Intro
to the table of thirds
February 1, 2003
Presented by Bruce C. Friedman Last modified: October 10, 2004. |
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There are numerous tables of hkt divisions on the two tablets from Cairo. Some appear as many as five times. The following table of one-third of various hkt quantities is found twice on these tablets. Both sets of calculations of thirds are without error.
Journal: Archiv Orientalni - The Quarterly Journal of Asian and African Studies, Praha, Czech Republic, 2002 Article: The Wooden Tablets from Cairo: The use of the Grain Unit hk3t in Ancient Egypt. Author: Hana Vymazalova. |
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ANALYSIS OF 1/3 TABLE: Modified and corrected 10/9/04 as per H. Vymazalova. The scribe first determines the value of one-third of five by operating
with duplications as follows. Five ro [r3] is equivalent to one-sixty-fourth hkts. Line 1: To be read as 1/3 of one is = a third
To be read as 1/3 of two is = two-thirds
To be read as 1/3 of four is = one and one-third Here, the scribe combined the result of one-third of one, and one-third of four, to find that five-thirds is equal to one-third of five.
To be read as 1/3 of one/64 hkt is = [(//3* /320)+(/320)] = 5/960
= /192 = correct!
To be read as 1/3 of one/32 hkt is = [(/3* /320)+(3*/320)] = 10/960
= /96 = correct!
To be read as 1/3 of one/16 hkt is = [(//3* /320)+(/320) + (/64)]
= 6 2/3 ro = 20/960 = /48 = correct!
To be read as 1/3 of one/8 hkt is = [(/3* /320)+(3*/320) + (/32)]
= 13 1/3 ro = 40/960 = /24 = correct!
To be read as 1/3 of one/4 hkt is = [(//3* /320)+(/320 + /64 + /16)] = 26 2/3 ro = 80/960 = /12 = correct! One third of /4 is /12.
To be read as 1/3 of one/2 hkt is = [(/3* /320)+(3*/320) + /32 + /8)] = 53 1/3 ro = 160/960 = /6 = correct! One third of /2 is /6.
To be read as 1/3 of one hkt is = [(//3* /320)+(/320 + /64 + /16
+ /4)] = 106 2/3 ro = 320/960 = /3 =correct!
To be read as 1/3 of two hkts is = [(/3* /320)+(3*/320) + (/32 +
/8 + /2)] = 213 1/3 ro = 640/960 = //3 = correct!
I am studying each and every transcribable entry
for errors which may more clearly suggest the method(s) that generated these identities. |
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