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El. knyga: Babylonian Mathematical Astronomy: Procedure Texts

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This book contains new translations and a new analysis of the procedure texts of Babylonian mathematical astronomy, the earliest known form of mathematical astronomy of the ancient world. The translations are based on a modern approach incorporating recent insights from Assyriology and translation science.

The work contains updated and expanded interpretations of the astronomical algorithms and investigations of previously ignored linguistic, mathematical and other aspects of the procedure texts.

Special attention is paid to issues of mathematical representation and over 100 photos of cuneiform tablets dating from 350-50 BCE are presented.

In 2-3 years, the author intends to continue his study of Babylonian mathematical astronomy with a new publication which will contain new editions and reconstructions of approx. 250 tabular texts and a new philological, astronomical and mathematical analysis of these texts. Tabular texts are end products of Babylonian math astronomy, computed with algorithms that are formulated in the present volume, Procedure Texts.



Based on a modern approach incorporating recent insights, this book offers new translations and a new analysis of the procedure texts of Babylonian mathematical astronomy, the earliest known form of mathematical astronomy of the ancient world.

Recenzijos

From the reviews:

"This book is unquestionably the most significant publication on Babylonian mathematical astronomy since Neugebauers ACT. Living up to the standard set by Neugebauer is no small challenge, but there is no doubt that Ossendrijver has succeeded in that task, producing both a clearly written and technically outstanding study of these highly important texts." (J.M. Steele, Journal for the History of Astronomy, August, 2013)

The available corpus of Babylonian texts concerning mathematical astronomy consists of about 440 tablets, dating roughly between 450 and 50 BC. very readable photographs of the tablets are provided. this book will allow scholars with an inclination toward mathematics, and an interest in the history of science in antiquity, to be in contact with its raw products without having to devote their entire lives to such study. (Bruno Poizat, Mathematical Reviews, April, 2013)

Preface vii
Acknowledgements viii
Abbreviations and symbols xviii
Bibliographical abbreviations xviii
Assyriological abbreviations xix
Astronomical abbreviations and symbols xxi
Names of the planets, zodiacal signs, months, regnal years and units xxv
1 Procedure texts
1(16)
1.1 The corpus of mathematical astronomy
1(4)
1.1.1 History
1(1)
1.1.2 Purpose and applications
2(1)
1.1.3 Discovery and historiography
3(2)
1.2 Selection of the texts
5(1)
1.3 Archaeological and archival aspects
6(4)
1.3.1 Babylon
6(2)
1.3.2 Uruk
8(2)
1.4 Physical characteristics
10(2)
1.5 Transmission and evolution
12(1)
1.6 Approaching procedure texts
12(3)
1.6.1 Translation issues
13(1)
1.6.2 Procedure texts and `scientific discourse'
14(1)
1.7 Didactical, rhetorical and comparative aspects
15(2)
1.7.1 Rhetorical aspects
