Peet – The Rhind Mathematical Papyrus, British Museum 10057 and 10058 (Liverpool/London 1923; scan is the Kraus Reprint, Nendeln 1970) — OCR (Apple Vision)

Source and licence

share: publicnone

Source: corpus/incoming/e-2/peet-rhind-1923/ — Apple Vision OCR (tools/e2_ocr.py, worker E-2, 2026-09-29) of corpus/incoming/middle-egyptian-texts/peet_rhind-mathematical-papyrus_1923.pdf, 169 PDF pages; provenance and verification in corpus/incoming/e-2/STAGING.md

Attribution: Peet – The Rhind Mathematical Papyrus, British Museum 10057 and 10058 (Liverpool/London 1923; scan is the Kraus Reprint, Nendeln 1970); public domain in Canada (published 1923; author T. Eric Peet (title page corpus/incoming/middle-egyptian-texts/peet_rhind-mathematical-papyrus_1923.pdf pdf p. 1: "… by T. Eric Peet, Brunner Professor of Egyptology in the University of Liverpool … MCMXXIII — Kraus Reprint, Nendeln/Liechtenstein 1970"; pdf p. 2 reprint notice; preface signed Liverpool June 1923); death year UNVERIFIED — the PDF has no Author field and no in-folder authority record gives Peet's dates · note (PROPOSED-scan_copyright-E-2.csv): middle-egyptian-texts/README.md §3 states "died 1934" with no source — not counted (E-2 volume peet-rhind-1923) · Lead D authority lookup 2026-09-29 (outputs/REPORT-DEATH-YEARS-2.md, DEATH_YEARS_EVIDENCE.tsv): Peet d. 1934, BnF cb12504101w + IdRef); OCR text by the Kemetic project, Yousef Hanna 2026.

Licence: public domain in Canada (author died ≤ 1971, verified; LICENCES.md §7) — US position (recorded, does not gate the class; PD-CA 2026-09-26): PD-US (published ≤1930); the scan is the 1970 Kraus reprint, "Reprinted by permission of the original publisher" (no new authorship)

Jurisdiction note: this text is public domain under Canadian law (the project is published from Canada; LICENCES.md §7: author died in or before 1971). It may still be in copyright elsewhere — in countries with a life + 70 term, or where a later edition claims its own rights. The licence line above says what was verified. If you are outside Canada, check your own law before re-using it.

Full provenance and citation

The text — part 2 of 2

1,505 lines · a line number is a link to itself

ref	L0 witness (OCR)
p. 130
5828	126 RHIND NATHEMATICAL PAPYRUS
5829	No. 83. making for 10 ro-geese 1 hekat of Lower Egyptian barley
5830	for 10 days 10 hekat
5831	for a month 30 hekut
5832	Daily allowance of food for a fatted
5833	ro-goose, what (it) eats is (1 + 3'z) hekat + 3} ro, per bird
5834	terp-goose (: + 3b) hekat + 3} ro
5835	crane1 (*+ 32) hekat + 3} ro
5836	set-bird" (3g + 87) hekat + 1 ro
5837	ser-bird 6t hekat + 3 ro
5838	turtle-dove 3 3 ro
5839	quail * 3 rо
5840	Total" (sic)
5841	No. 83 consists of three separate sections, the mathematical content of which is of very
5842	small value.
5843	The meaning of the first, which occupies the first three lines, is clear. If 4 birds
5844	eat one henu of food, i.e. 32 ro, then the share of one bird will be 8 ro, or 7t hekat (which
5845	is 5 ro) plus 3 ro. The wording, however, is not quite so straightforward, owing to the fact
5846	that line 2 has been lost and incorrectly restored on a fresh strip by the ancient mender
5847	the papyrus. Thus the two signs after oo are meaningless and unnecessary. Moreover,
5848	the word hnw is incomplete, and where the signs • stand we need &i: in any case,
5849	a nominal sentence with pu after ir meaning "if" is suspect. The restorer would seem to
5850	have worked on the analogy of the second part of the example (line 5 below), not noticing
5851	that the method of statement was slightly different. We could of course save pw by taking
5852	ir as the particle, "As for the food of....," but this gives a much poorer sense to the
5853	whole, which, as being the statement of a problem, demands a conditional clause.
5854	The distinction between the geese who are "cooped up" and those who are allowed to
5855	enter the pond was first perceived by Griffith. The feminine form ltmyt must be wrong, for
5856	the r-goose is masculine. The restorer is again at fault. Possibly the whole word is wrong,
5857	for he certainly restored it as a word giving a suitable contrast with lc.f r sš in line 4.
5858	• The second portion of the example, lines 4-8, is little more than a statement .of the
5859	fact that (7= + 3b) hekat + 2 ro is equivalent to 32 ro or 1 henu. This allowance is then
5860	worked out for ten geese during a month.
5861	The third portion of the section (lines 9-end) would seem to concern the poultry farmer
5862	more than the mathematician. It is a list of various kinds of domesticated birds, showing the
5863	The word "total" at the end suggests that a simple addition in
5864	dimidiated parts of the hekat was intended, but it was never carried out, or at least was not
5865	The various types of bird mentioned are all well known from the monuments, and some
5866	offering lists such as Beni Hasan I, PI. XVII, and Cairo sarcophagus 28001. For good illustra-
5867	tions consult DüMICHEN, Resultate, Pl. IX (Ptahhotep); El Bersheh, I, PI. XXII; BORCHARDT,
5868	Grabdenkmal des Sahure, II, Bl. 55 and 56, and text thereto. Compare also Pap. Kahun, PI. VIII,
5869	where the values of some of these birds are compared with that of the st-duck.
5870	* L.D., II, 61, 150; B.M. Stela 134 (1164).
5871	" The long-tailed duck, Dafila acula, Linn. See Ree. Trav., 33, 59-64.
5872	3 Pigured in the tomb of Rekhmara. (Y. SeTHE, Crl., IV, 1124; cj. Davies, Mustaba of Ptahhetep, I, 20,
5873	and PI. VIII, 113; GrırrırH, Hieroglyphs, 20.
