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Abbreviations and Bibliography

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AHw: Wolfram von Soden. Akkadisches Handworterbuch. Wiesbaden: Otto Harrassowitz. 1965-1981.

al-Rawi. Farouk N. H .• and Michael Roaf. 1984. "Ten Old Babylonian Mathematical Problem Texts from Tell Haddad. Himrin". Sumer 43 (1984. printed 1987). 195-218.

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Amiet. Pierre. 1979. "Archaeological Discontinuity and Ethnic Duality in Elam". Antiquity 53. 195-204. pI. xx-xxi.

Arrighi. Gino (ed.). 1970. Piero della Francesca. Trattato d·abaco. Dal codice ashbumhamiano 280 (359*-291 *) della Biblioteca Medicea Laurenziana di Firenze. A cura e con introduzione di Gino Arrighi. (Testimonianze di storia della scienza. 6). Pisa: Domus Galileana.

Arrighi. Gino (ed.). 1973. Libro d·abaco. Dal Codice 1754 (sec. XIV) della Biblioteca Statale di Lucca. Lucca: Cassa di Risparmio di Lucca.

Arrighi. Gino (ed.). 1987. Paolo Gherardi. Opera mathematica: Libro di ragioniLiber habaci. Codici Magliabechiani Classe XI. nn. 87 e 88 (sec. XIV) della Biblioteca Nazionale di Firenze. Lucca: Pacini-Fazzi.

Artmann. Benno. 1990. "Mathematical Motifs on Greek Coins". Mathematical Intelligencer 12:4. 43-51.

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Abbreviations and Bibliography 419

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Index of Tablets

A 24194. Published in [MCT 107-112, PI 15]. 349 nA13, 350

A 24195. Published in [MCT 119-122, PI 16]. 349 nA13, 351 nA14

AO 6484. Published in [MKT I 96-99, III 53]. 2, 132, 389, 390, 392 nA85, 397 nA88, 405

AO 6770. Published in [MKT II 37/; cf. III 62ff]. 20, 125 n.147, 179-182,209,225,307,337, 341-343, 351, 366, 372, 387

AO 8862. Published in [MKT I 108-113, II Taf. 35-38; III 53]. 20, 30 n.52, 31, 37, 38, 125 n.147, 134, 162-174, 178, 179 n.204, 180, 181, 216 n.243, 217 n.244, 221, 225, 249, 259, 278, 287,289 n.330, 292, 301, 307, 328, 336 n.393, 337, 338, 338 n.395, 340-345, 347, 348, 372, 378, 381, 387, 407

AO 10822. Published in [MKT I 123f, III 53]. much improved in [Friberg 2001: 90/]. 350

AO 17264. Published in [MKT I 126/]. 347 nA09, 387

BM 13901. Published in [ThureauDangin 1936a]. 11 n.15, 13, 17 n.25, 50-55, 57-60, 66-77, 70 n.95, 99-103, 108-111, 125 n.149, 132-136, 156, 161, 163, 172, 191, 193, 198, 199, 216, 221, 222-226, 241 n.266, 250, 251 n.279, 252, 253 n.284, 257, 267, 269, 280, 284, 286 n.323, 288, 290, 290 n.331, 292, 294, 295, 298 n.340, 302-306, 324 n.371, 330 n.379, 339, 343,

346, 348, 349, 351, 351 nA14, 354, 355, 356, 358, 368, 373, 374, 376, 380-383, 387, 413

BM 15285. Published in [MKT I 137]; with an additional fragment in [Saggs 1960]; with yet another in [Robson 1999: 208-217]. 2, 25 n.39, 40, 59-60, 69 n.94, 89 n.119, 105, 252, 262, 304-307, 330 n.379, 357

BM 34568. Published in [MKT III 14-17].22,389-399,405,406, 408-410

BM 80209. Published in [Friberg 1981a]. 225, 287, 304, 305, 330 n.381, 350, 371, 372

BM 85194. Published in [MKT I 143-151; cf. III 53].2,30,36, 76 n.102, 156 n.187, 217-222, 233, 272-275, 281, 286, 307, 318,329-331, 329 n.378, 330 n.381, n.382, 350, 385, 386

BM 85196. Published in [MKT II 43-46]. 223, 275, 276, 300, 301, 307, 318, 329, 330, 330 n.381, 331, 331 n.382, 334 n.388, 349, 350, 382 nA71, 385, 386

BM 85200+VAT 6599. Published in [MKT I 193ff, II PI 7-8 (photo), PI 39-40 (hand copy)]. 20, 35, 50 n.75, 66, 137, 145-166, 173-175, 173 n.199, 175 n.199, 193,260,267 n.305, 269, 283 n.320, 286, 295, 300-303, 305, 318, 320, 324, 329-331, 330 n.379, n.381, 331 n.382, 347, 348 nAIl, 349, 381

BM 85210. Published in [MKT I 219-223, III 55]. 2, 30, 50 n.75, 261 n.295, 318, 329-441, 330 n.379, n.381, 331 n.382, 343, 357

BM 96957. See also VAT 6598. 28 n.48, 88, 268 n.306, 385

CBM 12648. Published in [MKT I 2341], much improved in [Friberg 2001: 149].344,354 n.419, 360 n.429, 377 n.463

CBS 43. Published in [Robson 2000: 39]. 253 n.284, 354, 355, 383 n.472

CBS 154+921. Published in [Robson 2000: 40]. 354, 355

CBS 165. Published in [Robson 2000: 43]. 354, 355

CBS 11681. Published in [Robson 2000: 32/]. 344, 354, 355

CBS 19761. Published in [Robson 2000: 36/]. 28 n.47, 35 n.59, 224, 354, 355

Dbz-146. Published in [Baqir 1962]. 70 n.95, 155 n.185, 224 n.249, 257-261,319 n.361, 322-324, 332, 341, 344, 352, 385-387, 406

Haddad 104. Published in [AlRawi and Roaf 1984]. 28, 32 n.55, 322, 323, 325, 332, 334, 376 n.462, 378

1M 43993. Preliminary publication in [Friberg and al-Rawi 1994a]. 85 n.111, 322-324, 322 n.368, 338, 343, 372

1M 52301. Published in [Baqir 19S0a]. 27 n.45, 156 n.187, 213-217,230,231,248,257, 259, 260, 283 n.320, 322-325, 336 n.393, 344

1M 52916+52685+52304. Published in [Goetze 1951]. 216 n.243, 239 n.264, 286, 322-324, 328, 336 n.393, 338, 339, 349, 354, 358, 376, 381

Index of Tablets 429

1M 53953. Published in [Baqir 1951: 31]. 319 n.361

1M 53957. Published in [Baqir 1951: 37]. 319 n.361, 321, 341 n.399, 366, 382, 387, 405


1M 53965. Published in [Baqir 1951: 39]. 155 n.185, 319 n.361, 320, 341 n.400, 351


1M 54011. Published in [Baqir 1951: 45].319 n.361. n.362, 320, 320 n.365, 324

1M 54464. Published in [Baqir 1951: 43]. 319 n.361, n.362, n.363, 320, 322, 333

1M 54478. Published in [Baqir 1951: 30]. 319 n.361, 320, 331 n.382

1M 54538. Published in [Baqir 1951: 33]. 319 n.361, 320 n.365

1M 54559. Published in [Baqir 1951: 41]. 155 n.185, 319 n.361, n.363, 320, 323 n.369

1M 55357. Published in [Baqir 1950]. 231-234, 257, 266 n.303, 274, 322-325, 326 n.374, 332, 334 n.388, 343, 350, 351, 353, 357, 357 n.424, 376, 377

1M 58045. Published in [Friberg 1990: 541 = §4.4]. 237

1M 121613. Preliminary publication in [Friberg and al-Rawi 1994a]. 322-324, 338, 372

1st S 428. Published in [MKT I 80/]. 347 n.409

M 10, John F. Lewis Collection, Free Libr. Philadelphia. Published in [Sachs 1952: 152]. 29 n.50, 297 n.339

MIO 1107. Published in [ThureauDangin 1897: 13, 15]. 104, 103

430 Index of Tablets

MLC 1354. Published in [MCT 56/, PI 21]. 329-332

MLC 1842. Published in [MCT 106, PI 22]. 206 n.234, 286, 323 n.369, 332

MLC 1950. Published in [MeT 48, PI 2]. 329 n.377, 331, 332, 335, 337

NBC 7934. Published in [MeT 55, PI 2]. 27, 350

Plimpton 322. Published in [MeT 38, PI 2 (A)]. 337, 386

Str 362. Published in [MKT I 239/; cf. III 56]; hand copy [Frank 1928: #6 = pi iv-v]. 209, 335-337, 351

Str 363. Published in [MKT I 244f]; hand copy [Frank 1928: #7 = pi v-vi]. 76 n.102, 77, 136, 252, 330 n.379, 335, 336, 343

Str 364. Published in [MKT I 248-250], hand copy [Frank 1928: #8 = PI vi]. 335, 337, 341 n.400, 351

Str 366. Published in [MKT I 257, III 56], hand copy [Frank 1928: #9 = pi vii]. 31 n.53, 335, 336

Str 367. Published in [MKT I 259/], hand copy [Frank 1928: #10 = pi viii]. 28 n.47, 30, 31, 213, 239-244, 283 n.320, 284, 285, 335, 337, 377

Str 368. Published in [MKT I 311], hand copy [Frank 1928: #11 = pi ix]. 22, 37, 335-337, 341 n.400, 351

TMS I. Published in [TMS 22/, PI 1]. 105, 265-268, 274, 307, 385, 386, 399

TMS II. Published in [TMS 23/, PI 2-3]. 105, 382

TMS III. Published in [TMS 25-27, PI 4-5]. 188 n.211, 239 n.263, 262, 386

TMS V. Published in [TMS 35-49, PI 7-10]. 16 n.20, 20, 69 n.94, 125 n.149, 189 n.212, 216 n.243, 221, 286 n.323, 290 n.331, 293, 301, 303-306, 336 n.393, 349, 354, 358

TMS VI. Published in [TMS 49-51, PI 11-13]. 189 n.212, 339, 354, 358

TMS VII. Published in [TMS 52-55, PI 14-15].85, 181, 185-188, 256 n.288, 288 n.328, 289 n.330, 293, 326, 343 n.402, 384, 407