15(1)
1.7.2 Other Mesopotamian instructional texts from the first millennium BC
16(1)
2 Mathematical concepts - from numbers to computational systems
17(38)
2.1 The sexagesimal place-value system
17(2)
2.2 Arithmetical operations
19(8)
2.2.1 Identity of quantities and symmetry of operations
19(1)
2.2.2 Addition
19(1)
2.2.2.1 `To add'
20(1)
2.2.2.2 `To append'
21(1)
2.2.2.3 `To accumulate'
21(1)
2.2.3 Subtraction
22(1)
2.2.3.1 `To tear out'
22(1)
2.2.3.2 `To subtract'
22(1)
2.2.3.3 `To diminish'
23(1)
2.2.3.4 `To deduct'
24(1)
2.2.4 Multiplication
24(1)
2.2.4.1 `To go Q1 times Q2'
24(1)
2.2.4.2 `To raise'
25(1)
2.2.5 Division and reciprocals
25(1)
2.2.6 The copula u, `and', as a placeholder for arithmetical operations
26(1)
2.2.7 Diachronic overview of arithmetical terms and a comparison with mathematical texts
26(1)
2.3 Other elementary operations
27(2)
2.3.1 Introducing initial data
27(1)
2.3.2 Conditions
28(1)
2.3.2.1 Conditions involving a threshold value
28(1)
2.3.2.2 Conditions involving the change of a quantity or the relative position
28(1)
2.3.3 Coordination
29(1)
2.4 Additive and subtractive numbers
29(3)
2.5 Coordinate systems
32(3)
2.5.1 The event frame
32(1)
2.5.2 Temporal coordinates
32(1)
2.5.2.1 The calendar
32(1)
2.5.2.2 Time degrees
32(1)
2.5.2.3 Mean tithis
33(1)
2.5.3 Angular coordinates
33(1)
2.5.3.1 Zodiacal position (B)
33(1)
2.5.3.2 Distance to the ecliptic (E)
34(1)
2.6 Procedures and algorithms
35(19)
2.6.1 Composite procedures and subprocedures
35(1)
2.6.2 Initial and final statements of a procedure
35(1)
2.6.3 Procedures as verbal representations of algorithms
36(1)
2.6.3.1 Example-based and abstract formulation
36(1)
2.6.3.2 Deficient procedures
37(1)
2.6.4 Representing procedures, algorithms and functions
37(1)
2.6.4.1 Columns, functions and parameters
37(1)
2.6.4.2 Template procedures
37(1)
2.6.4.3 Formulaic and graphical representations
38(1)
2.6.4.4 Flow charts
39(1)
2.6.5 Purposes of the algorithms
39(1)
2.6.5.1 Computing or updating a function
39(1)
2.6.5.2 Verification
40(1)
2.6.5.3 Theoretically oriented procedures
40(1)
2.6.6 The basic period relation of a function
40(1)
2.6.7 Interpolation
40(2)
2.6.8 Zigzag functions of the event number
42(1)
2.6.8.1 Templates and algorithm
42(2)
2.6.8.2 Period relations
44(1)
2.6.8.3 Elementary steps
45(1)
2.6.8.4 Net differences for intervals longer than 1 synodic cycle
46(1)
2.6.8.5 Checking rule for function values on opposite branches
46(1)
2.6.8.6 Empirical aspects and the construction of a zigzag function
46(1)
2.6.9 Zigzag functions of the zodiacal position
47(1)
2.6.10 Step functions for the synodic arc
47(1)
2.6.10.1 Updating the zodiacal position with a step function for the synodic arc
48(3)
2.6.10.2 Period relation and mean synodic arc
51(1)
2.6.10.3 Elementary steps
51(1)
2.6.10.4 Net displacements for intervals longer than 1 synodic cycle
52(2)
2.7 Computational systems
54(1)
3 Planets
55(56)
3.1 Planetary phenomena
55(3)
3.1.1 Apparent motion
55(1)
3.1.2 Synodic phenomena
56(2)
3.2 Composition of the tablets
58(1)
3.3 Algorithms for the planets
58(10)
3.3.1 Algorithms for the zodiacal position (B)
59(1)
3.3.1.1 Updating B with the synodic arc (σ)
59(1)