5874	* A.Z., 30, 25.
p. 131
5875	RHIND MATHEMATICAL PAPYRUS 127
5876	No. 84. (Pl. X.) No. 84.
5877	"Estimate of the food of a stall of oxen.
5878	...food ordinary... food (?)
5879	hekat hekat
5880	Bull; that which 4 eat, good bulls of Upper Egypt 24 hekat 2 hekat
5881	2 good bulls of Upper Egypt 22 hekat 6 hekat
5882	3 ordinary... cattle 20 hekat 2 hekat
5883	1 • • . cattle 20 hekat
5884	Total of this food 8 (sic) 6 hekat 10 hekat
5885	Making in spelt 9 (?) „ "
5886	Amounting in 10 days to 90 75 "
5887	Amounting in a month to 200 90 "
5888	Making in double-hekat (?) (61} + 1) hekat 30 hekat."
5889	+ 3 ro
5890	With this problem the papyrus reaches its limit of unintelligibility and inaccuracy. The
5891	question is to calculate the food of certain cattle, which are apparently to be fed on two different
5892	kinds of food the names of which it is not easy to transeribe.
5893	From this it is to be expected that in the table which follows we should have three figures
5894	in each line, viz. the number of cattle of a particular kind, the quantity of the first food and the
5895	quantity of the second. This actually appears to be the case.
5896	four dots (not strokes, oddly enough) to represent the four bulls: under the heading of the first
5897	kind of food we find two strokes followed at once by 4 dots, which in the hekat notation means
5898	24 hekat: under the other type of food stand two dots, meaning 2 hekat.
5899	far there is no serious difficulty. When the addition comes to be made the
5900	numbers of bulls are not adder at all, being unessential to the result. The hekat in the
5901	last column are correctly added up to 10, rightly expressed by a stroke. In the centre
5902	column, however, the strokes, of which there are eight, each standing for 10 hekat, are
5903	mistaken for units and added up to 8, while the dots are added separately to give, quite
5904	rightly, 6 hekat.
5905	In the next line, where this food is reduced to terms of spelt, the 8 is calmly neglected,
5906	the 6 hekat of the one food give 9 hekat of spelt, while the 10 hekat of the other food give
5907	7} hekat of spelt. As we know nothing of the foods in question we cannot judge of the
5908	accuracy of this. This is evidently a daily allowance, for it is now correctly multiplied by
5909	10 to get the ration for 10 days, 90 and 75 hekat respectively. Next the allowance for a
5910	month is found, but, sad to relate, three times 90 is given as 200 and three times 75 as
5911	90. A final resolution into double-hekat gives opportunityfor twomore errors, half
5912	helat being given as (61} + }) hekat + 3 ro, and half of 90 hekat as 30. Griffith
5913	by these last figures to suggest the a triple-hekat.' Ninety hekat
5914	triple-hekat would become 30 and 200 would become 66}, to which the figure given, 61393,
5915	is at least a better approximation than it is to 100. Unfortunately the sign
5916	between the ) and the * in the name of the unit is very uncertain, the reading ..
5917	leing far from convincing, and we may well re-echo Griffith's own words, "The treble hekat is
5918	extremely doubtful."
5919	Such is. the calculation contained in this example. clearly full of mathematical
5920	errors, and there are obviously other mistakes soserious that any attempt to guess at
5921	originally stood in the text would be the merest waste of time.
5922	1 P.S.B.A., XIV, 428.
p. 132
5923	128 RHIND MATHEMATICAL PAPYRUS
5924	No. 85. No. 85. (Pl. X, bottom, left.)
5925	The Mathematical Papyrus proper ends with No. 84, which takes us well into the fourth
5926	leaf of the verso of Papyrus 10058. In the blank which remains between this and the end
5927	of the roll in its present state is written, upside down, the curious group of signs numbered
5928	85 by Eisenlohr and found on Pl. XXI of the British Museum facsimile, on the right-hand side. The signs are rather cursive hieroglyphs written in black in two vertical columns. eac create hitr ot the meted It
5929	e weiure na ola cprogemn ith o mcani of ae It seems equally possible
5930	that it is a mere random group written in order to try a pen or to practise the formation
5931	of the signs.
5932	No. 86. No. 86. (PI. Y.)
5933	This number is given by Eisenlohr to certain fragments of a papyrus of accounts
5934	used in ancient times to mend a weak place in the roll. They now lie near the right-hand
5935	end of 10057 verso (PI. XXI, left, in B.M. Facs.). A rapid examination will show that there
5936	are here three separate fragments or strips placed vertically, but not in position relative to
5937	one another. They may easily be correctly arranged. The narrow strip on the left should be
5938	cut out and placed to the immediate left of the broad strip at the top. The central strip in the
5939	lower half must be turned upside down and placed so that the double horizontal line becomes
5940	continuous with that on the main strip to the right.
5941	This re-arrangement has now been carried out in the original papyrus, presumably since
5942	the making of the facsimile, but the work has not been quite accurately done, and the lower
5943	strip, with the left-hand portions of lines 13 to 18, has been set a few millimetres too far
5944	In the centre of line 9 there is a tiny patch which, as the double black line
5945	and red traces show, should be turned upside down and placed between the two main strips
5946	The resulting text is a mere fragment from a papyrus of accounts. If the transcription
5947	Ta at the beginning of line 1 is correct, and there is not much doubt about it, it must have
5948	been preceded by a date and a king's name, and therefore a considerable portion of each line is
5949	probably lost on the right. In a text so mutilated as this translation is difficult and almost
5950	worthless, and even transcription is very far from certain. The rendering here given is
5951	presented mainly for the sake of completeness. Any attempt at comment would be a waste of
5952	time and space.
5953	The writing of these accounts is considerably more cursive than that of the mathematical
5954	papyrus, but little if at all later in date; compare the forms ofthe signs
5955	with those of other papyri of the Hyksos Period. Griffith even attributes it to the scribe
5956	of Rhind."