TMS VIII. Published in [TMS 58, PI 16].60, 101, 182, 188-193, 289 n.330

TMS IX. Published in [TMS 63/, PI 17]. 37, 85, 85 n.112, 89-96, 100,103,163,171,172,181, 182 n.207, 203, 205, 206, 221, 221 n.247, 289 n.330, 291, 292, 339, 343, 372, 379, 383

TMS XII. Published in [TMS 78j. PI 21]. 15 n.19, 88, 294, 335 n.391

TMS XIII. Published in [TMS 82, PI 22]. 9, 206-208, 244 n.271, 280, 281, 286, 323 n.369, 381

TMS XVI. Published in [TMS 9lj, PI 25]. 33, 35 n.60, 59 n.83, 60,85-89,89 n.117, 94,101, 102, 134, 150 n.176, 161, 181, 182, 206, 241 n.266, 289 n.330, 291, 296, 343

TMS XVII. Published in [TMS 95, PI 26]. 101, 216 n.243, 336 n.393

TMS XIX. Published in [TMS 101, PI 28/]. 194-200, 205, 280, 381,385

TMS XX. Published in [TMS 101-103, PI 30]. 351

TMS XXv. Published in [TMS 122j. PI 37/]. 351

TMS XXVI. Published in [TMS 124f. PI 39]. 326, 328, 330 n.381

VET V, 121. Published in [Vajman 1961: 248]; ct. [Friberg 2000: 35/].353

VET V, 858. Published in [Vajman 1961: 251]; ct. [Friberg 2000: 38f]. 285 n.322, 344 nA04, 352 nA15, 353, 402 nA90

VET V, 859. Published in [Vajman 1961: 254f]; ct. [Muroi 1998: 20lj] and [Friberg 2000: 39]. 26 nA2, 27 nA4, 36 n.64, 253, 326 n.374, 343, 352, 354, 376

VET V, 864. Published in [Vajman 1961: 257f]; cf. [Kilmer 1964], [Muroi 1998: 200] and [Friberg 2000: 37]. 26 nA2, 27 nA4, 69 n.94, 125 n.149, 224, 225 n.250, 250-253, 304, 325, 350, 352, 354, 388, 401

VAT 672. Published in [MKT I 267, II Taf 43].

VAT 7531. Published in [MKT I 289f, II Taf 46; III 58].

VAT 7532. Published in [MKT I 294f. II Taf 46; III 58].

VAT 7535. Published in [MKT I 303-305, II Taf 47].

VAT 672. Published in [MKT I 267, II Taf 43]. 331 n.383

VAT 6469. Published in [MKT I 269, II Taf 43]. 331 n.383

VAT 6505. Published in [MKT I 270f, II Taf 43; III 56f]. 331 n.383

VAT 6546. Published in [MKT I 269, II Taf 43].301,331 n.383

VAT 6597. Published in [MKT I 274f. II Taf 43, 45]. 159 n.189, 323 n.369, 329, 330, 330 n.380, n.381

VAT 6598. Published in [MKT I 278-280, II Taf 44]; new publication including BM 96957 in


[Robson 1999: 231-244], brick problem section of the latter tablet in [Robson 1996]. 268-272, 300, 318, 329, 330, 330 n.380, n.381, 331 n.382, 332, 334 n.388, 350, 385, 386

VAT 6599. See BM 85200+VAT 6599.

VAT 7528. Published in [MKT I 508-511, II Taf 45]. 3':::9 nAB, 350

VAT 7530. Published in [MKT I 287f, II Taf 46; III 57f]. 335, 337

VAT 7531. Published in [MKT I 289f, II Taf 46; III 58]. 335, 337

VAT 7532. Published in [MKT I 294f. II Taf 46; III 58]. 16, 20, 30, 31 n.53, 36, 59, 59 n.84, 60,64,76 n.102, 209-213, 215, 243 n.268, 280, 281, 285, 286, 318,335,335 n.391, 336, 337, 382 nA71

VAT 7535. Published in [MKT I 303-305, II Taf 47]. 30, 31 n.53, 37, 212, 318, 335-337, 335 n.391, 341 nAOO, 351

VAT 7537. Published in [MKT I 466-469, II Taf 48]. 293, 294, 349 nAB, 350

VAT 7620. Published in [MKT I 314f. II Taf 48]. 335

VAT 7621. Published in [MKT I 291, II Taf 48; III 58]. 335, 337

VAT 7848. Published in [MeT 141, PI 20]. 389, 390

VAT 8389. Published in [MKT I 317-319, II Taf 49; III 58]. 18, 37,77-82,103,173,234,284, 333, 334, 334 n.389, 335, 338 n.395,358

432 Index of Tablets

VAT 8390. Published in [MKT I 335j, II Taf 501.61-64, 125 n.147, 134, 193,216 n.243, 288 n.328, 333-336, 343

VAT 8391. Published in [MKT I 319-323, II Taf 51; III 581. 37, 82-85, 103, 238, 284, 333-335, 338 n.395, 348 nA12

VAT 8512. Published in [MKT I 34lj, II Taf 521. 105, 234-238, 243, 245, 247, 248, 333-335, 340 n.398

VAT 8520. Published in [MKT I 346j, II Taf 531. 19, 182 n.207, 333-335

VAT 8521. Published in [MKT I 351-353, 380, II Taf 54; III 58/1. 146 n.169, 333-335, 333 n.386, 335 n.390

VAT 8522. Published in [MKT I 368j, II Taf 55; III 611. 159 n.189, 323 n.369, 333, 334, 334 n.387,335

VAT 8523. Published in [MKT I 373-375, II Taf 55+56; III 611. 333-335

VAT 8528. Published in [MKT I 353-355, 380, II Taf 56+57; III 59/1. 333, 333 n.386, 335, 335 n.390, 348 nA12

W 23273. Published in [von Weiher 1993 #1721. 316 n.354, 388

W 23291. Published in [Friberg 19971. 388, 390, 392 nA85, 410 nA99

W 23291-x. Published in [Friberg, Hunger, and al-Rawi 1990al. [388, 389, 4101.

YBC 4186. Published in [MCT 91, Pill]. 333-335

YBC 4607. Published in [MCT 9lj, PI 121.27,305,346,349,350

YBC 4608. Published in [MCT 49ff, PI 3, PI 28]. 20, 125 n.147, 159 n.189, 216 n.243, 323 n.369, 335-337, 336 n.394,

351,359 nA26 YBC 4612. Published in [MCT

103j, PI 141. 305 n.343, 343 nA01, 346 nA07, 349, 378

YBC 4652. Published in [MCT 100f, PI 131. 305, 327, 346, 349, 357 nA23

YBC 4657. Published in [MCT 66j, PI 61. 286, 305, 346, 346 nA06, 349

YBC 4662. Published in [MCT 71f, PI 81. 155 n.185, 301, 305, 329, 340 n.398, 344-350, 346 nA06

YBC 4663. Published in [MCT 69, PI 71. 301, 305,340 n.398, 345, 346, 346 nA06, 347

YBC 4666. Published in [MCT 76f, PI 91. 305, 345, 346, 346 nA07, 349

YBC 4668+4713+4712. Published in [MKT I 422-435, III 6lj, Taf 21.35, 101, 132 n.154, 136, 200-206, 200 n.231, 208 n.236, 244, 287, 289 n.330, 302,303,349 nAB, 350, 351, 351 nA14, 372

YBC 4669. Published in [MKT I 514, III 27j, Taf 31. 321 n.367, 338 n.395, 349 nAB, 350, 357, 377

YBC 4673. Published in [MKT I 507f, II 508, III 29-31, Taf 31. 338 n.395, 349 nAB, 350, 351, 357, 377

YBC 4675. Published in [MCT 44(, PI 1 (B)l. 24 n.36, 105,231, 238 n.261, 239 n.263, 244-249, 277,337,340 n.398, 341, 342

YBC 4695. Published in [MKT III 34-36, Taf 4]. 349 nAB, 350, 351 nA14

YBC 4697. Published in [MKT 1 485f, II 40/, III Taf 51. 350, 351

YBC 4698. Published in [MKT III 42f. Taf 5]. 286, 349 n.413, 351

YBC 4708. Published in [MKT I 389-394, II Taf 57; III 61]. 349 n.413,350

YBC 4709. Published in [MKT I 412-414, II Taf 58].343,351

YBC 471 O. Published in [MKT I 402-404, II Taf 58; III 61]. 295 n.337, 350, 351

YBC 4711. Published in [MKT I 503, III 45]. 351

YBC 4712. See YBC 4668+4712+ 4713. Hand copy in [MKT II Taf. 59].

YBC 4713. See YBC 4668+4712+ 4713. Hand copy in [MKT II Taf 59].

