User:Jccsvq/sandbox

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Tempo[edit | edit source]

137/2
 ABCD
 --+-
 137
   7
  +35
  3
 +15
 1
+05
 --+-
 0685
68.5
137/4
 ABCDE
 --+--
 137
   7
  +175
  3
 +075
 1
+025
 --+--
 03425
34.25
137/8
 ABCDEF
 --+---
 137
   7
  +0875
  3
 +0375
 1
+0125
 --+---
 017125
17.125
137/16
 ABCDEF
 --+---
 137
   7
  +4375
  3
 +1875
 1
+0625
 -+----
 085625
8.5625
137/32
 ABCDEFG
 --+----
 137
   7
  +21875
  3
 +09375
 1
+03125
 -+-----
 0428125
4.28125
137/64
 ABCDEFGH
 --+-----
 137
   7 Borrar 7 en C
  +109375
  3 Borrar 3 en B
 +046875
 1 Borrar 1 en A
+015625
 -+------
 02140625
2.140625
"+" indica la posición de la columna unidad antes y después de la operación.

1-digit Addition/Subtraction types[edit | edit source]

1-digit addition: type 1-digit subtraction: type
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
+1 1 1 1 1 2 1 1 1 1 3 -1 3 1 1 1 1 2 1 1 1 1
+2 1 1 1 2 2 1 1 1 3 3 -2 3 3 1 1 1 2 2 1 1 1
+3 1 1 2 2 2 1 1 3 3 3 -3 3 3 3 1 1 2 2 2 1 1
+4 1 2 2 2 2 1 3 3 3 3 -4 3 3 3 3 1 2 2 2 2 1
+5 1 1 1 1 1 3 3 3 3 3 -5 3 3 3 3 3 1 1 1 1 1
+6 1 1 1 1 3 3 3 3 3 3 -6 3 3 3 3 3 3 1 1 1 1
+7 1 1 1 3 3 3 3 3 3 3 -7 3 3 3 3 3 3 3 1 1 1
+8 1 1 3 3 3 3 3 3 3 3 -8 3 3 3 3 3 3 3 3 1 1
+9 1 3 3 3 3 3 3 3 3 3 -9 3 3 3 3 3 3 3 3 3 1
0 1 2 3 4 5 6 7 8 9
+1 1 1 1 1 2 1 1 1 1 3
+2 1 1 1 2 2 1 1 1 3 3
+3 1 1 2 2 2 1 1 3 3 3
+4 1 2 2 2 2 1 3 3 3 3
+5 1 1 1 1 1 3 3 3 3 3
+6 1 1 1 1 3 3 3 3 3 3
+7 1 1 1 3 3 3 3 3 3 3
+8 1 1 3 3 3 3 3 3 3 3
+9 1 3 3 3 3 3 3 3 3 3


0 1 2 3 4 5 6 7 8 9
-1 3 1 1 1 1 2 1 1 1 1
-2 3 3 1 1 1 2 2 1 1 1
-3 3 3 3 1 1 2 2 2 1 1
-4 3 3 3 3 1 2 2 2 2 1
-5 3 3 3 3 3 1 1 1 1 1
-6 3 3 3 3 3 3 1 1 1 1
-7 3 3 3 3 3 3 3 1 1 1
-8 3 3 3 3 3 3 3 3 1 1
-9 3 3 3 3 3 3 3 3 3 1
q1 d1
10000 1109889
20000 739889
30000 369889
40000 -111
50000 -370111
60000 -740111
70000 -1110111
80000 -1480111
90000 -1850111

SANGA[edit | edit source]

Proto-Cuneiform tablet: administrative account of barley distribution with cylinder seal impression of a male figure, hunting dogs, and boars. Probably from the city of Uruk. Jemdet-Nasr period circa 3100 –2900 BCE

"SANGA" character.

The "SANGA" character is believed to be a pictorial representation of a Sumerian abacus.


Woods, Christopher (2017), "The Abacus in Mesopotamia: Considerations from a Comparative Perspective", The First Ninety Years: A Sumerian Celebration in Honor of Miguel Civil, De Gruiter, ISBN 9781501511738 {{citation}}: Unknown parameter |editor1first= ignored (|editor-first1= suggested) (help); Unknown parameter |editor1last= ignored (|editor-last1= suggested) (help); Unknown parameter |editor2first= ignored (|editor-first2= suggested) (help); Unknown parameter |editor2last= ignored (|editor-last2= suggested) (help); Unknown parameter |editor3first= ignored (|editor-first3= suggested) (help); Unknown parameter |editor3last= ignored (|editor-last3= suggested) (help)

Diagrams[edit | edit source]

Write caption here!
A B C D E F G H I
T T T T T T T T 1


Write caption here!
A B C D E F G H I K J L M
9 18 9 0 0 1 0 0 0 0 9 9 9


5+2 abacus number representation
A B C D E F G H I J K L
0 1 2 3 4 5 5 6 7 8 9 10
5+2 abacus number representation (cont.)
A B C D E F G H I J K L
10 11 12 13 14 15 15 16 17 18 19 20
Starting division 998001÷999
A B C D E F G H I J K L M
9 9 8 0 0 1 9 9 9
Just after applying division rule 9/9>9+9
A B C D E F G H I J K L M
9 18b 8 0 0 1 9 9 9

Diagrams 2[edit | edit source]

A A
 A + 1 =  
4 5


text

A B A B
 B + 1 =  
0 9 1 0
Write caption here!
A B A B
 B+5 = 
4 6 F 1

text

Write caption here!
A B A B
 B + 5 = 
9 6 T 1

text

Tables[edit | edit source]

First 3 digits of preparing the dividend
Abacus Comment
ABCDEFGHIJKL
 4567890123 Enter x aligning digit pairs from AB, CD, etc.
-4 Subtracting 2^2 from first group
  567890123
  2839450615 Halving remainder and rest of digits pairsa
2 2839450615 Entering first root digit in A
21 Dividing BCD by A
 -2
  -05 Subtracting B^2/2=0.5 from CDE
21 789450615
213789450615 Dividing CDEF by AB
  -6
   -3
    -45 Subtracting C^2/2=4.5 from CEFG
213154950615
    etc.

^a as explained in Chapter: [[../../Division/Division by powers of two/|Division by powers of two]].


First 3 digits of preparing the dividend
Abacus Comment
ABCDEFGHIJKL
 4567890123 Enter x aligning digit pairs from AB, CD, etc.
-4 Subtracting 2^2 from first group
  567890123
  2839450615 Halving remainder and rest of digits pairsa
2 2839450615 Entering first root digit in A
21 Dividing BCD by A
 -2
  -05 Subtracting B^2/2=0.5 from CDE
21 789450615
213789450615 Dividing CDEF by AB
  -6
   -3
    -45 Subtracting C^2/2=4.5 from CEFG
213154950615
    etc.

Contributors[edit | edit source]

User Jccsvq (discuss•contribs) has contributed the base or initial text of this book by adapting some of his writings from his personal website jccAbacus.

Testing notes...[edit | edit source]

Article texta more textb more text c.

  • Bulleted textb
  • Bulleted textc.

(intervening text...)

Notes[edit | edit source]

  • ^a Text for note a.
  • ^b Text for note b.
  • ^c Text for note c (with extended highlighting).
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