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-
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11207 = 1; 3, 30. , , , 83 1 : 8 = 0; 7, 30 ( ; ) , , 3 0; 22, 30.
a : b , ( , ): b-1 a. , - . . , . , , 360 , 60 1 60 (Burton, 1991).
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-
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-
7/24 : 7/24 = 4+3/24 = 4/24 + 3/24 = 1/6 +1/8.
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0.25 1/5 = 0.20. , , , . , , ., : 7/24 , 1/3 , , 1/5 , 1/6 , 1/7 ,
...
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TO MATI TOY
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1 = 2/3 .
1/3 1/3 .
1 = 1/20 .
. :
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:
35 38 Rhind hekat.
35 :
: hekat. 1/3 hekat. ;
-
[, - 1/3 , hekat. : 3 + 1/3 = 1. ; ( ;) ]
1 3 1/3 ( 3 1/3 1.
1 3 1/3.
1 3 1/3 3 1/3 3 1/3. 1/10 1/3 1/10 3 1/3 1/3. 1/5 1/3 1/5 3 1/3
2/3. 5 1/10 1 1/5 1/10
1 1/5 1/10 1/5 1/10 1/5 1/10.
2 1/10 1/5 1/10 1/10.
3 10 1/3 1/5 1/10 1/10.
3 1/3 1 3 1/3 1/5 1/10 1.
1/5 1/10 hekat 1/3 1 hekat.
Rhind 1/5 1/10 hekat 96 . 96 3 1/3 320 1 hekat. 1/5 1/10 hekat
96 .
1 320 320 320.
1/10 32 1/10 320 32.
1/5 64 1/5 320 64.
: 96 1/5 1/10 96 .
: - .
-
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(4,75 ) , . , . .
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=
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Rhind
Rhind . - .
20 Rhind (10 ) ,
10 Rhind :
69
3,5 80 . . 320 , 3 . (3 x )
1120 80 : 80 1120 ( 1120:80)
14 1/32 4 .
80 3 :
3 1/2 80
[ 2/3 2 1/3]: / . 10 10 3 35, 70 2 1/10 70 7. 2/3( 1/3 2) 1/3 7
2 1/3. 1/21 : , 1/21 1/14 2/3 (2 + 1/3): 14 = 1/6 1/21 ; 79 1/3,
2/3 80. 2/3=1/6 . 1/6
-
3 . : 1/6 2 1/3 1/12 2. 2+12=14. 2/3 14 21.
70 71 69, 7 ( 72 78) .
73 :
100 10 15. ;
: 100 : 100:10= 10 . 15 15 10, 150. .
6 73, . :
74:
1000 5 : 10 20. ;
1000 5 200 200 100. 100 10= 1000 10
100 20=2000 20.
-
76:
1000 10 20 30. ;
20, 1/20 .
30, 1/30 .
1/20 + 1/30= 1/12 2 , . 12 .
1000 10 100 .
10 12 1200 .
unitary method.
:
1000 10 100 1 20 20 1 30 30
:
3 60 20 2 60 30. 5 60 100 60 20 1200 .
:
-
RHIND .
O ( 2/3 ) ( ) ( ), -, - 1/n , . . ( ) , . , , . . Rhind (.,
1.4)
-
(1600 . . 1850.).
RHIND
Rhind ( , 1650 ..), A. H. Rhind, 1858 , , ( Brooklyn). , 33 6 ,
( 1800 ..) , , (2000-1800 ..)
-
. : , , . , , . , , , . , , , .
-
1.4: - Rhind. , (. Fauvel & Gray, 1987).
, : . , , . , , , . .
RHIND;
. . , 19 , . , , . , , , , , , .. .
, . . , . ...
-
(;) , , ... . () , 730 [7: , . 52,3 45 ] , 55 , 120 , " 60 , 30
, . 15 5 . , , . : - , ! ! ... , ' ;
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5
9 .
;
:
1/9 , 1.
8.
