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E-raamat: Magic Squares in the Tenth Century: Two Arabic Treatises by Antaki and Buzjani

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Magic Squares in the Tenth Century: Two Arabic Treatises by Antaki and BuzjaniSuurem pilt
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This volume contains the texts and translations of two Arabic treatises on magic squares, which are undoubtedly the most important testimonies on the early history of that science. It is divided into the three parts: the first and most extensive is on tenth-century construction methods, the second is the translations of the texts, and the third contains the original Arabic texts, which date back to the tenth century. 

Arvustused

The inclusion of the original Arabic texts together with the translations and the accompanying commentary make this book a very valuable source for historians of mathematics. (Shahriar Shahriar, Mathematical Reviews, April, 2018)

Part I Tenth-century construction methods
Introduction
3(1)
§1 General notions on magic squares
3(6)
§2 The two texts from the tenth century
9(10)
A Text A
9(1)
1 Author and manuscript
9(2)
2 The Introduction to Arithmetic by Nicomachos
11(2)
3 Contents of text A
13(3)
B Text B
16(3)
Chapter I Ordinary magic squares
19(24)
§1 Construction of odd-order squares
20(6)
A Particular case of order 3
20(1)
1 Uniqueness of the square of order 3
20(1)
2 Construction of the square of order 3 `by displacement'
20(1)
3 A Construction `Without Displacement'
21(1)
B Square of order 5
21(2)
C Later developments
23(3)
§2 Construction of even-order squares
26(17)
A Square of order 4
26(1)
1 Constructions by displacement
26(1)
2 A Construction Without Displacement
27(3)
B Square of order 6
30(1)
C Square of order 8
31(1)
D Allusion to a generalization
31(1)
1 Evenly even orders
32(2)
2 Evenly odd orders
34(2)
E Later developments
36(1)
1 Equalization rules
36(1)
2 Case of evenly even orders
37(3)
3 Case of evenly odd orders
40(3)
Chapter II Bordered magic squares
43(24)
§1 Construction of odd-order bordered squares
43(8)
A Empirical discovery of a method
43(1)
1 Square of order 5
43(3)
2 Higher odd-order squares
46(2)
B Description of the general method
48(1)
C Mathematical basis for this method
49(2)
§2 Construction of even-order bordered squares
51(16)
A Construction of bordered squares of evenly even orders
51(1)
1 Description of the method in A and B
51(2)
2 Description of the general method
53(1)
3 Mathematical basis for this method
54(1)
(α) General theory
54(4)
(β) The tenth-century method
58(1)
B Construction of bordered squares of evenly odd orders
59(1)
1 Particular case of order 6
59(2)
2 Description of a general method in A
61(1)
3 Other description of the general method
61(1)
4 Mathematical basis for this method
62(5)
Chapter III Separation by parity
67(37)
§1 Structure of the rhomb according to B
67(2)
A The rows of the rhomb
67(1)
B Largest square within the rhomb
68(1)
§2 The partially empirical construction of B
69(3)
§3 Filling the rhomb according to A
72(2)
§4 Placing the even numbers around the rhomb
74(30)
A Situation after filling the rhomb
74(1)
1 Determining the number of remaining empty cells
74(1)
2 Determining the sum required
75(3)
B Rules for placing the even numbers
78(7)
C Case of the order n = 4t + 1 (with t ≥ 2)
85(1)
1 First border
85(1)
2 Other borders
86(4)
3 Recapitulation
90(2)
4 Completing the construction
92(3)
D Case of the order n = 4t + 3 (with t ≥ 1)
95(1)
1 First border
95(1)
2 Other borders
95(4)
3 Recapitulation
99(2)
4 Completing the construction
101(1)
E Particular case of order 5
102(2)
Chapter IV Composite magic squares
104(13)
§1 Subsquares having same size and unequal sums
104(3)
§2 Subsquares having same size and equal sums
107(1)
§3 Parts having different sizes
108(9)
A Method of the cross
108(5)
B Method of the central square
113(4)
Part II Translation
Editorial procedure
117(2)
Text A
119(88)
Chapter I Of Book III
120(23)
Chapter II Science of the magic square
143(1)
§1 Science of odd-order (squares)
143(21)
§2 Science of even-order (squares)
164(6)
Composite magic squares
170(10)
Chapter III Determining the hidden number
180(27)
Text B
207(46)
(Introduction)
208(2)
(Construction of ordinary magic squares)
210(12)
(Construction of bordered magic squares)
222(18)
(Particular cases of odd-order squares)
240(10)
(Particular cases of even-order squares)
250(3)
Opuscule on the magic square by al-Kharaqi
253(4)
Part III Arabic texts
Editorial procedure
257(2)
Text A
259(76)
Chapter I Of Book III
262(20)
Chapter II Science of the magic square
282(1)
§1 Science of odd-order (squares)
282(17)
§2 Science of even-order (squares)
299(4)
Composite magic squares
303(13)
Chapter III Determining the hidden number
316(19)
Text B
335(48)
(Introduction)
335(2)
(Construction of ordinary magic squares)
337(12)
(Construction of bordered magic squares)
349(19)
(Particular cases of odd-order squares)
368(10)
(Particular cases of even-order squares)
378(5)
Opuscule on the magic square by al-Kharaqi
383(2)
Bibliography 385(4)
Index 389
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