YBC 4714. Published in [MKT I 487-492, II Taf 60]. 16 n.20, 20, 80 n.106, 111, 115-141, 163, 200, 216 n.243, 223, 224, 286 n.323, 289 n.330, 290, 292, 295 n.336, n.337, 298, 302-305, 330 n.379, 383

YBC 4715. Published in [MKT I 478-480, II Taf 60]. 181, 350

YBC 5022. Published in [MCT 132, PI 18]. 337

YBC 5037. Published in [MCT 59f, PI 5]. 305, 346, 349, 350

YBC 6295. Published in [MCT 42, PI 22]. 65, 66, 111, 149, 154, 333, 334, 335 n.390, 335

YBC 6504. Published in [MKT III 22f, Taf 6]. 25 n.39, 31 n.53, 39 n.70, 50 n.75, 70 n.95, 135, 174-179,221,330 n.379, 331 n.382, 337, 342, 343, 345, 348, 351, 353, 356, 357, 374, 376, 387

YBC 6967. Published in [MCT 129, PI 17]. 34, 35, 55-58, 159 n.191, 281, 332, 347,401

YBC 7164. Published in [MCT 81/,


PI 10]. 305, 345, 346, 346 n.407,349

YBC 7243. Published in [MCT 132, PI 23]. 261, 337

YBC 7289. Published in [MCT 42f]. 261-265, 269, 272, 385


YBC 8588. Published in [MCT 75, PI 21]. 333-335

YBC 8600. Published in [MCT 57, PI 21]. 333-335

YBC 8633. Published in [MCT 53, PI 4]. 37, 66, 85, 103, 254-257, 333-335, 384-387

YBC 9852. Published in [MCT 45, PI 1]. 244 n.272, 337


YBC 9874. Published in [MCT 90, Pill]. 337, 342


YBC 10529. Published in [MCT 16]. 29 n.50, 297 n.339

YBC 10772. Published in [MCT 98, PI 4]. 338 n.395

Index of Akkadian and Sumerian Terms and Key Phrases

Only discussions of terms and phrases are indexed, not their appearance in the texts; metrological units are indexed only where they are discussed or referred to as such, not when they merely serve as units. In cases where a declinated form or a whole phrase is listed separately (e.g., tammar, "you see", atta ina epesika, "you, by you procedure"), a cross-reference is given under the relevant lexical form or forms (in case amiirum, "to see", and epesum, "proceed"/"proceeding"), unless the two are immediate neighbours.

a.na 326 n.374, 343, 377 a.na us ugu sag dirig 351 a.na.am 26 n.42, 326 n.374, 352, 352 n.415, 353, 361 a.ra 21,21 n.33, 22, 163, 180,

182, 215 n.242, 248, 327, 328, 331,331 n.384, 339, 344, 347, 350, 353, 375, 388, 389, 391

a.ra.kara 248 a.sa 5 n.7, 34--36, 36 n.64, 224,

298 n.340, 300, 328, 336, 375 n.459,376

a.sa SU.BA.AN.TU 216 n.243 a.sa.ga 36 n.64 abo 251 n.280 adi sinisu 348 aliikum 22, 23, 182, 327, 331

n.384, 357, 357 n.423 .am 326 n.374, 352, 360 n.428 amiirum 28, 40, 336 n.394, 359

n.426 See also tammar

ammatum 389 an.na 376 apin 5 n.7 arakarUm 248 aramaniiitum 215 n.242, 248 arUm 180, 182

as as 180, 375 aSsum 38, 319, 323, 327, 328, 330

n.381, 334, 336, 336 n.394, 376, 389 n.479

aUa 332, 334, 335 aUa ina epesika 319, 332, 338, 341 BA (for biimtum) 31 n.53 ba 31 n.53 ba 31 n.53, 74 n.100, 332 ba. 27 n.44 ba.a 31 n.53 ba.se.e 27 n.45, 213, 376 ba.si 27,335,335 n.390 ba.si l-lal 146 n.169, 335 n.390 ba.si s 27,66, 182,253,323,332,

353, 355, 361, 375, 375 n.460, 376

ba.sis.e 26 n.42, 27 n.44 ba.zi 355,356 bal 150, 330 n.379 biimtum 12, 31, 31 n.53, 32, 163,

179,320,324,331,332,336. 340-342. 345. 348. 361. 377

ban 208 n.235 bandum 74 n.100 banum 125 n.147. 134. 248. 336 bar 262. 262 n.296 basum 27. 39 n.69. 182. 216

Index of Akkadian and Sumerian Terms and Key Phrases 435

n.243, 336 n.393, 376 berum 21 n.29, 407 .bi 378 bi. 27 n.44 bur 17, 17 n.22, 36, 78, 81, 209,

284 burtum 36 .da 74 n.100 da 74 n.100 dab 19, 27 n.44, 139 n.158, 328,

343,347,355 n.421, 389 dakasum 250, 252, 253 n.283, 352,

356 See also dikistum

dal 239, 239 n.263, 272, 304 dikistum 253, 352, 356 dirig 21,88, 179, 188,294,343,

343 n.402, 351 du 32 n.55 du 7.du 7 24, 25 n.39, 177 n.200,

177 n.201, 336, 343, 345 dus 28, 28 n.47, 30, 251 n.280,

347 .e 52,66, 111 edum 335, 337, 341. 351 elum 22,28 n.47, 40, 199,319,

319 n.363, 332, 342, 377, 389 EN (en.nam) 350 en.nam 26 n.42, 26 n.43, 39, 146

n.169, 326, 326 n.374, 329, 331, 334-336, 343, 346, 347, 352, 355, 356, 361, 376

engar ·5 n.7 epesum 32 n.55, 248, 343

See also alta ina epesika eqlum 5 n.7, 35, 77 n.105, 224,

376 esepum 23, 331, 336, 391 ese 17 n.22 ezebum 334, 336, 337, 350 ga.ga 323 n.370, 375, 376 gaba 234, 327 gagar 36 n.64 gal 28 GAM (depth) 36, 139 n.158 GAM (for a.ra) 391

gam 139 n.158 GAN 180,375 GANA 248 gar 26 n.42, 39, 39 n.70, 88, 327,

332, 333, 336, 345, 375 See also IN.gar.

gar.gar 19,323 n.370, 328, 331, 334, 347, 375, 389

garim 77 n.105 gaz 31 gi 209, 225, 382, 388 gi.na 36,89 gin 305 n.344 gin 7.nam 377 gis 5 n.7 giSapin 5 n.7 gu.la 252 gU 7 23 n.35, 23, 24 n.36, 344 gu 7.gu 7 24 gub 89 n.119 GUS 89 n.119 gur 78, 208 n.235 gur 139 n.158 fJarasum 20, 163, 301, 320, 323,

325. 325 n.372, 328, 330, 332, 339-342, 345, 347, 348, 351, 355, 361. 377

fJasabum 351, 377 be.ib.si s 253 fJepum 13, 31, 320, 334, 343, 347 .bi.a 92 n.124 tlI.A 92 n.124, n.126 fJulum 88 i.gi 213 I.gu7 245 n.274 i.gu 7 24,245 n.274, 248, 331

n.382 i.gu 7.gu 7 23,24,331 n.382, 345,

361. 377 ib.sa 27 n.45 ib.se.e 320, 325 ib.si 27,320,325,327,328,353,

376 ib.si s 12,25, 25 n.39, 25, 26,26

n.43, 27, 28 n.47, 31 n.53, 35, 61,111,146 n.169, 177 n.201,

436 Index of Akkadian and Sumerian Terms and Key Phrases

179, 216 n.243, 224, 261, 261 n.295, 320, 323, 325, 327, 328, 330, 330 n.379, 331. 332, 335, 335 n.390, 336, 337, 341-343, 345, 347 n.409, 347, 348, 354, 356,357,357 n.424, 361, 375, 375 n.460, 376, 377

ib.si s x e11.de 360 n.429 ib.tag 4· 334 n.388, 350, 353, 357 id 239 n.264 igi 28-31,28 n.47, n.48, 30 n.52,

35, 143 n.165, 182, 340, 347, 376, 389 See also i.gi

igi n 28, 30 igi ... gal 29 igi n gal 28 n.46, 28, 30, 340,

375 igi n gal.bi 28 igi.bi 182,376 igi.du 326,377 igi.dus 326,350,357,377 igi.gub 18,30,228,239 n.263,

257,261,261 n.295, 262, 272, 291. 337, 338 n.395, 341, 386, 389, 390 n.481

igi.te.en 200 igi.te.en sa us sag.se 208 n.236 igibum 30 n.5l, 35, 55, 57, 138,

158-160, 159 n.191, 162, 182, 281, 299, 302, 305, 376, 381, 390

igigubbum 389 igitenum 200 igum 30 n.51, 35, 55, 57, 138,

158-160, 159 n.191, 162, 182, 281, 299, 302, 305, 376, 381, 389-391

IKU 375 iku 17 n.22, 180 il 2~ 333, 336, 389 IM.SU 132 n.153 imta!JIJar 224, 225, 253 n.284, 330

n.379, 331, 334, 355 IN.gar 343, 353 inanna 38, 159 n.189, 338

fnum 28 inuma 38,319,323,328,330

n.381,376 itamlJurum 25 n.38 itti 6, 195 n.220 KA+GAR 328 KAK 34 n.58 kalakkum 36 kamiirum 12, 19,21, 163, 298

n.340, 323 n.370, 327, 328, 334, 350, 375, 383 n.472 See also kimirtum,

kimriitum, kumurrCtm kara 248 kasiirum 66

See also maksarum KAS 4 KI 36, 36 n.63, 137 ki 89 n.119, 195 n.220 kr 39 kf masi 39, 320, 323, 323 n.369,

326, 326 n.374, 327, 329, 334, 335, 338, 341, 342, 345, 346, 347, 355 361. 377

ki.du.du 89 n.119 ki.gub.gub 89 n.119, 383 KI.GUB.GUB 89 n.119 ki.la 36,345,346 ki.ta 376 kiam 327, 330, 346 kibsum 330 kid, see za.e lid.da.zu.de etc. kidudum 89 n.119 kima 39, 60, 64, 89, 101, 180, 293,

377 kimirtum 163 kimriitum 20, 163, 338, 340 kznum 36, 257 n.290 kiyii 39, 159 n.189, 253 n.284,

323, 323 n.369, 330 n.380, 334, 335, 355, 377

k6 23 n.35 kud 325 n.372, 328, 351, 377 kullum 6 n.9, 23, 40, 80 n.106, 88

See also reska likz1, sutiikulum, takz1tum


kumurrtlm 19, 334 kur 80 0.106, 230 0.256 kus 17, 18, 22, 36, 137, 157, 389 la watar 169 0.195, 338 LAGAB 24 0.37, 25, 125 0.149,

303, 328 lagab 354 LAGAB.LAGAB = NIGIN 24 0.37 lal 21, 134, 294, 295, 295 0.336,

295, 392 0.485 lapatum 40, 332, 347 laqum 280.47, 39 0.69, 125 0.147,

1900.215, 332, 333 0.386 lawum 24 0.37 letflm 324 libbum 13, 20, 34, 51, 3920.485 limtalJiJar 253 lu 50.7 lu.es.gid 361 0.430 lui 36 ma.oa 305 0.344 -ma 6, 39, 390.68,40, 1390.158,