5957	1. .living for ever. List of the food in Hebenti (?).*
5958	2. •[his] brother, the steward Kamöse....
5959	3. ....of his year, 50 pieces of silver twice a year (??)....
5960	4. ....2...., i.e. 3 pieces of silver, in the year.
5961	5. ....one (?), twice, i.e. one sixth and one sixth. Now as for one....
5962	6. ....12 henu, v.e. piece of silver; one......
5963	7. ....5 pieces of [silver]; their price therefor;" 120 fish (?), twice;....
5964	8. ....year: 90 quadruple-hekat of barley, 100 + x of spelt....
5965	9. ....90 of barley, 192 of spelt...
5966	1 P.S.B.A., XVI, 248.
5967	2 BRUGSCH, Dictionnaire Géographique, 469, records a place called Ly in the 14th nome of Upper
5968	Egypt.
5969	3 For sunt iri. Cf. Griffith, P.K., PI. XXXIX, Il. 3, 9, ete. Or read perhaps "Their price 120 iri-fish."
p. 133
5970	RHIND NATHEMATICAL PAPYRUS 129
5971	10. ....1462 (?); 185 (?) of barley, 300 + x of spelt. No. 86.
5972	11. ....*; there was delivered one donkey-load (?) of wine....
5973	....$ piece of [silver]....4 (?), ie....of silver....
5974	...I Thirty-six (?) henu of fat, ie.....of silver....
5975	....hundred and ninety-six....of barley, 410 quadruple-hekat of spelt."
5976	The lastline is repeated five times.
5977	No. 87. (PI. Y.)
5978	No. 87.
5979	This is written about the centre of the blank verso of 10057, at the top of the sheet. The
5980	translation is as follows:—
5981	"Year 11, second month of the harvest season, Heliopolis was entered.
5982	First month of the inundation season, day 23, the Army Commander (??) attacked (?
5983	Zaru. Day 25, information was received that Zaru had been entered.
5984	Year 11, first month of the inundation season, day 3. Birth of Set: the majesty of this god
5985	caused his voice to be [heard]* Birth of Isis, heaven rained.""
5986	These notes contain entries of two kinds, one referring apparently to military events
5987	and the other to weather conditions. They are dated in the eleventh year of a king whose name
5988	unfortunately is not given.
5989	Möller describes the entries as of somewhat later date than the mathematical portion of the
5990	payrus,possibly emanating from the same hand as No. 86. This is supported by the fact that
5991	endorsements on the back of a papyrus are not usually of much later date than the papyrus itself.
5992	Can this dating be supported by the evidence of the other entries, those which concern the
5993	weather? These were first translated and their import shown by Erman.® The voice of Set is
5994	doubtless the thunder, and the facts described are that it thundered on the birthday of Set and
5995	rained on the following day, the birthday of Isis.
5996	In a leaflet appended to his Historical Studies Petrie has discussed these entries and
5997	attempted to fix the date of the Hyksos period from them by the use of the Sothic Cycle. His
5998	argument is as follows. 1. The entries are of "about the same age" as the mathematical papyrus,
5999	which, it will be remembered, is dated in the 33rd year of Apophis I, the Hyksos king.? 2. The
6000	birthdays of Set and Isis, which of course fall on the third and fourth intercalary days, are here
6001	given as falling on the third and fourth of the first month of the year, because the scribe forgot
6002	the intercalary days and went straight on from the last month of one year to the first of the
6003	next. 3. If we accept the length of the period between the XIIth and XVIIIth Dynasties as
6004	only about 200 years, the date of the 33rd year of Apophis will be somewhere between 1600 and
6005	and 1750 B.c. At those dates the third and fourth intercalary days would have fallen early
6006	in September, when rain is practically unknown in Egypt. On the other hand, if we accept
6007	1 For the noun here cf. perhaps Pap. Turin, P. R. Pl. IX, line 6, and Pap. Leyden 343, recto, 5. 8.
6008	* Reading very uncertain. For twn see p. 77 above, and A.Z., 57, 38. Thesign after the ox can hardly be
6009	*f, however. It is tempting to read feelyp at the beginning of line 3, but so uncertain that it is not worth
6010	while to speculate on the possible identity of this general with the King Mr-mö whose statues, usurped by an
6011	Apophis, were found at Tanis (PETRIE, Tanis I, 8-9 and Pl. III, 17).
6012	3 For I in the passive with the place entered as subject compare Pap. Petrograd 1116B, recto 34.
6013	Lro (see Sinuhe, B, 140, and Gardiner's note thereto). In any case we cannot read@ as passive, for there * Thesignmust havebeen omitted here after Soe, for to utter the voice is not ralt kro but rodt
6014	is a superfluous o.
6015	• Here irt must be read as a śdmf, despite its incorrect form. Perhaps the scribe started out with an infinitive
6016	irt, parallel to rdit above, and then changed his mind.
6017	• Ä.Z., 29, 59.
6018	* Petrie actually takes as a working hypothesis for the date the l1th year of Ianias, the successor of Apophis.
p. 134
6019	130 RHIND MATHEMATICAL PAPYRUS
6020	No. 87. Petrie's long dating, by which the date of the calendrical entries would he about 2370 B.c., the
6021	rainy weather would occur on Feb. 14 (or March 16 if we adopt the Thoth-year). These dates fall
6022	into the rainy season, and therefore the higher dating should be correct.
6023	There are three assumptions in this reasoning: firstly that the notes are not much
6024	later in date than the mathematical part of the papyrus, secondly that the scribe forgot the
6025	intercalary days, and thirdly that the thunder and rain must fall into the usual
6026	The first of these assumptions has the support of Möller and is quite possibly correct. This
6027	is, however, a matter of small importance, for the third assumption is totally
6028	concerning the weather which are thought worthy to be set side by side
6029	with important military events, and which must therefore in all probability have been some-
6030	thing out of the ordinary. No one in England troubles to record, or even to remember, the
6031	occasions on which it snowed in December, but few forget the rare occasions when it snows in
6032	June. When therefore Petrie finds that on the short dating hypothesis these entries demand
6033	rain and thunder in the middle of September, a very unusual time, he is by no means
6034	liberty to argue that therefore the short dating is incorrect, nor is it in the least a matter for
6035	self-congratulation that the long dating would bring this wet weather into the usual rainy
6036	season in Egypt.
