רשומה קשורה ל-רשימה או טבלה: T-S Ar.39.380
רשימה או טבלה T-S Ar.39.380- ציטוט
- Jacques Sesiano, "Koptisches Zahlensystem und (griechisch-)koptische Multiplikationstafeln nach einem arabischen Bericht," Centaurus 32 (n.p., 1989).
- Relation to document
- דיון
- ציטוט
- 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
- דיון
- ציטוט
- 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 by 70, 80, and 90)
(Column 1)
(top lost: 70 × 1, 2, and 3, 12 lines)
1 [𐋰 𐋤 𐋴]𐋱
2 [𐋰] 𐋭 ͵𐋢[𐋺]
3 𐋰 𐋶 𐋢̈ ͵𐋨
4 𐋰 ͵𐋤 𐋫̈ 𐋨̈
————————
5 𐋰 𐋥 𐋵[𐋮]
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 𐋵𐋫
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)
(top lost: missing 80 × 6 and 80 × 60)
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)
(top lost: missing 90 × 1 and 90 × 10)
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: division by 12)
(top lost: 1, 2, 3, and 4 ÷ 12)
1 𐋥 𐋣ʹ 𐋪[𐋢ʹ]
2 𐋦 ⳽
3 𐋧 ⳽ [𐋪𐋢ʹ]
4 [𐋨 𐅷]
5 𐋩 ⳽ 𐋤ʹ
6 𐋪 ⳽ 𐋣ʹ
7 𐋫 𐋡 𐅷
8 𐋬 𐋢 ⳽
9 𐋭 𐋣 𐋣ʹ
10 𐋮 𐋤 𐋦ʹ
11 𐋯 𐋥
12 𐋰 𐋥 ⳽ 𐋣ʹ
13 𐋱 𐋦 𐅷
14 𐋲 𐋧 ⳽
15 𐋳 𐋨 𐋣ʹ
(Column 2: division by 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 𐋶𐋪𐋦𐅷
7 ͵𐋦 𐋷
8 ͵𐋧 𐋷𐋱𐋣 𐋣ʹ
9 ͵𐋨 𐋸𐋯𐋦𐅷
10 ͵𐋩 𐋹𐋮
11 𐋡̈ 𐋺𐋬𐋣 𐋣ʹ
————————
(Arabic note after column) بحسب القيرطين
(Column 3: division by 24)
(top lost: 1–20 ÷ 24)
1 𐋬 𐋡 [𐋤ʹ]
2 𐋭 𐋡 𐅷
3 𐋮 𐋢 𐋪𐋢ʹ
4 𐋯 𐋢 ⳽
5 𐋰 𐋢 ⳽ 𐋣ʹ 𐋪𐋢ʹ
6 𐋱 𐋣 𐋣ʹ
7 𐋲 𐋣 ⳽ 𐋤ʹ
8 𐋳 𐋤 𐋦ʹ
(Column 4: division by 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)
بحسب صور القيراط
(Column 5: division by 48)
(top lost: 1–10 ÷ 48)
1 𐋫 [𐋤ʹ 𐋦ʹ]
2 𐋬 ⳽ [𐋨ʹ]
3 𐋭 [⳽] 𐋣ʹ
4 𐋮 𐋡 𐋫𐋤ʹ
5 𐋯 𐋡 𐋤ʹ
6 𐋰 𐋡 𐋣ʹ 𐋨ʹ
7 𐋱 𐋡 𐅷
8 𐋲 𐋡 ⳽ [𐋣ʹ 𐋫𐋤ʹ]
(bottom lost: 100 ÷ 48)
p. 2 (multiplication by 70, 80, and 90)
(Column 1)
(top lost: 70 × 1, 2, and 3, 12 lines)
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 = 3[50]
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 = 320
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)
(top lost: missing 80 × 6 and 80 × 60)
1 [80 × 600] = 48,000
2 [80 × 6,000] = 480,000
————————
3 80 × 7 = 5[60]
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)
(top lost: missing 90 × 1 and 90 × 10)
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: division by 12)
(top lost: 1, 2, 3, and 4 ÷ 12)
1 5 (÷ 12) = ⅓ [1/]1[2]
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: division by 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) = 333⅓
6 5,000 (÷ 12) = 416⅔
7 6,000 (÷ 12) = 500
8 7,000 (÷ 12) = 583⅓
9 8,000 (÷ 12) = 666⅔
10 9,000 (÷ 12) = 750
11 10,000 (÷ 12) = 833⅓
(Arabic note after column:) according to the two qīrāṭs
(Column 3: division by 24)
(top lost: 1–20 ÷ 24)
1 30 (÷ 24) = 1[¼]
2 40 (÷ 24) = 1⅔
3 50 (÷ 24) = 2 1/12
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: division by 24)
(top lost: 200–2000 ÷ 24)
1 3,000 (÷ 24) = 1[25]
2 4,000 (÷ 24) = 166⅔
3 5,000 (÷ 24) = 208⅓
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:) according to the figures of the qīrāṭ
(Column 5: division by 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) = 1¼
6 70 (÷ 48) = 1⅓ 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 [𐋵𐋯]
6 𐋯 𐋯 [͵𐋣𐋸]
7 𐋯 𐋸 𐋣̈ [͵𐋦]
8 𐋯 ͵𐋦 𐋬̈ 𐋦̈
————————
9 𐋯 𐋧 𐋶𐋫
10 𐋯 𐋰 ͵𐋤𐋴
11 𐋯 𐋹 𐋤̈ ͵𐋢
12 𐋯 ͵𐋧 𐋭̈ 𐋢̈
————————
(Column 4 not preserved except for Arabic note; missing are 60 × 8, 80, 800, 8,000 = 4 lines, 60 × 9, 90, 900, 9,000 = 4 lines, and 60 × 10,000 = 1 line, likely with horizontal lines between groups)
نجم الزججية
رقعة ابن ابو شمعون (سمعون؟)
بن ازهر (ابرهيم؟)
والسلم
p. 4 (division by 48 continued)
(Column 1: division by 48)
(top lost: 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000 ÷ 48)
1 ͵𐋥 𐋳𐋤 𐋦ʹ
2 ͵𐋦 𐋳𐋫𐋥
3 ͵𐋧 𐋳𐋭𐋥 ⳽ 𐋣ʹ
4 ͵𐋨 𐋳𐋯𐋦 𐅷
5 [͵𐋩 𐋳]𐋱𐋧 ⳽
6 [𐋡̈ 𐋴𐋨] 𐋣ʹ
––––––––
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 = [360]
6 60 × 60 = [3,600]
7 60 × 600 = 3[6],000
8 60 × 6,000 = 360,000
————————
9 60 × 7 = 420
10 60 × 70 = 4,200
11 60 × 700 = 42,000
12 60 × 7,000 = 420,000
————————
(Column 4 not preserved except for Arabic note; missing are 60 × 8, 80, 800, 8,000 = 4 lines, 60 × 9, 90, 900, 9,000 = 4 lines, and 60 × 10,000 = 1 line, likely with horizontal lines between groups)
. . . .
Installment of the glassmaking (facility)
Note (or: order of payment) of Ibn Abū Shamʿūn (Samʿūn?)
ibn Azhar (Ibrāhīm?).
Farewell.
p. 4 (division by 48 continued)
(Column 1: division by 48)
(top lost: 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 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]
6 [10,000] (÷ 48) = [208]⅓
