,000 = 90,000
——
3 90 × 2 = 180
4 90 × 20 = 1,800
5 90 × 200 = 18,000
6 90 × 2,000 = 180,000
——
7 90 × 3 = 270
8 90 × 30 = 2,700
9 90 × 300 = 27,000
10 90 × 3,000 = 270,000
——
11 90 × 4 = 360
12 90 × 40 = 3,600
13 90 × 400 = 3[6],000
14 90 × 4,000 = 360,000
——
15 90 × 5 = 450
16 90 × 50 = 4,500
17 90 × 500 = 45,000
18 [90 × 5,000] = 4[5]0,000
p. 3 (division by 12, 24, 48)
_Column 1 (÷ 12)_
(top lost: 1–4 ÷ 12)
1 5 (÷ 12 =) ⅓ 1/12
2 6 (÷ 12 =) ½
3 7 (÷ 12 =) ½ 1/12
4 [8] (÷ 12 =) [⅔]
5 9 (÷ 12 =) ½ ¼
6 10 (÷ 12 =) ½ ⅓
7 20 (÷ 12 =) 1⅔
8 30 (÷ 12 =) 2½
9 40 (÷ 12 =) 3⅓
10 50 (÷ 12 =) 4⅙
11 [60] (÷ 12 =) 5
12 70 (÷ 12 =) 5½ [⅓]
13 80 (÷ 12 =) 6⅔
14 90 (÷ 12 =) 7½
15 100 (÷ 12 =) 8⅓
_Column 2 (÷ 12)_
(top lost: 200–800 ÷ 12)
1 900 (÷ 12 =) [75]
2 1,000 (÷ 12 =) 8[3⅓]
3 2,000 (÷ 12 =) [166⅔]
4 3,000 (÷ 12 =) 250
5 4,000 (÷ 12 =) 333[⅓]
6 5,000 (÷ 12 =) 416[⅔]
7 6,000 (÷ 12 =) 500
8 7,000 (÷ 12 =) 583[⅓]
9 8,000 (÷ 12 =) 666⅔
10 9,000 (÷ 12 =) 750
11 10,000 (÷ 12 =) 833[⅓]
(Arabic note after column)
the two qīrāṭs
_Column 3 (÷ 24)_
(top lost: 1–20 ÷ 24)
1 30 (÷ 24 =) 1[¼]
2 40 (÷ 24 =) 1⅔
3 50 (÷ 24 =) 2 1/1[2]
4 60 (÷ 24 =) 2½
5 70 (÷ 24 =) 2½ [⅓ 1/12]
6 80 (÷ 24 =) 3⅓
7 90 (÷ 24 =) 3½ ¼
8 100 (÷ 24 =) 4⅙
_Column 4 (÷ 24)_
(top lost: 200–2000 ÷ 24)
1 3,000 (÷ 24 =) 1[25]
2 4,000 (÷ 24 =) 166⅔
3 5,000 (÷ 24 =) 208[⅓] (?)
4 6,000 (÷ 24 =) 250
5 7,000 (÷ 24 =) 291⅔
6 8,000 (÷ 24 =) 333⅓
7 9,000 (÷ 24 =) 375
8 10,000 (÷ 24 =) 416⅔
(Arabic note after column)
the figures of the qīrāṭ
_Column 5 (÷ 48)_
(top lost: 1–10 ÷ 48)
1 20 (÷ 48 =) [¼ ⅙]
2 30 (÷ 48 =) ½ ⅛
3 40 (÷ 48 =) [½ ⅓]
4 50 (÷ 48 =) 1 [1/24]
5 [60] (÷ 48 =) 1[¼]
6 70 (÷ 48 =) 1[⅓ ⅛]
7 80 (÷ 48 =) 1⅔
8 90 (÷ 48 =) 1½ [⅓ 1/24]
(bottom lost: 100 ÷ 48)
T-S Ar.39.380 1v
p. 1 (multiplication by 50 and 60)
_Column 1_
(top lost: 50 × 5, 50 × 50)
1 [𐋮 𐋷] 𐋢̈ ͵𐋥
2 [𐋮] ͵𐋥 𐋫̈ 𐋥̈
——
3 [𐋮] 𐋦 𐋵
4 𐋮 𐋯 ͵𐋣
5 𐋮 𐋸 𐋣̈
6 𐋮 ͵𐋦 𐋬̈
——
7 𐋮 𐋧 𐋵𐋮
8 𐋮 𐋰 ͵𐋣𐋷
9 𐋮 𐋹 𐋣̈ [͵𐋥]
10 𐋮 ͵𐋧 𐋬̈ 𐋥̈
——
11 𐋮 𐋨 [𐋶]
12 𐋮 𐋱 ͵𐋤
13 𐋮 𐋺 𐋤̈
14 [𐋮] ͵𐋨 𐋭̈
——
_Column 2_
(top lost: 50 × 9, 50 × 90)
1 𐋮 [𐋻 𐋤̈ ͵𐋥]
2 𐋮 ͵[𐋩] 𐋭̈ [𐋥̈]
——
3 𐋮 𐋡̈ 𐋮̈
——
4 𐋯 𐋡 𐋯
5 𐋯 𐋪 𐋸
6 𐋯 𐋳 ͵𐋦
7 𐋯 ͵𐋡 𐋦̈
——
8 𐋯 𐋢 𐋳𐋫
9 𐋯 𐋫 ͵𐋡𐋴
10 𐋯 𐋴 𐋡̈ ͵𐋢
11 𐋯 ͵𐋢 𐋪̈ 𐋢̈
——
12 𐋯 𐋣 𐋳𐋱
13 𐋯 𐋬 ͵𐋡𐋺
14 𐋯 𐋵 𐋡̈ ͵𐋨
15 𐋯 ͵𐋣 𐋪̈ 𐋨̈
——
_Column 3_
(top lost: 60 × 4, 40, 400, 4000)
1 [𐋯 𐋥 𐋵]
2 𐋯 [𐋮 ͵𐋣]
3 𐋯 [𐋷 𐋣̈]
4 𐋯 [͵𐋥 𐋬̈]
——
5 𐋯 [𐋦] 𐋵[𐋯] (?)
