User:Jccsvq/sandbox

Tempo

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

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

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

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	18	8	0	0	1					9	9	9

Diagrams 2

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

First 3 digits of ${\sqrt {456.7890123}}$ 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 pairs
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 ${\sqrt {456.7890123}}$ 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 pairs
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

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...

Article text more text more text .

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Notes

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

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