3.3.1.2 Total synodic arc (Σ)
59(1)
3.3.1.3 Solar-distance principle
60(1)
3.3.1.4 Period relations and mean synodic arc
60(1)
3.3.1.5 Net displacements for various intervals
61(1)
3.3.2 Algorithms for the time (T)
61(1)
3.3.2.1 Updating T with the synodic time (τ)
61(2)
3.3.3 Subdivision of the synodic cycle
63(1)
3.3.3.1 Pushes and daily displacements
63(2)
3.3.3.2 Subdivisions involving constant values of the daily displacement
65(2)
3.3.3.3 Angular pushes between primary phenomena in type-A systems
67(1)
3.3.3.4 Interpolation schemes for v
67(1)
3.3.4 Distance to the ecliptic
68(1)
3.4 Mercury
68(7)
3.4.1 Synodic cycle
68(1)
3.4.2 System A1
69(1)
3.4.2.1 Updating B with the synodic arc
69(1)
3.4.2.2 Updating T with the synodic time
69(1)
3.4.2.3 Subdivision of the synodic cycle
70(1)
3.4.2.4 Omitted phenomena
70(1)
3.4.2.5 Net displacements for various intervals
71(1)
3.4.3 System A2
71(1)
3.4.3.1 Updating B with the synodic arc
71(1)
3.4.3.2 Updating T with the synodic time
72(1)
3.4.3.3 Subdivision of the synodic cycle
72(1)
3.4.3.4 Net displacements for various intervals
73(1)
3.4.4 System A3
73(1)
3.4.4.1 Updating B with the synodic arc
73(1)
3.4.4.2 Updating B with the net displacement for 3 cycles
74(1)
3.4.4.3 Net displacements for other intervals
74(1)
3.4.4.4 Updating T with the synodic time
75(1)
3.4.4.5 Subdivision of the synodic cycle
75(1)
3.4.5 Unidentified computational systems
75(1)
3.5 Venus
75(8)
3.5.1 Synodic cycle
75(1)
3.5.2 System A0
75(1)
3.5.2.1 Updating B with the synodic arc
76(1)
3.5.2.2 Updating T with the synodic time
76(1)
3.5.2.3 Net displacements for various intervals
76(1)
3.5.3 System A3
76(1)
3.5.3.1 Updating B with the synodic arc
76(1)
3.5.3.2 Net displacements for various intervals
77(1)
3.5.4 Systems A1 and A2
77(1)
3.5.4.1 Updating B with the synodic arc
77(1)
3.5.4.2 Net displacements for various intervals
78(1)
3.5.4.3 Updating T with the synodic time
79(1)
3.5.4.4 Subdivision of the synodic cycle
79(1)
3.5.5 System C3
79(1)
3.5.5.1 Updating B and T
79(1)
3.5.5.2 Subdivision of the synodic cycle
79(1)
3.5.6 System C4
80(1)
3.5.6.1 Updating B and T
80(1)
3.5.6.2 Subdivision of the synodic cycle
80(1)
3.5.7 Unidentified computational systems
80(1)
3.5.7.1 Subdivision of the synodic cycle
80(3)
3.6 Mars
83(6)
3.6.1 Synodic cycle
83(1)
3.6.2 System A
83(1)
3.6.2.1 Updating B with the synodic arc
83(1)
3.6.2.2 Updating T with the synodic time
84(1)
3.6.2.3 Subdivision of the synodic cycle
84(4)
3.6.2.4 Net displacements for various intervals
88(1)
3.6.3 System B
89(1)
3.6.3.1 Updating B and T
89(1)
3.7 Jupiter
89(17)
3.7.1 Synodic cycle
89(1)
3.7.2 System A
90(1)
3.7.2.1 Composition of the tablets
90(1)
3.7.2.2 Updating B with the synodic arc
90(1)
3.7.2.3 Updating T with the synodic time
91(1)
3.7.2.4 Net displacements for various intervals
91(1)
3.7.2.5 Rising time at FA and setting time at LA
91(1)
3.7.2.6 Subdivision of the synodic cycle
92(3)
3.7.3 Systems A1 and A2
95(1)
3.7.3.1 Updating B with the synodic arc
95(1)
3.7.3.2 Subdivision of the synodic cycle
95(1)
3.7.4 System A'
96(1)
3.7.4.1 Updating B with the synodic arc
96(1)
3.7.4.2 Updating T with the synodic time
96(1)
3.7.4.3 Subdivision of the synodic cycle