1600.192,251 0.281, 319, 328, 331, 333, 340, 341, 348, 352, 355,377

malJiirum 25, 179 0.204, 224, 225, 331, 347 0.409, 403 See also imtalJiJar, limtalJlJar, itamlJurum, melJrum, sutamlJurum

mak$arum 66, 103, 149, 154, 193, 228, 257, 333

mala 39, 64, 139 0.158, 326 0.374, 342, 343, 377

mala ma$i 326 0.374 mao 215 0.242 manatum 88 manum 88,2400.265 ma$um 39 matum 21, 59, 67 0.93, 293, 295 melJrum 25, 250.38, 27, 324, 327,

332 mi"num 26,280.47,39, 390.69,

320, 323, 326, 3260.374, 327, 329, 331, 334-336, 338, 341, 376

mir 230 n.256 mislum 12, 31, 163, 179, 343, 377 mitlJartum 7, 12, 13, 25, 25 n.39,

27,28 n.47, 35, 111, 125 n.149, 261 n.295, 298 0.340, 328, 343, 353, 354, 356, 402, 403

mu 389 n.479 mu ou zu.u 389 mulmul 50.7 mulapin 5 n.7 miilum 36 n.62 muttarittum 229 muttatum 324, 332 nadanum 40, 65 n.91, 317 n.356,

319 n.363, 327, 333, 333 0.386, 333, 335, 336, 340, 341, 342, 346, 347, 360, 377

nadum 40, 61, 332 nakalum 80 n.106 nakiisum 325 0.372, 351, 377 nakmartum 19 nam.lu.ulu 315 narum 239 n.264 nasalJum 20, 33, 163, 182, 301,

320, 323, 324, 327, 328, 330, 332, 334, 337, 339, 341, 345, 347, 348, 361, 376, 377, 389

nasilJum 182, 182 n.206 nasum 5,22, 220.34, 1600.192,

199,319 n.363, 333, 343, 377, 389

nepesum 320.55, 138 n.157, 322, 329

oig.sid 323 0.370, 375 NIGIN 24, 24 0.37, 25, 125 0.149,

191, 1950.220, 261 0.295, 262, 327, 328, 331 0.382, 350

nigin 24 0.37,350.61,38,159, 330

nim 22,220.34, 377,389, 392 n.485

oiodao 17, 17 n.22, n.24, 17, 18, 37,84, 111, 137, 209, 212, 223, 225, 229, 313, 389

nitkupum 24

438 Index of Akkadian and Sumerian Terms and Key Phrases

n u. 240 n.265 nu.zu 335,337,341,351,389 pas.sig 345 pad 251 n.281, 325, 352, 357,

360, 360 nA28, 377, 378 piinum 28, 28 nA8, 376 n.462 pariikutn 234 pa(iirum 28, 28 nA7, 343, 347 pi 208 n.235 pirkum 234, 239 n.263 putum 28 nA7, 34, 35, 224, 225,

250. 280, 320. 324. 354 qabum 4.38 qanum 209 qaqqarum 36. 36 n.63. 36. 36

n.64, 137, 269 .ra 130 n.152 RA 21,21 n.33. 251 n.281. 353.

357. 389 reska tikl7 40. 330 n.381. 334. 336 resum 35.40 sa 190 n.215, 355 sa.sa 190 n.215 sa 190 n.215. 355 sag 7. 10. 34. 34 n.58. 34-36. 60.

86.89. 101. 125 n.149. 182. 200. 224. 244, 250. 251 n.279. 280. 327. 375. 376 nA61. 376

sag an·.na 375 nA59 sag ki.ta 375 nA59 sag.du 34 n.58. 322 sag.KAK 34 n.58 sag.ki 320. 324 sag.ki.gud 244.256 sabar 36, 36 n.64. 137 sabiirum 38. 169 n.195. 319. 323.

330. 338, 342 salmum 240 n.265 santakkum 34 n.58 sar 17.17 n.22. 17. 17 n.23. 17.

18,37,78,103. 111, 137.229 sarrum 36 Sf 179. 343. 343 nA02 SI.A 88, 179. 343 sis 12, 25., 325. 347 nA09. 375

See also ib.si s, etc .. ba.si s'

etc .. sa sis.si s 190 n.215 sig 4 350 s i 1 a 78. 208 n.235 sukud 36 n.62 sum 40.240 n.265. 319 n.363.

330, 333 n.386, 335. 336. 345. 360.377

sibtum 19 siliptum 261 sa etab 132 n.154 sakiinum 39. 179 n.203. 333, 375 salum 28 nA7 siininum 190 n.215 sanum 257 n.290 sapiilum 20 sapiltum 20. 341 saqum #22. 23 .se 200 se 392 nA85 ses 159 n.189. 323 n.369 sid 323 n.370. 375 siddum 34. 35. 224. 280. 320. 320

n.365. 324, 376 nA61 su 182 n.207 SU.BA.AN.TU 125 n.147. 216 n.243 su.ba.an.ti 125 n.147 su.nigin 20, 142 n.163, 330 su.rLa 31.31 n.53. 31. 179.320.

343. 345. 353. 356. 361. 377 su.si 17. 18 sullusum 24 summa 32 n.55. 37, 319. 322, 322

n.368. 323, 326. 328. 329, 330 n.381, 334. 341, 355, 376. 389

Summa eqlam isdluqa umma suma 224

summa Ham isaalka umma suma 319

sumum 95 n.129 suplum 36 suqqum 23 susi 16.209 sutakulum 6. 6 n.9. 13. 23. 24

n.36, 24. 40. 57. 59 n.84. 195 n.220. 298 n.340. 320. 324.


327, 328, 332, 334, 336, 339, 342, 344, 347, 348, 351, 355, 361,377

sutamfJurum 25, 25 n.38, 25, 25 n.39, 31 n.53, 179, 327, 328, 330 n.379, 331, 331 n.382, 343. 351,377

sutbUm 20, 212 .ta. 251 n.280 ta 392 n.485 ta.am .27,224,331,350 tab 23, 132 n.154, 327, 331, 336,

350. 353, 357, 357 n.423, 391, 391 n.483 See also sa etab

tabiilum 20,301,347 tag 4 350

See also ib.tag 4

takl7tum 23, 57, 80 n.106, 195 n.220, 199, 200, 217 n.245, 320, 324, 327, 332, 334, 334 n.389. 336, 347 n.410

takkirtum 80 n.106 tal/um 239. 239 n.263, 321, 322,

325 tammar 40, 146 n.169, 319, 319

n.363, 327, 329, 330, 330 n.379, 338, 345-348, 350, 351, 357, 360, 377, 379

tarum 38, 169 n.195, 185, 323, 327, 328, 332, 335 n.391, 338

tawirtum 77 n.105, 239 n.264, 340 n.398

.te. 251 n.280 tul 36 tul.sag 36, 137 tur 134, 295 n.336 tepum 391 u 86, 179 n.203, 295 u.ub. 251 n.281251 n.281, 352,

377 U.ub.RA 251 n.281 ub.te.gu 7 344 n.404 UL.GAR 19,86,89 n.117, 160

n.192, 188, 327-331, 350, 389 UL.UL 24

ullum 22 UR 347 n.409 UR.KA 347 n.409 UR.UR 24, 347 us 60, 60 n.87, 111 us 7, 10, 34-36, 34 n.58, 60, 60

n.87, 86, 125 n.149, 182, 200, 244, 280, 303, 320, 324, 327, 328, 375, 375 n.459, 376, 376 n.461 , 376

us 2.kam 375 n.459 WA.ZU-BI 91 n.123 wabiilum 341, 342, 344, 355 wasiibum 12,19,20, 182,383

n.472, 389, 391 wiisbum 182, 182 n.206 wdsrtum 12-14,51,84,348,383 wasum (noun) 348 n.412 wasum (verb) 51, 84 watdrum 21, 59, 67 n.93, 188, 295,

343 See also Iii watar

watrum 320 wusubbum 91 n.123 za.e 33, 326, 329 za.e kid.da.zu.de 329 n.377,

335 za.e kid.ta.zu.de 329 n.377, 331 za.e kid 9/kid.da.zu.de 346 Zl 20, 27 n.44, 28 n.47, 30, 33, 88,

127 n.151, 301, 323, 324, 325 n.372, 327, 328, 330, 330 n.379, 334 n.387, 341, 343, 343 n.402, 351, 361, 375, 376, 389 See also ba.zi

zi.zi 323,323 n.370, 375, 376 zi.zi.i ga.ga 375 ZUR.ZUR 24, 336

Name Index

Abu Bakr 369-371, 369 n.446, 374, 379 n.466, 380 n.467, 387,406,408,410, 411,415,415 n.508, 416 n.511

Abu Kamil 364-367, 414, 415, 416 n.510

Abu'I-Wafa' 264 Alexander the Great 311 Apollonios 2, 404 Archibald, R. C. 1 Archimedes 98, 106, 107, 403 Aristippos 106 Aristotle 362, 366, 367 n.441,

402, 403 n.491 ibn al-Banna' 415 Brahmagupta 409,414 Bruins, E. M. 28, 87, 88, 93

n.128, 182 n.207, 193 n.217, 196 n.223, 215 n.240, 227, 228, 265, 266, 343 n.402

Cardano, Gerolamo 154, 154 n.184, 417, 417 n.512

Chemla, Karine 14 n.18 Dedekind, Richard 292 Descartes, Rene 279,404

n.492 Diophantos 2, 98, 298, 372

n.454, 373, 385, 402, 404, 414 n.506

Euclid 98, 402, 403 Frank, Carl 2 Friberg, Joran 8 n.13, 26 n.41,

29, 50 n.75, 241, 252, 322, 349 n.413, 353 n.417, 356, 386 n.475

Gandz, Solomon 3, 180,227,

228, 237, 244 n.270, 278

Gerard of Cremona 369-371, 369 n.447, 411, 411 n.502, n.503, 414, 415, 415 n.508

Goetze, A. 38 n.66, 317-319, 319 n.362, 328, 328 n.376, 329, 329 n.377, n.378, 332-335, 337, 338, 342, 343, 345, 348 n.411, 349, 356, 358, 386