8 8.
64.
64 .
1 =52,74 1 =1
-
58
93 1/3 ()
140 (). [: 5
1 ]
: ( )
:
140 70 [ ].
[
, 70: (93 1/3) ]
93 1/3 70.
1 93 1/3
/ 1/2 46 2/3 ( 23 1/3)
-
/ 1/4 23 1/3
1/2 1/4 ( )
Produce 1/2 1/4 of a cubit, the cubit being 7 palms.
1 7
1/2 3 1/2 ( 7)
1/4 1 1/2 1/4 ( 7)
5 1 .
:
140 70 [ ].
[
, 70: (93 1/3) ]
93 1/3 70.
1 93 1/3
/ 1/2 46 2/3 ( 23 1/3)
/ 1/4 23 1/3
1/2 1/4 ( )
Produce 1/2 1/4 of a cubit, the cubit being 7 palms.
1 7
1/2 3 1/2 ( 7)
1/4 1 1/2 1/4 ( 7)
5 1 .
-
:
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Simon Stevin, . . .
Simon Stevin
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, . 4000 .. , . 60 , 10. 60 . , , .
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, . Leonardo of Pisa (Fibonacci) , .
. John Halifax 1253, . John of Meurs Regiomontanus, ,
Stevin.
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Giovanni Antonio Magini (1592 ..). Thomas Masterson . 1593
Christoph Klau .
Johann Hartmann, . Stevin, .
John Napier , 1617. Henry Brigg 1624, ,
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1. , .
2. .
3. .
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1820 (CGS) , , . Carl Friedrich Gauss 1862. CGS Ohm. 1901 CGS.
1960, , S.I. (, ...) , British Imperial System.
-
23.09.1999 SA , .
Stevin
Simon Stevin
Simon Stevin 1548 Bruges 1620 . . , . , .
, 1571-1577 , . . Maurits , . 26 . .
1585 Stevin La Thiende La Disme . , , .
To Astronomers, Land-meaters, Measurers of Tapistry, Gaudgers ,
Stereometers in generall, Money-Masters, and to all Marchants,. ( ,
, , , )
, , , , , . , .
Stevin , ( ). ( )
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, . . Stevin . , . . . Stevin , .
. , , . Stevin . .
Simon Stevin
DISME: The Art of Tenths (Decimal Arithmetike) Stevin , . . ,
.
I. :
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* Every tithe soul, mongst many thousand dismes( , )* If we have
lost so many tenths of ours( )* The value of one ten( )
Stevin . , :
Of common ounces? () With spans and inches so diminutive
Ounces :
Spnas: ()
Inches: ()
Hector Though no man lesser fears the Greeks than I As far as
toucheth my particular, 10Yet, dread Priam, There is no lady of
more softer bowels, More spongy to suck in the sense of fear, More
ready to cry out 'Who knows what follows?' Than Hector is: the
wound of peace is surety, Surety secure; but modest doubt is call'd
The beacon of the wise, the tent that searches To the
-
bottom of the worst. Let Helen go: Since the first sword was
drawn about this question, Every tithe soul, 'mongst many thousand
dismes (), Hath been as dear as Helen; I mean, of ours: 21If we
have lost so many tenths of ours, To guard a thing not ours nor
worth to us, Had it our name, the value of one ten, What merit's in
that reason which denies The yielding of her up? , , , , : ; . . .