97(1)
3.7.4.4 Net displacements for various intervals
97(1)
3.7.5 System A"
98(1)
3.7.5.1 Updating B with the synodic arc
98(1)
3.7.6 System A"'
98(1)
3.7.6.1 Updating B with the synodic arc
99(1)
3.7.6.2 Setting time at LA and rising time at FA
99(1)
3.7.7 System A6
99(1)
3.7.7.1 Updating B with the synodic arc
99(1)
3.7.7.2 Net displacements for various intervals
99(1)
3.7.8 System B
100(1)
3.7.8.1 Updating B with the synodic arc
100(1)
3.7.8.2 Updating T with the synodic time
100(1)
3.7.8.3 Algorithm involving τ and Π
101(1)
3.7.9 System B'
101(1)
3.7.9.1 Updating B with the synodic arc, T with the synodic time
101(1)
3.7.9.2 Net differences for various intervals
102(1)
3.7.10 Unidentified computational systems
102(1)
3.7.10.1 Subdivision of the synodic cycle
102(3)
3.7.10.2 Distance to the ecliptic
105(1)
3.7.10.3 Procedures involving trapezoids
106(1)
3.8 Saturn
106(5)
3.8.1 Synodic cycle
106(1)
3.8.2 System A
106(1)
3.8.2.1 Updating B with the synodic arc
107(1)
3.8.2.2 Updating T with the synodic time
107(1)
3.8.2.3 Net displacements for various intervals
107(1)
3.8.2.4 Subdivision of the synodic cycle
108(1)
3.8.3 System A'
108(1)
3.8.4 Systems B, B' and B"
108(1)
3.8.4.1 Updating B and T
109(2)
4 Moon
111(92)
4.1 Lunar phenomena
111(4)
4.1.1 Apparent motion
111(1)
4.1.2 Lunations
112(1)
4.1.3 Eclipses
113(1)
4.1.4 Lunar Six intervals
113(2)
4.2 Lunar systems K, A and B
115(1)
4.3 System K
116(5)
4.3.1 Zodiacal position of the Moon (B)
116(1)
4.3.2 Duration of the night (D)
117(1)
4.3.3 The Moon's distance to the ecliptic? (E)
117(1)
4.3.4 Duration of the synodic month (G)
117(1)
4.3.5 Time of the lunation (M)
118(1)
4.3.6 Lunar Six intervals
119(1)
4.3.6.1 Step
1. Preliminary monthly difference d1
119(1)
4.3.6.2 Step
2. Optional subtractive correction d2 corresponding to a shift by 1d
120(1)
4.3.6.3 Step
3. Correction d3 involving M and D
121(1)
4.3.6.4 Step
4. Correction d4 involving E
121(1)
4.4 System A
121(57)
4.4.1 Composition of the tablets
122(1)
4.4.2 Algorithms for lunar system A
123(1)
4.4.2.1 Algorithms for the synodic tables, template tables and eclipse tables
123(1)
4.4.2.2 Algorithms for the daily motion tables
124(1)
4.4.2.3 Other algorithms for lunar system A
124(1)
4.4.3 Duration of 223 synodic months (Φ)
125(3)
4.4.4 Zodiacal position of the Moon (B)
128(2)
4.4.5 Duration of day (C) and night (D)
130(3)
4.4.6 Distance to the ecliptic (E)
133(6)
4.4.7 Eclipse magnitude (Ψ)
139(2)
4.4.8 Eclipse magnitude (Ψ')
141(2)
4.4.9 The Moon's daily displacement along the zodiac (F)
143(2)
4.4.10 The Sun's daily displacement along the zodiac (ν)
145(1)
4.4.11 Duration of the synodic month (G)
145(7)
4.4.12 Duration of 6 synodic months (W)
152(1)
4.4.13 Duration of 12 synodic months (Λ)
153(2)
4.4.14 Zodiacal correction to G (J)
155(1)
4.4.15 Zodiacal correction to W (Z)
156(1)
4.4.16 Zodiacal correction to Λ (Y)
157(1)
4.4.17 Monthly, 6-monthly and 12-monthly differences of the time of the lunation (K, K(6), K)
158(1)
4.4.18 Time of the lunation (M, M(6), M)
159(2)
4.4.19 Lunar Six intervals
161(2)
4.4.19.1 Step
1. Time interval between lunation and Lunar Six event (N)
163(2)
4.4.19.2 Step
2. Zodiacal displacement of the Moon (ΔB) and the Sun (ΔB)