Hammurapi, king 310 Heiberg, J. L. 368, 368 n.443,

369 n.444, 371, 406, 406 n.494, 407

Hero of Alexandria 103, 103 n.136, 264, 368 n.443, 382, 406, 406 n.494, 407, 409

Hippocrates of Chios 402 Jacopo da Firenze 102 n.134,

n.135, 339 n.396, 416, 416 n.510

Jean de Murs 339 n.396, 371 n.451

Jordanus of Nemore 404 n.492 Kant, Immanuel 98 al-Karaji 415 al-Khayyami 404 n.492 al-Khwarizmi 298, 369 n.445,

372, 382, 382 n.469, 409-417, 412 n.505, 414 n.506, 416 n.510, 417, 417 n.512

Kronecker, Leopold 292 Leonardo Fibonacci 263, 370,

371, 371 n.450, 379

n.466, 387, 396 n.487, 398 n.489, 405, 406, 410 n.500, 411, 414-416, 414 n.506, 415 n.508, 416 n.511, 417 n.512

Luca Pacioli 370, 371, 371 n.450, n.451, 379 n.466, 411, 416, 417 n.512

Mahavira 364, 364 n.433, 371, 372, 372 n.455, 374, 380 n.467, 409

Mahoney, Michael 279, 281, 298

al-Ma'mun 411, 412 n.505, 413

Millas y Vallicrosa, J. 370 n.448

Muroi Kazuo 89 n.l19, 188 . n.211, 250 n.275, n.277, 252, 253, 253 n.282, 293, 352

Nesselmann, G. H. F. 107, 298,299

Neugebauer 1-3, 7, 7 n.12, 8 n.13, 10, 12-15,21,21 n.32, 33 n.56, 41, 65 n.91, 66, 72, 80 n.l06, 111 n.141, 156 n.186, 162, 222, 223, 243 n.269, 244, 244 n.270, 262, 263 n.299, 269, 270, 274 n.312, 278, 279,294,295,298,317 n.355, 318, 329, 330, 335, 346, 348-350, 385, 390 n.480, 400

Newton, Isaac 98, 244 n.270 Nietzsche, Friedrich 366 Nisaba, Goddess 164, 307 Nunez, Pedro 243 n.269, 383

. n.473 Orwell,George 377 n.464 Paolo Gherardi 416

Name Index 441

Pappos of Alexandria 33 n.57 Peano, Giuseppe 292 Piero della Francesca 370,

371,379 n.466, 411, 416, 416 n.511

Plato 262 n.297, 367, 370 n.448,402

Plato of Tivoli 370 n.448 Proc1os Diadochos 262 n.297 Ritter, Jim 88 n.l15, 190 n.215 Robson, Eleanor 18 n.26, 64,

73,81 n.107, 132 n.153, 263, 268 n.306, 325,352

Rodet, Leon 409, 414 Roriczer, Mathes 264 Rosen, Frederick 411, 411

n.502, n.503, 412 n.504 Rozenfeld, Boris A. 411,411

n.502, n.503 Rudolff, Christoph 365 n.438 Savasorda (Abraham bar

Hiyya) 370, 387, 405, 406,411,415

Schuster, H. S. 1 n.2, 3 Sulgi, king 314, 323, 325, 375 Struve, V. V. 2, 3 Tartaglia, Niccolo 154 n.184 ibn Thabat 371, 411 Thabit ibn Qurrah 367, 402411

n.503, 412 n.505, 414, 415

Theaetetos 367 Theodoros Theon of Smyrna 262 n.297,

408 Thureau-Dangin, F. 3, 7, 11,

12, 14, 15,23,26 n.41, 27,28 n.47, 41, 42, 67 n.93, 72, 154, 156 n.186, 162, 179 n.203, 227, 228, 239 n.264, 244 n.270, 278, 348

ibn Turk 413 'Vmar, caliph 413 Van der Waerden, B. L. 7, 243

442 Name Index

n.269 Vit!te, Fran~ois 33, 33 n.57,

98, 279, 280, 285, 383, .383 n.473, 404 n.492

Vogel, Kurt 1 n.2, 3, 137 n.156, 151 n.178, 229, 244 n.270, 278

von Soden, Wolfram von 88, 91 n.123, 189 n.214, 200, 244 n.270, 287

Wallis, John 404 n.492 Wei!, Andre 299 n.341 Westenholz, Aage 80 n.106,

169 n.195 ibn al-Yasamin 415

Subject Index

Abacus, Greek 107 "Accounting technique" 58,

73, 75, 100, 110, 132, 263, 303, 382

and concept of coefficient 60, 101

Additive operations 19, 51, 160

identity-conserving 19, 57, 347, 355 n.421

symmetric 19; -, and plural sum 20, 163, 338; -, reversed by "singling out" 21 n.29

Aegina, coins with geometric diagrams 402

"Akkadian method". See Quadratic completion

al-jabr 369 n.445, 404 n.492, 411, 412 n.505, 413, 414, 414 n.506, 415, 417

originally without geometric proofs 412 n.S05

Algebra a plurality of algebraic

ways of thought 282 Mahoney's minimal defini

tion 279, 298 Algebra, Babylonian

"art", not "episteme" 281 built on reasoned pro

cedures, not "empirical" 279 n.318, 280, 283 n.321

distinct discipline within DB mathematics

logograms as symbols? 7,

10, 33 n.56, 111 n.141,298

Mahoney's rejection of concept 279

measured by Mahoney's criteria 280

pretext for sexagesimal computation 381

rhetorical according to Thureau-Dangin 7

the arithmetical interpretation 3,6,7,7 n.12, 12, 13, 278; -, and "superfluous" words 12, 13,34

the standard representation 10, 34

transformation of the riddle legacy 170

Algebra, Greek Calculators' Algebra, Italian vernacular

415,416 n.5l0 geornetrization 416

Algebra, second-degree discovery of Babylonian 1 supposed Arabic beginning

2 supposed Indian beginning

2 Ambiguity of mathematical

texts, to be resolved from context and numbers 111, 205, 298 n.340, 298, 299, 3

Analysis infinitorum 271, 404 n.492

Analysis/synthesis, relation to distinction naive/critical 404 n.492

444 Subject Index

Analytical approach and naive strategy 98 and need for identification

37,283, 285 fundamental to algebraic

thought 33, 33 n.57, 58, 279

in Old Babylonian mathematical texts 52, 98, 280

in the "surveyors' riddles" 380

of the "single false position 101, 280

Analytical geometry 199 Angle concept

absent from Babylonian thought? 227

as quantifiable magnitude: not Babylonian 228

heavenly distances not to " be understood as angles 228 n.252

right angle understood in relation to area determination 228

Anthology texts 983 Application of areas 96, 99,

278 Area determination

existing rectangles 22 trapezia 22, 31, 230 trapezoids 22 triangles 22, 31, 229 See also Circle ...

An"thmos 373, 414 n.506 Assyrian empire 311 Ausdehnungslehre 199 "Average and deviation" 162,

202,217,247,350,375 and arakarum 248 in Greek mathematics 402,

405 in Liber mensurationum

408,410 not used in Demotic texts

408 not used in Seleucid texts

397 reverse use by Mahavira

409 Babylonian mathematical cor

pus, text categories 8 "Baby Ionian mathematicians"

a misnomer? 8, 302 in which sense justified

384 Babylonian mathematics

centred on computation 8, 307

history of its historiography 1,ln.l,2

less cognitive autonomous in Late Babylonian times 316

known from school texts 8 no mystico-religious affin

ities in the OB period 164 n.194

OB cognitive autononomy 307

periodization 3, 311 (pretended) practical origin

209, 276, 287 See also Late Babylonian mathematics; Seleudic mathematics

Bakhshali manuscript 409 Biquadratic equations 71, 194,

199, 279 n.318, 303, 381

Bisection a distinct operation 31,32

Bracket function, algebraic 39, 343, 377

"Breaking" 14, 31, 155, 174, 208, 216, 217, 320, 323, 334, 336, 339, 340, 345, 347, 348

abstract? 69 implying "making hold"

163, 217 n.244, 344

omitted together with preceding "repetition" 76, 76 n.102, 221

Brick problems 163, 268 n.306, 287, 305, 321, 338, 338 n.395, 341, 342, 378, 381, 407

Broad lines 19 n.27, 22, 51 n.76, 52, 84, 96, 135, 163, 169, 180, 226, 242, 243 n.269, 272, 291, 291 n.335, 292, 315, 328, 339, 339 n.396, 348, 354 n.420, 355, 382, 383, 383 n.473,388

"critical" justifications of practice 292, 383

Broken-reed problems 36, 37, 209, 280, 281, 285, 286, 299, 307, 32~ 321, 325, 335 n.391, 341, 341 n.400, 351, 381,381 n.468

"Building" of a line 215, 216 of surfaces 23, 24, 64, 125

n.147, 134, 163, 169, 215, 216 n.243, 225, 248, 336, 336 n.393; -, and verbal equalside 336 n.393

reference to a surveyors' idiom? 134, 215 n.241

Bundling method 60, 66, 103, 149, 228, 256, 257, 327, 333

generalized to non-homogeneous cases 154, 193

Calculation errors 72, 195 0'.222, 196 n.224, 272

Calculators' algebra, Greek 402

Canons in OB mathematics adoption/adaption of bor

rowed materia 349,

Subject Index 445

360 adaptions revealed by

lapses 324, 347, 384 and exclusion 324 concerned with format as

well as critique 360 n.427

created intentionally 324, 328, 332, 360, 383

elimination of Dr III stylistic traits 322, 324, 356

local 77, 324, 328, 335, 337, 344, 348, 349

"Cascades of squares" 405, 405 n.493

Catalogue texts 9 "Change of variable" in OB algebra

36, 37, 99, 100, 169, 188, 405 Chinese mathematics 98, 103 Circle

area "held" 342 basic parameter: diameter

or circumference 372 compass-drawn 105, 265 understood as bent line

272, 372 n.453 "tripling" of diameter 331

n.384 Circle problems, algebraic 304,

371, 373, 374 n.458, 381, 382, 405, 409

Circles, concentric 276, 388 Close reading, principle of 14 Coefficient in equation, OB

concept of 60, 101, 132 n.154, 206

Completion of triangle 237, 266 n.303 see also Quadratic comple

tion Complex second-degree prob

lems reduced to square or rectangle? 155, 157, 158, 215, 221

Concentric circles 276, 388 Concentric squares 69, 69

446 Subject Index

n.94, 99, 134,224, 225 n.250, 252, 267, 285,286, 301, 304,305,371, 373, 379, 388, 399, 401