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:
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http://tefcrosmichaelides.wordpress.com/2009/10/12/%CE%B2%CE%B9%CE%BF%CE%B3%CF%81%CE%B1%CF%86%CE%B9%CE%BA%CF%8C/
http://www.biblionet.gr/main.asp?page=showauthor&personsid=17297
, 23:29, 11 2011
, 07:33, 4 2011
iii. www.in2life.gr/culture/book/.../article.asp...
iv. www.bestprice.gr/.../oi-pyramides-ths-aigy...
v. www.biblionet.gr/main.asp?page...227
vi. www.greekbooks.gr/valtari-mika.personarthistory.ab...
vii. , 10:23, 27 2012
: http://en.wikipedia.org/wiki/Ancient_Egypt
(http://eureka.lib.teithe.gr:8080/bitstream/handle/10184/574/kok_main.pdf?seque
A..A..A..T..M..M.. www.misraimmemphis.org .
https://bolko.wordpress.com/tag/%CE%B1%CE%B9%CE%B3%CF%85%CF%80%CF%84%CE%B9%CE%B1%CE%BA%CE%BF%CE%AF-%CE%B8%CE%B5%CE%BF%CE%AF/
http://www.eemaa.eu/books/aegyptiake-gonia/me-dyo-patrides/22
.
http://el.wikipedia.org/wiki/_
http://blogs.sch.gr/8lykkall/2008/05/23/----/
http://3.bp.blogspot.com/_ZshOK0-cvEs/TA6Ke42nFOI/AAAAAAAAKCo/rm5n5dTCBVA/s1600/mummy+-+1.jpg
http://www.troktikaras.com/2011/03/blog-post_3392.html
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http://el.wikipedia.org/wiki/%CE%A0%CF%85%CF%81%CE%B1%CE%BC%CE%AF%CE%B4%CE%B5%CF%82_%CF%84%CE%B7%CF%82_%CE%93%CE%BA%CE%AF%CE%B6%CE%B1%CF%82
http://www.focusmag.gr/articles/view-article.rx?oid=699
http://www.nea-acropoli-athens.gr/index.php?option=com_content&view=article&id=222:2009-01-03-19-19-08&catid=43:2008-03-11-08-23-52&Itemid=74
http://www.metafysiko.gr/?p=2476
http://www.mistiria.com/ancientgreece/piramides.html
http://www.dimitriskaranikolas.gr/main.asp?ElementId=13860
http://sfrang.com/historia/selida102.htm
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: : , . : B.L van der Waerden. : , 2007 : L.Bunt- P. Jones- J.
Bedient.
: , 1981
http://el.wikipedia.org/wiki/%CE%8F%CF%81%CE%BF%CF%82
http://en.wikipedia.org/wiki/Eye_of_Horus
https://www.google.gr/search?q=Wedjat,+eye+of+Horus&hl=el&safe=off&sa=G&prmd=imvns&tbm=isch&tbo=u&source=univ&ei=cfCST_TJEI_a4QSi4fXQDw&ved=0CEMQsAQ&biw=1280&bih=623&sei=3feST8rSE4bN4QTdss3QDw
http://planetmath.org/encyclopedia/HekatDivisionsEgyptianWeightsAndMeasures.html
Gillings R. 1971 -Mathematics in the time of pharaohs
B. L. Van Der Waerden .
http://en.wikipedia.org/wiki/Egyptian_pyramids
http://www.math.uoa.gr/me/dipl/dipl_pantsidis.pdf
VAN DER WAERDEN B.L. , : , 2000 .
Marshall Clagett: Ancient Egyptian Science: A Source Book;
Volume Three: Ancient Egyptian Mathematics, American Philosophical
Society, Philadelphia, 1999.
http://www.youtube.com/watch?v=XdEuhhtivMw&feature=relmfu
:Britannica Online Encyclopedia The MacTutor History of
Mathematics archive
www.wikipedia.gr : - , 2006
: Magic is No Magic The Wonderful World of Simon Stevin,
J.T.Devreese
http://el.wikipedia.org/wiki/%CE%95%CE%BB%CE%BB%CE%B7%CE%BD%CE%B9%CE%BA%CF%8C_%CF%83%CF%8D%CF%83%CF%84%CE%B7%CE%BC%CE%B1_%CE%B1%CF%81%CE%AF%CE%B8%CE%BC%CE%B7%CF%83%CE%B7%CF%82
http://www.math.uoa.gr/me/dipl/dipl_pantsidis.pdf
-
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