165(1)
4.4.19.3 Step
3. Elongation of the Moon (η)
166(1)
4.4.19.4 Step
4. Zodiacal position of the Moon (B'D) and the Sun (B') at the Lunar Six event
167(1)
4.4.19.5 Step
5. Coefficient `for the zodiac' (q')
168(1)
4.4.19.6 Step
6. Moon's distance to the ecliptic at the Lunar Six event (β'
169(1)
4.4.19.7 Step
7. Coefficient `for height and depth' (r')
170(2)
4.4.19.8 Step
8. Contribution to Lunar Six resulting from Moon's distance to ecliptic (R)
172(1)
4.4.19.9 Step
9. Contribution to the Lunar Six resulting from the lunar elongation (Q)
172(1)
4.4.19.10 Step
10. Disk correction (Δ)
173(1)
4.4.19.11 Step
11. Assembling the Lunar Six interval
174(1)
4.4.19.12 Step
12. Optional renaming of SU2, NA, ME or GI6
175(3)
4.4.19.13 Step
13. Optional shift of the Lunar Six event by 1d
178(1)
4.5 System B
178(25)
4.5.1 Composition of the tablets
178(1)
4.5.2 Algorithms for lunar system B
179(1)
4.5.2.1 Algorithms for synodic tables, template tables and eclipse tables
179(1)
4.5.2.2 Algorithms for the daily motion tables
179(1)
4.5.2.3 Other algorithms
180(1)
4.5.3 Synodic arc of the Moon and the Sun (A)
180(1)
4.5.4 Zodiacal position of the Moon (B) and the Sun (B)
181(1)
4.5.5 Duration of daylight (C) and night (D)
182(1)
4.5.6 The Moon's distance to the ecliptic (E)
183(1)
4.5.7 Eclipse magnitude (Ψ")
183(2)
4.5.8 Monthly difference of eclipse magnitude (ΔΨ')
185(1)
4.5.9 Eclipse magnitude (Ψ)
186(2)
4.5.10 The Moon's displacement along the zodiac per day (F) or time degree (F')
188(1)
4.5.11 The Sun's daily displacement along the zodiac (ν)
189(1)
4.5.12 Duration of the synodic month (G)
190(1)
4.5.13 Monthly difference of J (H)
191(1)
4.5.14 Correction to the synodic month (J)
192(1)
4.5.15 Corrected duration of the synodic month (K)
193(1)
4.5.16 Time of the lunation with respect to the preceding midnight (L)
193(1)
4.5.17 Time of the lunation with respect to sunrise or sunset (M)
194(1)
4.5.18 Lunar Six intervals
195(1)
4.5.18.1 Step
1. Time interval between lunation and Lunar Six event (N)
196(2)
4.5.18.2 Step
2. Zodiacal displacement of the Moon (ΔB) and the Sun (ΔB)
198(1)
4.5.18.3 Step
3. Corrected elongation of the Moon (O)
199(1)
4.5.18.4 Step
4. Zodiacal position of the Moon (B) and the Sun (B) at the Lunar Six event
199(1)
4.5.18.5 Step
5. Coefficient `for the zodiac' (q)
200(1)
4.5.18.6 Step
6. Moon's distance to the ecliptic (β)
200(1)
4.5.18.7 Step
7. Coefficient `for height and depth' (r)
200(1)
4.5.18.8 Step
8. Contribution to Lunar Six resulting from Moon's distance to ecliptic (R)
201(1)
4.5.18.9 Step
9. Contribution to Lunar Six resulting from the Moon's elongation (Q)
201(1)
4.5.18.10 Step
11. Assembling the Lunar Six interval
201(1)
4.5.18.11 Step
12. Optional renaming of SU2, NA, ME or GI6
202(1)
4.5.18.12 Step
13. Optional shift of the Lunar Six event by 1d
202(1)
5 Critical editions
203(320)
5.1 Conventions and notation
203(4)
5.1.1 Transliterations
203(2)
5.1.2 Translations
205(1)
5.1.3 Critical and philological notes and commentaries
206(1)
5.2 Planets
207(137)
5.2.1 Mercury
207(1)
No. 1 (ACT 820a) System A1: various procedures
207(2)
No. 2 Systems A1, A2: various procedures
209(3)
No. 3 System A2?: updating B with the synodic arc?