Conformal translation 18, 41, 42

Connotations determining terminological choice 20,

-163, 300-302, 339 Constant coefficients 30

chosen as regular numbers 29

tables of 8, 18, 228, 239 n.263, 257, 261, 261 n.295, 262, 272, 307, 337, 386, 390 n.481

"Conversion" of the length/ width/depth 153, 154, 156

Copyist's mistakes 42, 151 n.179, 152 n.181, 196 n.224, 212, 213

"Core" text groups and mathematics 38, 38 n.66, 206, 253, 329 n.377, 329, 331 n.382, 337, 345, 348 n.411, 351, 355, 356, 359-361, 359 n.426, 377, 386, 387

texts from group 2 345 see-also Larsa, ... ; Nippur,

... ;-Ur, ... ; Uruk, ... "Counterpart"

in square 27, 39, 57, 94, 174, 193,197,260,324

in square to be constructed 259

in triangle 233, 234 of a moiety 216,324 originally loose usage 324

Counting board used for additive computations 73, 195 n.222

"Critique" 367, 404 delineation of concept 98,

100 n.133 Euclidean, in Fibonacci

417 in Greek mathematics 98,

100, 401, 402, 405 in OB mathematics 100

n.133, 383-385 in Viete 383 n.473, 404

n.492 "Crucial discriminators" 243,

243 n.269 Cube problems 65, 149, 321,

354 Cube roots, table of 65, 154 Cuneiform writing 4

ambiguity 4, 5 "rebus principle" 4, 23 transliteration versus tran-

scription 4 n.5 use of phonetic comple

ments 5, 5 n.7 use of semantic deter

minatives 5, 5 n.7 Cut-and-paste procedures 54,

97, 135, 137, 159 n.191,263

examples 51, 53, 55, 57, 75, 94

in geometric problems 276, 280, 354

in the Sulbasutras 408 not visible in Seleucid

sources 397 proof of Pythagorean rule

386 underlying Elements II 98,

401 See also Naive geometry

Data, marking of 39 De mensuris 264 "Descendant" 228, 229, 233,

234, 234 n.260 Didactic texts

outside Susa 85, 161, 162, 256 n.288

Susa 85, 87 n.114, 89,

101, 181,384 Division

by irregular divisors 29, 330, 333, 336, 344, 353; -, third millennium BeE 263 n.298, 313, 353 n.417

by regular numbers 28 problem and operation 27

Drawings of cut-and-paste procedures

not on the tablets 103 possible media 106

djnamis 402,403 Each/the four front(s}/sidesl

equalside(s}, texts referring to 27, 125 n.149, 224, 225, 250, 253, 350, 353-358, 369, 370, 379 n.466 , 380,380 n.467, 381, 389

Early Dynastic period 310 Egypt

Demotic mathematics 261, 321, 405, 408

Pharaonic mathematics 306, 307, 321, 405

Elliptic procedure descriptions 149 n.175, 155, 155 n.185, 158, 173, 260, 320, 324, 347

Elliptic writing 9, 31 n.53, 86, 111, 114 n.143, 224

ensuing textual ambiguity 111 n.141, 114 n.143, 130 n.152, 298

equals ide and word order 26 n.43 being (verb) 26, 27, 27

n.44, 28 n.47, 146 n.169, 216 n.243, 320, 323-325, 327, 330, 330 n.379, 336, 336 n.393, 341, 343, 345, 348, 361, 375, 375 n.460

Subject Index 447

cubic 27 generalized uses 27, 146

n.169, 335 n.390 grammar reinterpreted by

Akkadian speakers 26 n.42

noun 26, 27, 27 n.44, 39 n.69, 57, 216 n.243, 323, 325, 328, 332, 335, 336 n.393, 342, 345, 347, 361, 375 n.460

regarded as a plurality 27 three different "equalsides"

151, 153 underlying grammar 25,

353 n.416 verb or noun 26

"Equalside, 1 appended" 146 n.169, 152

Equations adequacy of concept 282 Babylonian algebra 38,

282 first-degree, transformation

of 85, 134, 185, 187, 205,206

order of members 174, 225, 295. 295 n.337, 371

"Equilateral, 1 diminished" 335 n.390

Eshnunna a centre for the formation

of Akkadian mathematics 315, 321, 345, 356, 359

Law Code 318 n.358, 360 mathematical texts 34, 37,

38, 85, 125 n.149, 213, 224, 224 n.249, 231, 257, 280, 283 n.320, 318, 319, 332, 334 n.388, 338, 339, 345, 347, 351, 354 n.420, 357 n.424, 359, 361,

448 Subject Index

372. 376. 376 n.462. 382. 386; -. range of topics 321

particularities of mathematical terminology 27 n.44. 32. 34. 155 n.185. 224. 253. 319. 325. 326. 339. 361. 375 n.460. 376 n.462. 382

political history 325. 359 Euclid

Data 228. 403 Elements I 25.403 Elements II 2. 70. 97. 96.

99. 267. 278. 370. 373. 385. 400-402. 404. 406 n.494. 414. 415; -. and the surveyors'

. tradition 401 Elements VI 99. 100.403 Elements X 282. 367. 401 Elements. in general 70.

98.401.402 excavation problems 36. 137.

286. 303. 305. 321. 323 n.369. 345. 346. 348 n.411. 349. 350. 354. 381. 384

depth and length interchanged 156

in igum-igibUm formulation 158. 160

inhomogeneous third-degree 149. 154. 280

of the first degree 159 of the second degree 154 terminology 36. 137. 269.

300 See also Cube problems

Factorization 151. 153. 154. 303

False position double 82. 103. 103 n.136.

306 single 20. 30. 59. 60. 87.

101. 102. 133. 193. 194. 197. 211. 212. 228. 280

False values 37 Favourite configurations 69

n.94. 276. 285. 285 n.322

Favourite problems 285-287. 313.372

Field plans 103. 228 Fields. inventory of real 230

n.256 Filling problems 321. 341

n.399. 359. 366. 405 Format of mathematical texts

9. 32 tense and person 9. 32.

338. 342. 344. 353. 370. 392 n.486

Formula. computational. delineation of pertinent concept of 230 n.254

Formulae closing prescription 32. 32

n.55. 323. 327. 346. 347

opening prescription 32. 319. 322. 326. 328. 329. 334. 335. 346. 355

opening statement 32. 32 n.55. 34 n.58. 319. 322. 326. 329. 334

fractions composite 16 n.20. 134 simple. with special signs

16 written as ordinals 16

Functional abstraction 10. 58. 280-282

no characteristic of the surveyors' riddles 380

General rules in Late Babylonian mathe

matics 389. 396 in OB mathematics 179.

181. 213. 261, 281.

341, 341 n.399, 342, 383; -, eliminated 344 nA03, 383

in oral traditions 383 nA74 Geometric configuration, pre

cedence over algebraic structure and technique 136, 137, 161, 162, 174

Geometrica 336 n.392, 368, 368 nA43, 370-372, 382, 402 nA90, 406, 406 nA94, 407

not by Hero 406 nA94 Geometrie der Lage 199 "Going" as repetition of oper

ation 182, 189, 327, 357 nA23

Greco-Egyptian mathematics 414 n.506

Greek mathematics, the role of theoretical problems 367

Greek practitioners' mathematics 406

Half "accidental" 31 "natural", and bisection

31, 51, 260; -, nonstandard terms 323,

"334,336 "natural", no Sumerian

concept 31, 31 n.53 "Hand, method of the", a free

invention 182 n.207 Height of an isosceles triangle

in Late Babylonian mathematics 390

in DB mathematics 265 "Humanism", scribal 315, 384 Identifiers

for numbers 37, 37 n.65, 64,94

numbers used as 37, ISO, 161, 179, 283, 285

i g i, see also term index

Subject Index 449

as part of something 30 as reciprocal 28 as "share" 30 n.52 origin and etymology 28 terminological distinction

between functions 30 igum-igibum problems 35, 55,

138, 158, 159, 159 n.191, 160, 281, 299, 381, 390

use of accounting terminology 20, 159

Indeterminate problems 181, 188, 364

Indian mathematics 281, 298, 364, 374, 408, 409, 410 nA98, 413, 414

algebraic schemes 298, 409

"Inscription" of numbers 40, 59, 59 n.84, 64, 69, 75, 163, 170, 260, 332, 339, 344, 347, 348, 354

Interrogative phrases 39, 159 n.189, 253 n.284, 320, 323, 326 n.374, 327, 329, 330, 330 n.380, 334, 335, 338, 341, 346, 352, 355, 357 nA24, 361, 376, 377

Inversion of given and unknown magnitudes 132 n.154, 220, 268 n.307, 274, 276

Irrationals Greek investigation of 367 no Babylonian reason to

discover 297 Jaina mathematics 409 Kassite period 310

mathematics 387 socio-cultural change 315 virtual absence of math-

ematical texts 315, 387

"Know, You/l do not" 30, 335,

450 Subject Index

337,341,351,354, 389, 389 n.479, 391

Languages Akkadian 4, 310 Assyrian 4, 310 Babylonian 4, 310 See also Sumerian

Larsa a (likely) centre for the

formation of Akkadian mathematics 315, 345, 356, 359, 359 n.426, 360, 387

mathematical texts probably from (= group 1) 337

Late Babylonian mathematics 388

terminology 389 texts owned by "exorcists"

388 "Lay practitioners' mathemat

ics" adoption into the scribe

school 321 n.367, 322, 340, 344, 359, 374, 382-384, 389

readoption in Late Babylonian period 316, 391

"Lay" mathematical practice and practitioners 316, 324, 326, 339, 340, 345, 349, 350, 355, 360, 361, 368, 379, 380, 381 n.468, 382, 383, 386, 400, 404, 409,417

Linguistic criteria, Goetze's 317 n.357, 318, 319 n.362, 328, 328 n.376, 386

Loanwords Akkadian in Greek 209 Akkadian in Sumerian 352 Sumerian in Akkadian 27,