6 𐋯 𐋯 [͵𐋣𐋸]
7 𐋯 𐋸 𐋣̈ [͵𐋦]
8 𐋯 ͵𐋦 𐋬̈ 𐋦̈
——
9 𐋯 𐋧 𐋶[𐋫]
10 𐋯 𐋰 ͵𐋤𐋴
11 𐋯 𐋹 𐋤̈ ͵𐋢
12 𐋯 ͵𐋧 𐋭̈ 𐋢̈
——
(Column 4 not preserved except for Arabic note)
.....
رقعة ابن ...
ازهر
والسلم
p. 4 (division by 48 continued)
_Column 1 (÷ 48)_
(top lost: 200–4000 ÷ 48)
1 ͵𐋥 𐋳𐋤 [𐋦ʹ]
2 ͵𐋦 𐋳𐋫𐋥
3 ͵𐋧 𐋳𐋭𐋥 [𐅵 𐋣ʹ]
4 ͵𐋨 𐋳𐋯𐋦 [𐅷]
5 [͵𐋩 𐋳𐋱𐋧 𐅵]
(bottom lost: 10,000 ÷ 48)
p. 1 (multiplication by 50 and 60)
_Column 1_
(top lost: 50 × 5, 50 × 50)
1 [50 × 500] = 25,000
2 [50] × 5,000 = 250,000
——
3 [50] × 6 = 300
4 50 × 60 = 3,000
5 50 × 600 = 30,000
6 50 × 6,000 = 300,000
——
7 50 × 7 = 350
8 50 × 70 = 3,500
9 50 × 700 = 3[5],000
10 50 × 7,000 = 350,000
——
11 50 × 8 = [400]
12 50 × 80 = 4,000
13 50 × 800 = 40,000
14 [50] × 8,000 = 400,000
——
_Column 2_
(top lost: 50 × 9, 50 × 90)
1 50 × [900 = 45,000]
2 50 × [9,000] = 4[5]0,000
——
3 50 × 10,000 = 500,000
——
4 60 × 1 = 60
5 60 × 10 = 600
6 60 × 100 = 6,000
7 60 × 1,000 = 60,000
——
8 60 × 2 = 120
9 60 × 20 = 1,200
10 60 × 200 = 12,000
11 60 × 2,000 = 120,000
——
12 60 × 3 = 180
13 60 × 30 = 1,800
14 60 × 300 = 18,000
15 60 × 3,000 = 180,000
——
_Column 3_
(top lost: 60 × 4, 40, 400, 4000)
1 [60 × 5 = 300]
2 60 × [50 = 3,000]
3 60 × [500 = 30,000]
4 60 × [5,000 = 300,000]
——
5 60 × [6] = 3[6]0 (?)
6 60 × 60 = [3,600]
7 60 × 600 = 3[6],000
8 60 × 6,000 = 360,000
——
9 60 × 7 = 4[2]0
10 60 × 70 = 4,200
11 60 × 700 = 42,000
12 60 × 7,000 = 420,000
——
(Column 4 not preserved except for Arabic note)
.....
Note of Ibn ...
Azhar
Farewell
p. 4 (division by 48 continued)
_Column 1 (÷ 48)_
(top lost: 200–4000 ÷ 48)
1 5,000 (÷ 48 =) 104[⅙]
2 6,000 (÷ 48 =) 125
3 7,000 (÷ 48 =) 145[½ ⅓]
4 8,000 (÷ 48 =) 166[⅔]
5 [9,000] (÷ 48 =) [187½]
(bottom lost: 10,000 ÷ 48)