212(1)
No. 4 System A2: various procedures
213(1)
No. 5 (ACT 816) System A3: updating B; net displacements
214(3)
No. 6 (ACT 800) Unknown system: various procedures
217(2)
5.2.2 Venus
219(1)
No. 7 (ACT 821b) Systems A1 and A2: various procedures
219(3)
No. 8 (ACT 421a) System A2?: various procedures
222(2)
No. 9 System C3: subdivision of the synodic cycle
224(2)
No. 10 (ACT 824) System A3: net displacements
226(1)
No. 11 (ACT 815) Unknown system: various procedures
227(1)
5.2.3 Mars
228(1)
No. 12 (ACT 803) System A: subdivision of the synodic cycle
228(2)
No. 13 (ACT 811a) System A and B: various procedures
230(7)
No. 14 System A: various procedures
237(5)
No. 15 (ACT 821aa) System A: various procedures
242(2)
No. 16 (ACT 811b) Various procedures
244(3)
5.2.4 Jupiter
247(1)
No. 17 (ACT 820aa) System A: updating B and T
247(1)
No. 18 (ACT 813) Systems A, A1, A2, A', A,", A"', B, and B': various procedures
248(17)
No. 19 (ACT 813a) System A, other (?): various procedures
265(2)
No. 20 (ACT 823a) System A': various procedures
267(1)
No. 21 (ACT 813b) Systems A, A"', unknown system: various procedures
268(2)
No. 22 Unknown system, system A: various procedures
270(2)
No. 23 (ACT 814) Systems A and A': various procedures
272(3)
No. 24 (ACT 823) System B: updating B and T
275(1)
No. 25 System A: various procedures
276(2)
No. 26 System A: various procedures
278(1)
No. 27 (ACT 819b) System A: subdivision of the synodic cycle, scheme S1
279(2)
No. 28 (ACT 821) System A: updating B and T
281(1)
No. 29 Systems A, A' (?) and A": various procedures
282(2)
No. 30 Systems A, A", unidentified system: various procedures
284(2)
No. 31 (ACT 805) Systems A', B: various procedures
286(2)
No. 32 (ACT 810) System A': various procedures
288(3)
No. 33 (ACT 820) System B': various procedures
291(1)
No. 34 (ACT 818) System A': various procedures
292(2)
No. 35 (ACT 822) System A': updating B and T
294(2)
No. 36 (ACT 821a) System B: updating T and B
296(2)
No. 37 System B: updating B and T
298(2)
No. 38 (ACT 817) Unknown system: various procedures
300(4)
No. 39 (ACT 819a) Unknown system: subdivision of the synodic cycle
304(3)
No. 40 Unknown system: various procedures
307(2)
5.2.5 Saturn
309(1)
No. 41 (ACT 802) Systems A, B, B": various procedures
309(3)
5.2.6 Mixed content
312(1)
No. 42 (ACT 801) Mercury system A1; Saturn system A: various procedures
312(4)
No. 43 Mercury, unknown system; Mars system A: various procedures
316(4)
No. 44 (ACT 811) Jupiter A6, Saturn A, Mars A: various procedures
320(3)
No. 45 (ACT 819c) Saturn system A, B: period relations
323(1)
No. 46 (ACT 812) Jupiter systems A', B; Venus systems X, A0: various procedures
324(10)
No. 47 Jupiter, Saturn and Mars: unidentified systems; various procedures
334(2)
5.2.7 Unidentified planets
336(1)
No. 48 Outer planet: various procedures
336(3)
No. 49 Mercury or Venus: various procedures
339(2)
No. 50 A planet: various procedures
341(2)
No. 51 A planet: various procedures
343(1)
5.3 Moon
344(179)
5.3.1 System K
344(1)
No. 52 Various procedures
344(14)
5.3.2 System A
358(1)
No. 53 (ACT 200+200aa) Various procedures
358(21)
No. 54 (ACT 200e) Computations involving E