6037	Equally unjustified is Petrie's second assumption, namely that the scribe forgot the inter-
6038	calary days on which the gods' birthdays fell and attributed the birthdays to the first five days of
6039	the new year. It is conceivable that in certain complicated cases a scribe should inadvertently
6040	omit the intercalary days, as he seems to have done in the Ebers calendar, but that he should
6041	wrongly attribute the birthdays of the gods to any other days is practically unthinkable.
6042	Under these circumstances it would appear that to attempt to draw any chronological
6043	conclusions from these entries is but to ask for failure. They are not to be exploited either for or
6044	against the short dating.
6045	At the same time they do contain a problem which we are not entitled to shirk. How are
6046	we.to explain the attribution of the two birthdays to the third and fourth of the first month instead
6047	of to the third and fourth intercalary days. Two possibilities may be suggested. It may be that
6048	here we have a comparison of civil and Sothic years similar to that given in the Ebers calendar.
6049	Thus the birthdays of Set and Isis fell on the third and fourth intercalaries according to the civil
6050	was furnished, as the Ebers calendar shows, with its months and days. In this case it will readily calendar, but on the third and fourth of the first month according to the Sothic year, which, Lntea ur eo iter aulo in generel, rtl ro leg to min.
6051	be seen that the civil year was at this time five days out of coincidence with the Sothic year, and
6052	only be that of 1321 B.c. In this case we get a date of about 1341 for the entries.
6053	completely at variance with Möller's opinion with regard to the date of the script, and on this
6054	ground may be rejected.!
6055	The other possibility is that we have here a trace of that remarkable event in the Egyptian
6056	calendar first pointed out by Gardiner, namely the change by which the first month of the year
6057	ceased to be Mesore and became Thoth. This change took place probably some time before the
6058	late XIXth Dynasty. How long before this we cannot say, but Gardiner has shown that in the
6059	1 It is perhaps just worth while to remember that cursive hieratic material for the late Intermediate Period
6060	and XVIIIth Dynasty is almost wanting, and comparisons are consequently impossible. Should this subsequently
6061	be discovered in any quantity it might foree us to modify our opinion concerning these very rapidly scrawled
6062	They contain two or three forms which seem to be rather XVIIIth Dynasty than Hyksos, but these may
6063	well be due to the fact that the cursive script. was always ahead of the official copy-hand in innovations.
6064	simple form of the word-sign for luci "to strike" here used hardly survived the beginning of the XVIIIth Dynasty.
6065	That the entries should be as late as 1341 B.C. is almost out of the question. For the little that is known con-
6066	cerning XVIIItl Dynasty hieratie bands see Müller in A.Z., 56, 34 ff.
6067	: Ä.Z., 43, 166 #f.
p. 135
6068	RHIND MATHEMATICAL PAPYRUS 131
6069	XIXth Dynasty itself there existed some confusion between the new and the old systems. The No. 87.
6070	way in which this change took place is not actually known, but we do know that the order of the
6071	months, i.e. their relative position with regard to one another, remained unaltered. The most
6072	likely supposition seems to be that at some period the intercalary days were moved from
6073	their position immediately before Mesore and placed immediately after it. Let us suppose
6074	this done in some particular year. Then after Epiphi 30 would follow the new Mesore 1,
6075	and the new Mesore 30 would fall on the old Mesore 25. The intercalary days now fall on
6076	the old Mesore 26-30, but a scribe having in mind the old system in which Thoth 1 followed
6077	on Mesore 30 might well make the mistake of attributing the five divine birthdays to Thoth
6078	1-5 (Mesore 26-30 old reckoning).
6079	This explanation is but a suggestion. Should it be judged fanciful, one may reply that it is
6080	more likely to be correct than the theory that a scribe under normal circumstances forgot that the
6081	five divine birthdays fell on the intercalary days. It affords of course no basis at all for fixing the
6082	date uf the entry.
