The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Inactive » math-history-list

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Why study Egyptian fraction math?
Replies: 20   Last Post: Nov 20, 2012 9:25 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Milo Gardner

Posts: 1,105
Registered: 12/3/04
Re: Why study Egyptian fraction math?
Posted: Nov 5, 2012 5:42 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

The Heqanakht Papers
First letter
(Writing) that the ka servant Heqanakht (HqA-nxt) sends to his household of Nebsyt (nbsy.t).
Words by ka servant Heqanakht (HqA-nxt) to Merisu (Mr-sw).
As for every part of our land that is flooded, you are the one who shall cultivate it, taking heed, and all my people as well as you. Look, I shall hold you accountable. May you be very diligent in cultivating. Take care that my seed is guarded and that all my property is protected. Look, I shall hold you accountable. Take very good care of all my property. -

Middle Kingdom
Deir el Bahri, tomb complex of Ipi

-Nebsyt: location south of Thebes
-ka servant: mortuary priest
-I shall hold you accountable: lit. I count it against you
Arrange to have Heti's (Htj) son Nakht (nxt) and Sanebniut (zA-nb-n'.t) go down to Perhaa (Pr-hAA) to cultivate for [us] 2/4 [A]H.t of land on lease. They should take its lease from that cloth woven here (where you are). If they have collected the equivalent value of that emmer that is (owed me) in Perhaa, they should use it there as well. Should you have nothing more (to do with) that cloth of which I have said: "Weave it!", they should take it after purchasing it from Nebesyt (nbsy.t) and lease land for its value. Now, if it pleases you (all) to cultivate 2/4 AH.t of land there, cultivate it. You should find land, ¼ AH.t of land in emmer, ¼ AH.t of land in Lower Egyptian barley, in the [good] land [of] Khepeshyt (xpSy.t). Don't descend on the land of just anybody. You should ask from Hau the Younger (hAw-Srj). If you don't find (any) with him, you will have to go before Herunefer (hrw-nfr). He is the one who can put you on qb.t land of Khepeshyt. -Perhaa: location south of Thebes
-AH.t: measure, 10 arouras - about 27,000 m²
-Weave it: much of the linen produced in ancient Egypt was woven by the female family members of the peasants.
-value: Sna.t, value equivalence in silver, during the New Kingdom one twelfth of a deben, 7.6 grammes.
-Khepeshyt: location south of Thebes
-qb.t: lit. calm or cool, perhaps resting, i.e. fallow.
Now look, (Merisu), before I came upstream here, you apportioned to me the lease for ¾ AH.t of land in Lower Egyptian barley alone. Mind you! do not defraud even of a sack of Lower Egyptian barley. Do not deal with his/its (?) own Lower Egyptian barley, because you have damaged the lease which belongs to me, yielding only Lower Egyptian barley as well as its seed. Now look, when dealing with Lower Egyptian barley, 69 (?) sacks of Lower Egyptian barley from ¾ AH.t of land, corresponding to 9 sacks of Lower Egyptian barley from 1 aroura of land, is not a bad yield. Behold, 4/4 AH.t of land will yield 100 sacks of Lower Egyptian barley. Mind you, do not be bold with (even) one oipe of Lower Egyptian barley belonging to it. Behold, this is not the year of indolence for a man towards his master, towards his father, towards his brother. -seed: the ratio between seed and yield is estimated to have been about 1 to 10.
-sack: XAr =10 heqat, either 48 or 96 litres during the Middle Kingdom.
-is not a bad yield: cf. grain yields
-oipe: jp.t - a grain measure: bushel, about 19.2 litres during the New Kingdom
Now, concerning all that Heti's (Htj) son Nakht (nxt) in Perhaa will do for me, behold, I have not calculated more than one months income (as) surplus for him, consisting of a sack of Lower Egyptian barley, calculating a second one of 5 oipe of Lower Egyptian barley for his dependents on the first day of the month.
Behold, if you exceed this I will consider it as theft on your behalf. As for that which I told you with the words: "Give him a sack of Lower Egyptian barley per month," you should give (it) to him as 8 oipe of Lower Egyptian barley per month. Beware! -income: aq.w, lit. loaves of bread
Now, what about Sahathor (ZA-Hw.t-Hr) coming to me with old, dried-up Lower Egyptian barley that was in Djed-sut (Dd-sw.t), without giving me those 10 sacks of Lower Egyptian barley as new, good Lower Egyptian barley? Don't you have it good, eating good Lower Egyptian barley while I am on the (naked) earth? Now, the boat is moored in your harbour, and you do everything that is evil. If you have old Lower Egyptian barley brought to me in order to deliver that new Lower Egyptian barley, what can I say? How good is this? (But) if you can't apportion a single (measure) of Lower Egyptian barley to me as new Lower Egyptian barley, I shall not apportion any to you for all eternity. -old, dried-up Lower Egyptian barley: stored grain was often infested with rodents, grain eating insects and moulds which ruined a significant percentage of the cereal.
-Djed-sut: short for Djedsut Teti which was the name for the pyramid complex of Teti, 'Enduring-are-the-places-of-Teti'
Now, didn't I say "Snefru (snfr.w) has grown up"? Take good care of him! Give him an income. And greetings to Snefru as Khenti-kheti (xnt.j-X.ty) says, a thousand times, a million times. Pay attention, now that I have written. Now, when my land is watered, he should cultivate it with you and Anpu (jnpw), as you take care, and Sahathor. Look after him well! Send him to me after the plowing. Have him bring me 2 sacks of zwt-emmer along with whatever Lower Egyptian barley you find, but only from the excess of your incomes until you reach summer. [Don't] be neglectful of anything I have written to you about. Behold, this is a year when a man works for his master.
Now, as for all the affairs of my district and all the affairs of my watered land in Sinwi (sjn.wj), I have planted it with flax. Do not allow anybody to descend upon it! Moreover, if anyone will speak to you, you should go because of it (?). Now, you should plant Lower Egyptian barley on that watered land. Don't plant emmer there. But if it will come as a great inundation, you should plant it with emmer.
Take good care of Anpu and Snefru. You die with them (and) you live with them. Beware! Look, there is nobody above him (i.e Anpu and Snefru) in this house, including you. Be not negligent.
Now, expel that housemaid Senen (znn) from my house! Beware, on the day Sihathor reaches you (with the letter), she shall spend (only) one (more) day in my house. Is it really you who lets her do ill to my second wife. Have I ever allowed ill to be done to you? What did she do against (any of) you, you (Merisu) who hates her?
And greetings to my mother Ipi (jpj) a thousand times, a million times. And greetings to Hetepet (Htp.t), and the whole household, and Nofret (Nfr.t). Now, what shall be done about these bad deeds committed against my second wife? Do your duty. Are you not established as my partner? How good it would be for you to stop it (i.e. the evil deeds).
And have a record sent of what was collected from those of Perhaa. Beware, don't be neglectful.
(Address:) That which the ka servant Heqanakht is sending to his household at Nebsyt.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.