30 n.51, 74 n.100, 182,200,215 n.242, 248, 376, 389, 391

Logical operators 37, 38, 319, 323, 327, 330 n.381, 334, 336, 355, 377

seemingly no Ur III antecedents 376

Logograms 4 and genuine ideograms 24

n.37, 25, 347 n.410 in Akkadian writing 4

Mathematical problems constructed from the solution 29, 196 n.225, 221,221 n.247, 288

exceptions 159, 267, 267 n.305,268

Mathematical texts identification by museum

number 11 n.15 meant as support for

memory 130 n.152, 299

metalanguage 32 Old Babylonian 315;-,

division into groups 317

to be understood "by default 34 n.58, 132

Mental geometry 59 n.84, 77, lOS, 110, 15~ 281, 285

implications for the order of computational steps 110

Mesopotamia geographical divisions 309 historical periodization 2

n.4, 309-311 Metrological tables 8, 18,81,

307 Late Babylonian 388, 410

n.499 Metrological units made

explicit in algebra texts

77, Ill, 209, 223, 225, 351 n.414

Metrologies 16 Metrology

and sexagesimal principle 18

and "units" 17 "basic units" 17, 78 for area 17, 229 for horizontal distance 17 for vertical distance 17 for volume 17 Kassite and subsequent

periods 315, 388 proto-literate 311 units as semantic deter

minatives 17 Mock reckonings 321, 341,

382, 387 eliminated from mature OB

school mathematics 382

"Model documents" in proto-literate mathemat

ics teaching 313 in U r III mathematics

teaching 314, 375 Multiplication, Tables of 8, 18 Multiplicative operations 21

brickwork calculation 22 concrete, "category-con

serving" ("raising" etc.) 22,291

determination of areas 22, 229

and "going" 23 number by number 22 repetition 23 "raising" and determination

of volumes 22 Naive geometry

consolidated in Elements II 98,401

in al-Khwarizml 412 in Piero della Francesca

371

Subject Index 451

Old Babylonian 97, 100 "Naive" approach

delineation of concept 98 in OB mathematics 98

"Name" of an entity 95 n.129 "Natural" coefficients

eliminated from mature OB school mathematics 381

notion of 21, 21 n.32, 59, S9 n.83, 294374

Negative numbers not found in Babylonian mathematics 21, 21 n.32, 59, 59 n.83, 294

Neo-Sumerian period. See Ur III

Nested algorithms 76 n.102 Nested areas and volumes 199 Nippur

mathematical texts 35 n.59, 125 n.149, 224, 253 n.284, 280, 344, 352,354

particularities of mathematical terminology 354, 355, 357, 360 n.429, 376, 377 n.463, 382

Non-Euclidean geometry 292 "Norm of concreteness" 58,

82, 155, 155 n.185, 174, 178, 320, 324, 347, 348, 383

Number notations non-place-value notations

16 the place value system 12,

15; -, decimal seximal 15 n.19; -, origin 314

Number words, Indo-European 291 n.333

Numbers in the conformal translation 12, 15

Numbers "merely known" 87, 89 n.118, 93, 95, 99,

452 Subject Index

150, 157,161,213, 234, 283, 354

"Numerical tablets" 312 n.349 Old Akkadian period. See Sar

gonic period Old Babylonian period 310,

314 the collapse 315

Omina, format 37 Oral culture, general character

istics 324 n.371, 340, 340 n.397, 365, 383 n.474

Oral instruction in DB mathematics 85, 161, 272 n.310, 283, 283 n.320, 338, 384

Parthian period 311 Partitioned surfaces. See Sub

divided figures; Striped figures

"Periphery" text groups and mathematics 38, 38

. n.66, 224, 253, 283 n.320, 315, 329, 329 n.377, 331 n.382, 332, 337, 340, 345, 348-350, 348 n.411, 355, 359-361, 386, 387

texts from group 5 332, 359 n.426

See also Eshnunna ... ; Susa, ... ; Sippar, ...

Perpendicularity not understood as

verticality 229 understood in relation to

area determination 228 "practical" 34 n.58, 228-

230 Persian period 311 Pole-against-wall problems

275, 307, 385, 394, 398, 399, 406

"Positing" 29, 39, 40, 51, 64, 73,81,82 n.108, 87,

179, 180, 185, 197, 211,241,296,375

Practitioners' knowledge sys-tems, pre-Modem

autonomous 362 general characteristics 363 "sub-scientific" and

"scholasticized" 363 Problem statements, separation

of general information and actual situation 338 n.395

Problem texts 8 Procedure texts 8

structuration 37, 38 "Projection" and "broad line"

51 Proofs of problem solutions

38,63,81,84,215, 218, 222, 258, 260, 323, 330 n.381, 334, 386

Protoliterate period 310,313 administration mathemat

ically planned 313 mathematics teaching by

model documents 313 metrology 311

Pseudo-coefficients eliminated from mature DB school mathematics 381

"Pythagorean rule" 197, 199, 254, 257, 260, 262, 266, 268, 272, 275, 385-387, 390, 399

cut-and-paste proof 386 discovered after the quad

ratic completion 387 Pythagorean triples 288, 386 Pythagoreans and Neopytha

goreans 372, 372 n.454

Quadratic completion 14, 19, 31, 55, 57, 94, 98, 155, 159,172,174,192, 237, 276, 297, 324,

347, 354 termed "the Akkadian

(method)" 94, 379 in school teaching 381 invention 379 Seleucid alternative 396 to rectangle 94

Quadratic equation, double solution not pertinent for the cut-and-paste procedure 221

Quotations from problem statement 33, 38

Quotient volume 151, 151-154, 151 n.178, 342

"Raising" in determination of rectangular areas 22, 60,64, 191,260

Rates, Problems about combined commercial 9, 10, 206, 206 n.234, 299, 321, 323 n.369

"Real" walking or section demarcation? 169 n.195, 185, 335 n.391

Reciprocals 28 approximate, of irregular

numbers 29, 29 n.50, 263 n.298

multiplication by 28 of irregular numbers, pe

riodicity not investigated 297 n.339

of regular numbers "not known" 30

or parts of 60? 28 n.46 standard table 28 tables of 8. 18 to be "detached" 28 n.47

Recording material 39 mental 40, 82, 82 n.l08.

373 n.456 Recreational problems

determined from methods 366

Subject Index 453

origin as specialists' riddles 159, 364, 365

role in scholasticized mathematics 364

See also "Supra-utilitarian knowledge"

Rectangle problems 34, 55, 158, 173, 188, 261, 286, 305 n.343, 307, 338, 339 n.396, 343 n.401, 346 n.407, 372-374,378,381,390, 391, 398, 401, 403, 405,406,408-411

basic set 305 n.343, 343 n.401; -, modified 174

of the first degree 182 primary with respect to

square problems? 173 Rectangular figure

conceptualization 34 more fundamental than tri

angle 34 n.58. 274 Rectangularization 23. 320.

331. 331 n.382, 334, 336, 339, 347, 355

and circle area 24 and "holding" of a

trapezoid 24 n.36, 248, 249, 342

coupled to number multiplication 163, 328. 339

of irregular quadrangles 24 n.36

"holding" or "eating"? 23 Reference volume 150-154,

193, 280, 354 regula recta 414 n.506 Regular numbers 27

rounding to 29 n.49 "Remarkable numbers" 67

n.93, 287, 295 subcategories 287

"Repeated" trapezia and triangles 211,215,220,

454 Subject Index

230,233 "Repetitiveness" 284

in symbolic algebra 284 Representation 58, 72

of surfaces and volumes by segments 72, 198, 381

Results, marking of 39 being "given" 40, 319

n.363, 335, 340-342, 344, 346, 347, 360

being "seen" 40, 253, 319, 323, 325-327, 329-331, 346, 350, 352, 356, 357, 360, 360 n.428, 378, 389

by .am 352,355,360 n.428

by -ma 40,319,331,333, 341, 348, 360 n.428

by "positing" 179, 343 "coming up" 40, 319, 319

n.363, 320, 323, 326, 332, 342, 344, 355, 360

Rhetorical algebra 7, 33, 111 n.141,298

Rhind Mathematical Papyrus 307, 321, 405

Riddle format 32, 224, 257, 319319, n.361, 322, 324, 325, 370, 374

Riddles in the Greek Anthology

306 order of actors 225, 371 eristic role in oral culture

365 Riddles, mathematical 306,

321, 325, 359 and mock reckonings 366 solution by tricks 339,

366, 379 Rough work, tablets for 8, 64,

73, 81, 217 Rule of three 102 Sargonic period 310, 314

appearance of new math-

ematical problem types 314

Scaling (in one dimension) 55, 75,76, 100, 110, 181, 208, 212, 215, 220, 233, 234, 238, 238 n.261, 247, 248, 276, 303, 379

coupled to its inverse in the other dimension 244

in school teaching 381 made by "raising" 55 of rectangle into square

55, 202, 208 n.236, 220, 233, 234, 238, 247

precedes determination of number of sides in square problems 75, 110, 158, 191, 216

Scaling factor or ratio, term for 200, 208 n.236

School exercises 106 n.137, 263 n.298, 267 n.304, 307 n.345, 313, 314, 363

format 371, 374 Scribal computation, traditional

type 326, 341 post-Ur III innovations

360,361 Scribal culture, Old Babylonian

315 Scribal profession

and emergence of suprautilitarian mathematics 313

appearance c. 2600 BCE

313 Kassite disappearance of

the school 315 Section demarcation 38, 319,

323, 327, 328, 332, 338 "Seleucid innovations"

also known from Demotic mathematics 406

in Mahiivira 409

Indian origin improbable but not excluded 410 n.498

no trace in Greek theory 405

traces in Greek "low" mathematics 408

Seleucid mathematics 316 igum-igibUm problems 390 new problems and methods

396 practical geometry 390 sums of series 390 supra-utilitarian rectangle

problems 391 terminological innovations

391 texts owned by "astrologer-

priests", etc. 390 Seleucid period 311 Semi-circle 24, 287 n.325 Series texts 9, 111, 125 n.147,