p. 136
6083	132 THE RHIND
6084	GEN
6085	Aauserre, 3, 33
6086	Account papyrus, 128-9
6087	Addition, 12; of fractions, 17 #.
6088	Ahmõse, scribe, 33
6089	Akhmim Papyrus, 8-9
6090	Algebra, supposed use of by the Egyptians, 60
6091	Amenenines III, 3,9
6092	Apophis, 3
6093	Area, measures of, 24-5
6094	Areas, calculation of, 88 ff.
6095	Aristotle, 31
6096	Astronomical instruments in Egypt, 32 n. 5
6097	Astronomy, 31
6098	Babylonian mathematics, 27-31
6099	Beer, strength of, 112 ff.
6100	Berlin mathematical fragments, 7-8, 14,20, 102
6101	Bread, corn-content of loaves of, 112 ff.
6102	Bulag 18, Papyrus, 7, 12 n. 1, 18, 22, 64, 81, 110, 11
6103	117 n. 1, 118
6104	Byzantine tables of fractions, 8,104
6105	Cairo mathematical tablets, 8
6106	Calendrical entries, 129-31
6107	Capacity, measures of, 25-6
6108	Circle, area of, 88-9, 90
6109	Common denominator, use of, 17-19, 54
6110	Completion calculations, 53-60
6111	Cone (?), batter of, 100-2
6112	Coptic ostracon with tables, 8
6113	Cube, volume of, 84-5
6114	Cubit, 24
6115	Cubit-of-land, 25, 89
6116	Cylinder, volume of, 80-4
6117	Deben, weight, 26
6118	Democritus, 31-2
6119	Demotic Mathematical Papyrus, 8
6120	Diodorus, 31
6121	Division, 13-14; of fractions, 20
6122	Division of loaves equally, 50-53
6123	Division of loaves unequally, 77-9, 107, 109
6124	Division of 2 by odd numbers, 33 ff.
6125	Equations, solution of, 20, 60 ff.
6126	Exchange of bread and beer, 112 f.
6127	Finger, as a measure, 24, 99
6128	Flour, various kinds of, 114
6129	Formulæ, general, lack of in the papyrus, 10, 35-6.
6130	Fractions, 45 ff.
6131	MATHEMATICAL PAPYRUN
6132	IERAL INDEX.
6133	Fractions, Babylonian, 28
6134	Fractions, table of multiplication of, 103-4
6135	Geometry, 21, 80 ff
6136	Geometrv. Babvlonian. 30
6137	Geometry, Egyptian origin of, 3
6138	Grain. various kind» of, 113-1
6139	Greek Mathematics, 10
6140	Greek view of Egyptian mathematies,
6141	Harperonaptai, 32
6142	Hebenti (?), a town, 128
6143	Hekat. 25-6
6144	Hekat, double-, 3 n. 1, 26, 124-5
6145	Hekat, quadruple-, 3 n. 1, 24, 26, 81, 88
6146	Hekut, triple-, 127
6147	Heliopolis, 129
6148	Henu, 24, 25, 122, 123, 125, 126
6149	1, 113, Herodotus, 31
6150	Horus-eye notation. 25-6
6151	Kahun mathematical fragments, 6, 9, 14, 20, 21, 22, 34,
6152	59, 81, 83-4, 104, 117, 118, 126
6153	Kamüse, 128
6154	Khaemhet, tomb of, 32
6155	Khar, 24, 26, 81
6156	Khet, 24,88-9
6157	Khet, square, 24, 88-9
6158	Khufu, weight with name of, 9
6159	Kite, weight, 26
6160	Land, measurement uf, 88 ff.
6161	Length, measures of, 24
6162	Liquid measures, 117
6163	Measures, Babylonian, 31
6164	Menena, tomb of, 32
6165	Methen, tomb of, y
6166	Moscow Mathematical Papyrus, 6, 9, 20, 22, 30, 64, 92 n.1,
6167	93, 121.
6168	Multiplication, 13-14; of fractions, 19
6169	Nemare, 3, 33
6170	New York fragments, 1,+7-9
6171	Notation, 11
6172	Numerals, names of, ll
6173	Palm, as a measure, 24, 98
6174	104 Parallelopiped, volume of, 87
6175	Plato, 10, 29, 31
p. 137
6176	THE RHIND MA
6177	Plutarch, 10
6178	Positional notation in Babylonia, 28
6179	Poultry, various kinds of, 126
6180	Practical nature of Egyptian mathematics, 4, 10, 98
6181	Proclus, 10, 31
6182	Progression, arithmetic, 21, 78, 108
6183	Progression, geometric, 21, 121-2
6184	Proof of sums, 21-4
6185	Proportion, 60, 79
6186	Pyramids, batter of, 97 f.
6187	Pythagoras, 10, 31
6188	Rectangle, area of, 89-90
6189	Rings of gold etc. as a medium of exchange, 106-7
6190	Ro, a measure, 7,25
6191	Rope, use of in land-measuring, 32
6192	Sesostris, 31
6193	Setat, 24, 88-9
6194	Sexagesimal units, 27 ff.
6195	Square root, 20
6196	Squaring, process of, 20
6197	Squaring, process of in Babylonia, 29
6198	Strabo, 31
6199	THEMATICAL PAPYRUS 133
6200	Subtraction, 12; of fractions, 19
6201	Sumerian mathematies, 27
6202	Sums, method of setting out,21-4
6203	Tables, use of, 4, 8, 20, 29, 33 ff., 36, 51, 103
6204	Tables of division, Babylonian, 29
6205	Tables of multiplication, Babylonian, 29
6206	Thoth, 31
6207	Thousand-of-land, 25, 89
6208	Trial, solution by, 60
6209	Triangle, area of, 91-5
6210	Truncated pyramid, volume of, 93
6211	Truncated triangle, area of, 91-5
6212	Two-thirds, treatment of, 15, 20
6213	Units and dimeusions, coufusion of in sums, 86, 95-7
6214	Volumes, 80 ff.
6215	Weights, 26
6216	Weights, Babylonian, 30
6217	Zaru, 129
p. 138
6218	131 THE RHIND
6219	INDEX OF EGY]
6220	sht "a field," 96
6221	it "group of fractions?" 7
6222	20n "cone?" 97, 10
6223	¿fa "rectangular, square," 80
6224	imt-pr "inventory, will," 12:
6225	iri, in sense of " multiply," 76 n. 2
6226	iri, kind of tish (very uncertain), 128 п. 3
6227	irw "numbering of cattle," 110 n. 1
6228	iśt, meaning doubtful, 90
6229	it "barley," 114
6230	‹; w0 "excess," 59, 118
6231	"hfw "quantity," 61
6232	"Ie "enter," passive construction of, 129 n. 3
6233	wil, of addition, 12
6234	wih tp "count, mnultiply," 13-14
6235	w°t "a unit,". 115-6
6236	w0r "how much," 86, 119
6237	wh3-tbt, 97-8
6238	wod:t "remainder," 12
6239	vodyt, a kind of Hour, 114
6240	b3kw "taxes, produce?" 110
6241	båi, a kind of grain, 114
6242	bdlt "spelt," 114
6243	p'rt "quail," 126 n. +
6244	pfś "to make the pfśw-reckoning " 120
6245	pféw, 112-13. 117
6246	pri "to be issued" (of rations), 110
6247	prw " surplus, excess," 108
6248	pr-m-vé, ·7-8
6249	pd šé "to stretch the curd," 32
6250	mnnut "turtle-dove," 126 n. 3
6251	mryt, meaning doubtiul, 91-3,95
6252	mh "cubit," 24
6253	ns "divide," 14; other uses, 14
6254	nt (pronoun ?), 53
6255	ntf, pregnant use of, 90
6256	nd "Hour" 114
6257	y "a part," 15
6258	r (= Bèn l3t), 25
6259	25
6260	rmm (= ‡ stit), 24
6261	rmtt pr, 109
6262	rlt "number, amount," 81
6263	MATHEMATICAL PAPYRUS
6264	TIAN WORDS DISCUSSE
6265	lsi (metaphorical use of1), 33, 72
6266	Hunti (t), a town, 128 n. 2
6267	lm (=1 kcst), 25-6
6268	hik "cut off the tail," 95
6269	Iir "in addition to," 12
6270	hśb "to break," 24
6271	h8p(==st3t), 24
6272	lk :1 "bushel," 25-6
6273	13, lsż "corn-measure," 122
6274	1 3% "measuring-tape, plumb-line,"
6275	lbi "subtract," 12; apparently "
6276	lypr, used of result, 14
6277	lIt (= 100 cubits), 24, 88
6278	Iıtm "to coop up (geese)," 126
6279	hir, 26, 81
6280	hry pluoi " the last," 108
6281	Iurt "the content," 113
6282	33 (=] stit), 25
6283	swnt " price," 128 n. 3
6284	sulc " dark," 33
6285	st " long-tailed duck," 126 n. 2
6286	sity "proof," 22
6287	ś10 (= 16 st3t), 25
6288	śaot "wheat," 114
6289	śpat "triangle," 91 f.