379(1)
No. 55 (ACT 200a) Various procedures
380(2)
No. 56 (ACT 200b) Various procedures
382(4)
No. 57 (ACT 200c) Updating E
386(2)
No. 58 (ACT 200d) Various procedures
388(2)
No. 59 (ACT 200f) Various procedures
390(2)
No. 60 (ACT 200i) Various procedures
392(3)
No. 61 (ACT 200i, 201, 201a, 201aa) Lunar Six intervals
395(26)
No. 62 (ACT 200aa) Various procedures
421(2)
No. 63 (ACT 203) Procedures involving Φ
423(2)
No. 64 Computing G from Φ
425(1)
No. 65 (ACT 204) Various procedures
426(6)
No. 66 (ACT 204a) Various procedures
432(2)
No. 67 (ACT 205) Computing G from Φ
434(2)
No. 68 (ACT 206) Computing G from Φ
436(2)
No. 69 (ACT 207a) Computing G from Φ
438(2)
No. 70 (ACT 207b) Computing G from Φ
440(2)
No. 71 (ACT 207c) Computing G from Φ
442(2)
No. 72 (ACT 207ca) Computing G from Φ
444(4)
No. 73 (ACT 207cb) Computing G from Φ
448(2)
No. 74 (ACT 207cc) Computing G from Φ
450(3)
No. 75 Computing G from Φ?
453(1)
No. 76 Computing G from Φ?
454(2)
No. 77 (ACT 208) Computing G from F
456(1)
No. 78 Subject unclear
457(1)
No. 79 (ACT 207d) Various procedures
458(7)
No. 80 Computations involving eclipse magnitude
465(1)
No. 81 (ACT 207e) Computing A from Φ
466(4)
No. 82 (`Saros Text') Various procedures involving Φ and G
470(8)
No. 83 Computations involving F
478(3)
No. 84 Computing G from Φ
481(1)
No. 85 Computing G from Φ
482(1)
No. 86 Various procedures
483(1)
No. 87 Computing A from Φ
484(2)
No. 88 (ACT 207) Computing W from Φ
486(1)
No. 89 Computing W from Φ
487(1)
No. 90 Computing W from Φ
488(1)
No. 91 Interpolation scheme
489(1)
No. 92 Various procedures
490(2)
5.3.3 System B
492(1)
No. 93 (ACT 202) Various procedures
492(3)
No. 94 (ACT 221) Computations involving F
495(1)
No. 95 (ACT 210) Various procedures for the Moon, Jupiter (?) and Saturn
496(6)
No. 96 (ACT 211) Various procedures
502(4)
No. 97 Various procedures
506(6)
5.3.4 Unidentified systems
512(1)
No. 98 (ACT 200h) Eclipses
512(1)
No. 99 (ACT 200g) Eclipses
513(2)
No. 100 Eclipses
515(2)
No. 101 Computations involving a solar quantity
517(1)
No. 102 Various procedures
518(5)
Appendices
523(72)
A Other instructional texts from the first millennium BC
523(2)
B Mean values of the synodic time and the synodic arc for the Moon and the planets
525(2)
C Multiple transitions of the zonal boundaries of a step function for the synodic arc
527(2)
D Interpolation schemes for lunar system A
529(4)
D.1 Interpolation scheme for computing W from Φ
529(2)
D.2 Interpolation scheme for computing A from Φ
531(2)
E Rising and setting times
533(6)
E.1 Rising or setting time of a short arc near the ecliptic
533(2)
E.2 Effects of refraction and use of disk rims on rising and setting times
535(1)
E.3 Contributions to the disk correction in lunar system A
535(2)
E.4 Temporal order of the Lunar Six intervals near Full Moon
537(2)
F Photographs of the cuneiform tablets
539(56)
Glossary
595(8)
Akkadian glossary
595(4)
Sumerograms and Akkadian abbreviations
599(4)
Bibliography
603(6)
Indices
609
Index of tablets and fragments
609(1)
Concordance with ACT
610(1)
Name index
611(1)
Subject index
612
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