132 n.154, 137, 192, 200, 203, 216 n.243, 223, 279 n.318, 286, 293-295, 298, 299, 303, 318, 327, 329, 330 n.379, 334 n.388, 343, 349-351, 349 n.413, 351 n.414, 353, 357, 357 n.424, 358, 374, 377, 381, 384

"Sexagesimalization" of thirdmillennium metrologies 313

Shortcuts illegitimate 174 intentionally avoided 76

Side-and-diagonal numbers 262, 263, 265, 267, 272, 379 n.466, 408

Sign names 4 Similarity of figures 228, 233

probably a primary concept 228

use of constant coefficients

Subject Index 455

228,256 "Simplicity", dependent on

culture and habit 290 n.332

Sophists' mathematics 367 n.441

Square, "front"/"width" of. See "Each ... "

Square, "length" of 125 n.149, 189 n.212, 328, 354 n.420

Square configuration and "counterpart" 25

See also "Counterpart" Square problems 34,50-53,

58, 73, 108, 111, 173, 221, 222, 225, 252, 286, 302-304, 330 n.379, 368, 369, 370, 373,409

about subdivision 58, 60, 61, 191,304

with double positive solution 221, 304 n.342

Square roots approximate computation

262,268 "extracted" from known

end result 72, 196 n.223, n.225

table of 159 Square side

lay favourite value 10 382 OB favourite value 30 382

Squares, Tables of 8 Squaring and square configur

ation 25 Standard diagrams 68, 70, 99,

172,260,343,387 Standard representation

and "real" fields 35, 87, 225,280

and "school-yard" dimensions 35 n.60, 77, 280, 351 n.414, 382

and standard problems 34

456 Subject Index

notion of 34 rare syllabic writings of

central terms 34. 324 the central Sumerograms

34. 35. 320. 324 Statements. opening of 32. 32

n.55. 34 n.58. 319. 322. 326. 329. 334

Stone riddles 305. 307. 327. 341. 351. 359

Striped figures 234. 239. 277. 285. 387

See also Subdivided figures Structural analysis. principle of

14 Structure diagrams 105. 107.

110. 256. 281 Subdivided figures 77. 82.

231. 234. 237. 239. 244. 254. 276

See also Striped figures "Subscientific" know ledge

systems carried by master-appren

tice networks 363 of oral cultural type 365 specialists'. not "folk"

knowledge 365 n.438 "Subtractive numbers" 59. 59

n.83. 296. 296 n.338 Subtractive operations 20. 52

comparison 21. 21 n.32. 59; -. reversed 21. 134

identity-conserving 20. 163. 292. 320. 323. 341. 347. 355

Sulbasutras 408. 409 Sulgi reform 314. 325

impact on mathematics 314. 325. 375

Sumerian a scribal language from Old

Babylonian times opward 315

as understood by Akkadian

native speakers 26 n.42

ergativity and case structure 25 n.40

history of the language 313 n.352

no longer spoken in the OB period 310

OB mathematical texts in 250. 344. 352. 354 n.419. 355

verbal prefixes 27 n.44 See also Unorthographic

Sumerian Sumerian mathematics 3 Sumerograms 4

as technical language 35 improper. in OB mathemat

ics 377 newly created in OB math

ematics 361 no proof of Sumerian ori

gin 315 n.353 Late Babylonian and Se

leucid reinvention with new meanings 316. 389

See also Logograms "Supra-utilitarian" knowledge

and mathematical exploration 384

delineation of concept 159 different in character from

theoretical knowledge 367

in OB mathematics 307 in OB scribal "humanism"

315. 384 in "subscientific" know

ledge systems 366 versus theoretical know

ledge 367 Supra-utilitarian problems 305.

305 n.343. 366 around 2600 BCE 313. 378 in early OB Ur 356

in theme texts 306, 346 Late Babylonian 316, 388 Sargonic 378 seemingly absent during Ur

III 314, 378 Seleucid 390, 391

"Surveyors' formula" 230, 244, 249

(mis)use in problem construction 231, 244

conditions for additivity 249

in Geometrica 406 n.494 in Mahiivira 409 rare example of erroneous

use 230 n.256 Surveyors' riddles 287 n.326,

372, 380, 388, 400, 404, 404 n.492, 413, 414

adopted into the OB school 162, 305, 324, 341, 356, 379, 381, 387

echoed in Neopythagorean sources 372

Euclidean critique 401 in Liber mensurationum

410 in Mahiivira 372 in Piero della Francesca

416 n.511, 416 "natural" coefficients 374,

380 no algebra 380 solved by naive geometry

380 used by al-Khwiirizmi 413

Surveyors' tradition 19 n.27, 314,350,351,351 n.414, 400

and naive geometry 408 discovery of the quadratic

completion 379 echoes in Demotic Egypt

405 echoes in Mahiivira 409

Subject Index 457

heritage in OB mathematics 356, 361

echoes in Greek "low" mathematics 407

probable date of Greek adoption 402

Susa a particular mathematical

environment 85 general history 310 mathematical texts 15

n.19, 33, 60, 87, 89, WI, 125 n.149, 161, 188, 206, 224, 256 n.288, 267, 283 n.320, 318, 326, 329, 354 n.420, 356 n.422, 358, 359,384

particularities of mathematical terminology 22, 33, 88, 331 n.384, 332, 351,357,382

scribes not native Akkadian speakers 33, 328

Susian method, supposed specific: a misreading 85 n.112, 93 n.128

Sy llabic writing 4 Symbolic algebra 7, 33, 36,

60, 111 n.141, 198 n.228, 244 n.271, 284, 298,299

Syncopated algebra 111 n.141, 298,299

Synthetic character of certain OB solutions 99 of Euclidean proofs 98, 99

Syro-Phoenician mathematics 107

Systematic variation 136, 290, 295, 345, 364, 382

characteristic of the OB school 281 n.319, 288, 351,374,384

consequence of scholastization 363, 381, 384

458 Subject Index

Table texts 8 Teaching strategies reflected in

mathematical texts 161, 162, 192, 243 n.268, 272 n.310

Technical terminology and daily language 5, 20,

25 n.38, 34, 257 characteristics 5, 300 or standardized used of

common language? 101, 300, 302

to be interpreted from use 5

Terminology of OB mathematics: standardized, not fully technical 300

Theme texts 9, 302 ordering 136, 348 theme defined by object

and type of questions 306

Thick surfaces 17, 22, 291 "Token system" 311,311

n.348 "Translation thesis", Neuge

bauer's 278, 278 n.316, 400

Trapezium, bisection of 237, 247, 248, 277, 353, 379

based on concentric squares and scaling 238, 248

generalized 245, 277, 341, 387

in Euclid 403,404 known before 2200 BeE

237, 314, 379 Tricks, non-generalizable

eliminated from mature OB school mathematics 379, 382

"True values" 35 n.60, 37, 87, 169, 256, 257

Unfinished-ramp problems 36, 217, 220, 233, 234, 281, 286, 381

Un orthographic Sumerian 27, 213, 325, 327, 357 n,424

Ur,OB earliest example of Old

Babylonian mathematics 315, 355-357, 359

mathematical texts 26 n,42, 27 n,44, 36 n.64, 224, 352-354; -, dating 250 n.276, 360

particularities of mathematical terminology 253, 325, 350, 352

Ur III 314 absence of supra-utilitarian

mathematics 314, 315, 378

mathematics teaching 375 no trace of a culture of

mathematical problems 376, 377, 384

school curriculum 323, 375

mathematical terminology 375,376

"Ur-III type" of computation 322, 325, 326, 359

nominal ib.si8 325, 332, 338,361

See also Scribal computation, traditional type; Sulgi reform

Uruk, mathematical texts possibly from (=group 3) 335

Uruk III 310 Uruk IV 310

formation of the bureaucratic state 311

Volume determination of 22 terminology 36, 36 n.64

Wax tablets 107, 410 n,499 Writing, protoliterate invention

of 311, 311 n.348

Writing direction 209. 229. 410 n.499

Zero final 293. 294 intermediate 293. 294. 327 outcome of subtraction

185. 293. 294

Subject Index 459

Sources and Studies in the History of Mathematics and Physical Sciences

Continued from page ii

J. H0yrup Length, Widths, Surfaces: A Portrait of Old Babylonian Alegbra and Its Kin

A. Jones (Ed.) Pappus of Alexandria, Book 7 of the Collection

E. Kheirandish The Arabic Version of Euclid's Optics, Volumes I and II

J. Liitzen Joseph Liouville 1809-1882: Master of Pure and Applied Mathematics

J. Liitzen The Prehistory of the Theory of Distributions

G.H. Moore Zermelo's Axiom of Choice

O. Neugebauer A History of Ancient Mathematical Astronomy

O. Neugebauer Astronomical Cuneiform Texts

FJ. Ragep Nasir ai-Din al-Tiisi's Memoir on Astronomy (al-Tadhkira ff ciim al-hay'a)

B.A. Rosenfeld A History of Non-Euclidean Geometry

J. Sesiano Books IV to VII of Diophantus' Arithmetica: In the Arabic Translation Attributed to Qus!il ibn Liiqil

B. Stephenson Kepler's Physical Astronomy

N.M. Swerdlow/O. Neugebauer Mathematical Astronomy in Copernicus's De Revolutionibus

GJ. Toomer (Ed.) Appolonius Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the Version ofthe Banii Miisil, Edited, with English Translation and Commentary by GJ. Toomer

GJ. Toomer (Ed.) Diocles on Burning Mirrors: The Arabic Translation of the Lost Greek Original, Edited, with English Translation and Commentary by GJ. Toomer

Continued from the previous page

C. Truesdell The Tragicomical History of Thermodynamics, 1822-1854

K. von Mcycnn, A. Hcrmann, VE Weisskopf (Eds.) Wolfgang Pauli: Scientific Correspondence II: 1930-1939

K. von Meycnn (Ed.) Wolfgang Pauli: Scientific Correspondence III: 1940-1949

K. von Meycnn (Ed.) Wolfgang Pauli: Scientific Correspondence IV, Part I: 1950-1952

K. von Mcycnn (Ed.) Wolfgang Pauli: Scientific Correspondence I V, Part II: t 953-1954

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