6290	śntt, 101
6291	ślın, 112
6292	ślıt "include?" 108
6293	śšmt " working out," 22-3
6294	ślcd "batter," 97-8
6295	sicm, 12-13, 53 f.
6296	śty "to pour out," 118
6297	śtuti (3) " content," 86, 87, 101
6298	śtit "acre," 24-5
6299	śdlm-f pw form in passive (f), 77 I
6300	śrlm-lır./form, 21 n. 3
6301	s;° "space, container ?" 80
6302	"ty "ring ?" 105-6
6303	šn" "slave-prison," 123
6304	šei " to fatten," 125
6305	Ienbt " square root," 20
6306	lerft, 105
6307	kelt, a weight, 26
6308	122
6309	divide," 97
6310	. I, 106, 118-19
p. 139
6311	Іст, 13 n., 54, 75
6312	gś " half," 15
6313	tist gbt, 104
6314	tit "aliquot part," 117
6315	tỉt gbt, 104
6316	twn, a verb, 129 n. 2
6317	twnw "common difference?" 21
6318	tp "an example," 21, 110
6319	tp r "base of a triangle," 91
6320	tp héb, 33
6321	tr "pray," 110
6322	thi "err," 56
6323	di lır "to ada," 12
6324	dbn (a weight), 20
6325	THE RHIND MATHEMATICAL PAPYRUS
6326	dbn "a cylinder," 80, 87
6327	dblı, a vessel for measuring
6328	dmd "total, add," 12
6329	dn, unknown verb, 118
6330	dé, a measure used for beer,
6331	dit "a crane," 126 n. 1
6332	dit "remainder," 12
6333	db: " exchange," 118-9
6334	, 77-9
6335	A "add," 63
6336	A "to square," 20
6337	A "to subtract," 63
6338	sm #= m~w 125
6339	68,108, 116
6340	lll
6341	135
6342	orn, 122
6343	117
p. 140
6344	EXPLANATION OF THE PLATES.
6345	IN order to avoid possible confusion the plates have been lettered from A to I (omitting I).
6346	Under each plate are noted the numbers of the plates of the British Museum Facsimile on
6347	which the sums transcribed on that plate will be found.
6348	Signs here underlined in black are written in red ink in the original.
6349	signs written in vertical colamns the line indicating red ink is drawn to the left of the column.
6350	In the transcription the arrangement of the original, chaotic though it sometimes is, has
6351	been retained, except in cases where its retention would have involved great waste of space
6352	and consequent expense.
6353	It should be remembered that the transcription is made not from the B.M. Facs. but
6354	from the original papyrus, and is therefore in some cases at variance with the Facsimile. The
6355	more important of these cases are noted in the critical notes. To note all the minor instances
6356	would have rendered the notes far too bulky.
6357	Square brackets [ ], very sparingly used, denote restorations of lost or damaged signs
6358	which may be regarded as practically certain.
6359	ERRATA.
6360	Plate A. Division of 2 by 5.-Last sign in top line should be P not
6361	Div. by 17.—The multipliers 3 and 4 in the left column should be ticked.
6362	Div. by 23.—The multiplier 1½ in the central column needs the tick.
6363	Plate D. Div. by 91.—Insert a tick after the first bird.
6364	Plate H. No.23.-Fortheunderlined 5%+fin the left half read 52+!.
6365	No. 24.—Insert a tick before the multiplier f in third column.
6366	Plate J. No. 30.—Insert a dot (the multiplier 1) before 13s), in the fourth line.
6367	Plate M. No. 37.—Insert ticks before the multiplier = in third column (fourth line from top);
6368	also before the multipliers f and s' in the bottom line of the left half of
6369	the sum.
6370	Plate P. No. 53.—For x marked sic we should perhaps substitute ,in both cases.
6371	Plate Q. No. 58, line 4.-For x read 1111 .•.
6372	No. 59, line 3.-For x read
6373	Plate S. No. 64.—In line 1 insert the plural strokes under the first .*.
6374	Plate U. No. 69.—In the multiplication on the left insert ticks before the multipliers 16 and 64.
6375	No. 70.—In line 7 of multiplication on left the fraction r2n should be set back close to 7'z-
6376	No. 71.—In the last line insert before the numeral 2 near the end.
6377	Plate V. No. 72, line 2.—Delete the reference to note a.
6378	Underline first six signs in Nos. 72 and 73, the word ki in Nos. 74-76, and the
6379	words tp n in No. 77.
p. 141
6380	: called erroneous.
6381	rile.
6382	IIn 9
6383	1111 -
6384	nn/
6385	-
6386	15 111
6387	I! =1
6388	1111
6389	111
6390	111
6391	\|11
6392	13
6393	D=001N1x
6394	DIV. OF 2
6395	TITLE 1Q
6396	Plate A
6397	rit koe bigh in facsis ent t00
6398	I 1 Ш0:
6399	-DEED₴ DEEE
6400	fEEl 1HI®
6401	B. M. Facs. Plates 1 ar
6402	b. With •=I t
6403	a. trag 111 1111 T I10
6404	Hlnn 1111 minnO • !!n T
6405	b.
6406	n
6407	23 -
6408	•CIInIn
6409	T
6410	21
6411	. „ in=1 in 111.
6412	# ПnA
6413	Innn
6414	1i1 \|11
6415	12
6416	nA
6417	TInT • III n
6418	111
6419	1117.19 =
6420	lnOn
6421	/ unan
6422	11
6423	/
6424	111
6425	1\|1
6426	9 111 • =\|.
6427	-
6428	IIN 1111/
6429	=\|\|I > •
6430	111
6431	7
6432	II. IIN
6433	1.I/'!="ETP3
6434	UI
6435	Щ -U 66vU
6436	UUUUI
6437	=
6438	•..UUIII
6439	Un Uhum "i
6440	.II o
6441	TUUIII
6442	VUU!!
p. 142
6443	B. M. Facs. Plates Il to V.
6444	", sii In ПOn Шinnnn !!!-
6445	39 =/. !!!! nnn IПЛO 5E
6446	=. Erased dot
6447	HI: "nnn 999
6448	...-TIoo 1n9 sis 111 ЩПn? '''' Пnn99"'• Inn0
6449	Innonn nnn IAn0n m=Allg53 aTmwn- " nan 992
6450	Hin n "Inn.
6451	• 37 Ш П IInn •109 !... ..- 119
6452	=\|.
6453	b. Dot omitted as often in to.
6454	n
6455	/ 51 innn
6456	VENEE sic
6457	1111 !!! H11
6458	IIIM 35 nn • IПП !!!?
6459	IHI
6460	49 ==imn HIDOn
6461	HInnO
6462	unan > .
6463	sic
6464	sic ]\|. n- пn09999
6465	L000
6466	33 =\| . 1I Ann =. ...-
6467	sis
6468	= I
6469	'!.- sis 47 ecl #n=Ii H!1 nnnn 999) I0i7
6470	111/ n? 1111
6471	sịc
6472	,ПП 31 їI Дan
6473	a. To clear inz original 45 1Inn 11 ПЛ =1. nnn
6474	"1''/
6475	sis "11 1999 e. I for il as often Erased dot. e.
6476	#n-Alf 29 Д 111 IH0N0
6477	sic s Daca
6478	"/ 1nnn
6479	sis
6480	=."m "2
6481	nI) 43 mоna Nal n !!!• In? 1999
6482	• 27
6483	1 n0A 0 E VE min gTimig Tiin
6484	"0'''• HION
6485	DIV. OF 2 Mn. 25 InN= A 1Q41
6486	Plate B
p. 143
6487	B. M. Facs. Plates IV to VI.
6488	1111 66 VUUI1II /U 666 6666U
6489	48 •E'''"y -'''G6UUUI UU 11
6490	IL uUUu! UUU GGG UUUHH 66 UUUTH Sgeu u
6491	UUUU 11
6492	VUUUHI
6493	6UHI UUUU 11 vuu • 1d
6494	UU !I
6495	UUI • •1=
6496	69 UUUIiI UUU UUM •1C U UTI GUUlI . = 6666 YUU 1111
6497	6666UI
6498	666 U
6499	Uull
6500	•I=lE UUU
6501	L9 LUUI!II UUU I Uu •1= I "!I U 666JU..1 = 88 UUUU UUUU"'! 666 ul1.'
6502	'60! •2 GluLu"
6503	UUUII
6504	UUUU
6505	UUUI 18 UUUU! UlU!!!I • \|=
6506	b. Dot omitted, as ofter un to
6507	GuI •= • "11 GE U"S UU'"' 111
6508	UU UUU
6509	UUU UU!! UUII UUUm / UUU = UUU •''''
6510	64 UUU0!!
6511	18-uu -..664UIIe 575 = 6666 LUU .!) 666 U /!!' 666333 575
6512	66UU!I. 'II 6666 UUU HI UU.II
6513	-!! 66 U
6514	8-tul•i=lu UU UUU
6515	69 UUUll! UU I11 •666иЙ) • 1 92 66 U UUU l UUUUT UUU 1E
6516	-" 6 UIII G6U#
6517	UHI
6518	UUIt
6519	UU I VI.1= 6UII
6520	=
6521	60. U1 i1
6522	• lthg
6523	E0
6524	-
6525	"6660l-1
6526	. UUU
6527	U
6528	.... "€666Ú!",
6529	666V..'. 111
6530	•1="
6531	b6é...
6532	6jшu • =
6533	G6b Juc!ll UUU!
6534	с6 VШ!1.
6535	c. With erro
6536	=
6537	в б чуб. "
6538	==0 =0
6539	!!I- 1100
p. 144
6540	(See also Plate E.)
6541	. M. Facs. Plates VI and VII.
6542	→ [99] / 111999 111999
6543	111999 111
6544	[.9] = 199
6545	(tnpn
6546	linnn
6547	linnn
6548	Wn 98 nnnn =l. > .
6549	/ 1111 111000999 I! nnn 999 ..I .
6550	1 n0n 999
6551	1111
6552	-
6553	I nO
6554	/ MInnn > /.
6555	iu nn
6556	ipon !=I. . I III 10000 999
6557	- n0n 99 0E=
6558	2LLE N000999
6559	nnn nnn !n =/.
6560	SLC
6561	95 Pan Il nnn nnn nnn n=1: 999 nann nann
6562	/ =!.
6563	nnn 1unnn Innnn . ID00
6564	nnn
6565	91 1hm0 -1. nomn
6566	FATRE.... — unn: 2m 333
6567	!!.-
6568	MlZ 89 #!ОnЛ0 →
6569	In00nn ,
6570	F- !!!in linnn
6571	I11 nnnn • 87 DIV. OF 2 HrinAA BI nn nnn? →. tonnn
6572	Plate D
6573	de restorations.
6574	n0n999
6575	0000999
6576	See text.
6577	I as often
6578	d brackets I1 den
6579	c. Very uncertai
6580	Ъ. 80 uritter
6581	• an 333?
6582	a. Dot omitico.
p. 145
6583	1335%% •1i=
6584	•X 201
6585	1231961 2235 ... % ja1i
6586	... 238
6587	000
6588	=î-Лå 2D LДI 00, 7,3
6589	30M3Cc
6590	1ks 32
6591	pA Plate E
p. 146
6592	A1-
6593	Tila A
6594	1334%
6595	ÉTia
6596	000
6597	080
6598	0000='
6599	JSaR
6600	"Іл.
6601	20
6602	920 -
6603	19%
6604	17
6605	"IÀ/4 0,31 "HiT• 121961
6606	1
6607	The New York and British Museum Fragments in Pos
6608	On the right unplacedNew York Fragments. (N.B.—Signs shown i
6609	000
6610	000
6611	4M, 0o
6612	22 00° =Ẫ—Ńå
6613	21
6614	24
6615	23
6616	25
6617	tion. See B. M. Facs. Pl. VII.
6618	outline are in red ink.) Scale 12/13.
6619	<132) 32
6620	33
6621	34
6622	BU
6623	LII.LE
p. 147
6624	1I IE
6625	=E0)
6626	Plate F
6627	noEb'ac{19e
6628	[#"1]
6629	=
6630	~genz-\|"a= 2
6631	S1=\|01l'0]=7
6632	h'0=140-
6633	ā \|\| …/
6634	20\|=1611= ..L'
6635	.LE
6636	"='!! '.I''
6637	0'IIO
6638	5
6639	1160
6640	#n1!!I !!!! -
6641	[^ =] "
6642	nE-IIse 6
6643	na9I "/ F T?.
6644	B. M. Facs. Plates VII and VIII.
6645	(See also Plate E.)
p. 148
6646	(ultered from
6647	In lighter ink
6648	11
6649	-
6650	18
6651	==
6652	9999*
6653	10999
6654	„n09999
6655	15
6656	DE-D0E050E 12
6657	=!!!
6658	→1II
6659	11
6660	7 REElmMIO
6661	Plate G
6662	6L
6663	9L n O= DEE -
6664	=
6665	VE=
6666	111
6667	B.M
6668	08
6669	LI
6670	UUm
6671	66g'''
6672	DEDEI \|
6673	DE DEE DEE DE
6674	E0 → •
6675	10 0E E=3== M 05E
p. 149
6676	Il'n
6677	Plate H
6678	•\| 22"RQ- 2=REE21
6679	'a''''. B id n =, n
6680	fla
6681	sic
6682	1[=3{ДП"• 12572=1=1 22
6683	\|\|I Ř'
6684	I I "IA .II #-
6685	"-2UnR'acss
6686	! нI HI TR=R=1T = 23
6687	1→ '''n --_ sLC Tolgellm! VE LENUE - BÜ ULLE
6688	#n20% 4-#ŽDY 24
6689	• ='''1. Dpfe 111 .-
6690	" Піі 1#Ii- #IIn "<
6691	1111- 1111=
6692	25
6693	Pr. #AI EP8O " T 111
6694	S!l1
6695	111 11 = Tn =
6696	!IIn * 111-
6697	"n-21"2'0=a
6698	''I'0 ;'Д=9ş''° '!!
6699	I'0 IIП ..../ 11I• n"/
6700	"n= 'l'" we ..I ''N&'''I !!I "
6701	Possibly mere prolongation of o. b With dash aebave, like de.
6702	B. M. Facs. Plates VIII and IX.
p. 150
6703	B. M. Facs. Plate IX.
6704	UE HI
6705	= ''''n
6706	111 C1
6707	W10 Hun
6708	HIN
6709	mInn0999 Innnn 1. mn? innn
6710	1nnnn
6711	=
6712	1 m333 linn 10009999 929 ! non
6713	=
6714	→A1 =10
6715	!! -
6716	н .''''
6717	"II = 7 ı
6718	31
6719	na lIn a 1=
6720	:9- n? w.nn Tl!II
6721	ULLE BU "n/!...-
6722	•9 .< 99088-10e
6723	30
6724	sicLPfo
6725	aalamaf
6726	• 2"1'02n-no
6727	28 -ILNTART
6728	.../
6729	SLC
6730	IIn
6731	"''• >\|l!
6732	27
6733	Plate J
6734	• AME=
6735	<]''''
6736	DEUC 1
6737	60 U
6738	Misplaced in ho 3
6739	With erroneous de
6740	Wilh eresed dot.
6741	111
6742	nnn
6743	nhi la=
6744	_-
6745	•= \|ß =
6746	→ \|I0 z
6747	= ''!!
6748	d D v
p. 151
6749	Dot placed. over qiu instead of befone it.
6750	66 UIII Ut!!!!
6751	6666 UU I11 UUUMI
6752	115 66666 UIl 6666
6753	U1II
6754	UUIT
6755	GGUUUU, YIllt U UlII 6666 UUml QUUHI 66666 6666 UII
6756	UUUUI 1111 ÜII
6757	UIl UIIII UUH UlIl 666UUH
6758	TlE''T'! 1'!
6759	= = VUI!I 6666 UUu:II UU1I 66666U1 5666
6760	111 U!!! 1TGUU11 Jull
6761	= = =
6762	• UH 6UMHI 66UmI
6763	= Uni
6764	0I—bd "
6765	6 UU u lll
6766	66 UlI1 Lnn / hil UUU IH UUU UUUHI
6767	U UUmI
6768	UUI UUmIl
6769	UUHI U
6770	UUIII 1 . U'!I!
6771	6UU uLlllI UII
6772	111 ()III UU!I UUII UU 1I 6об6ь UП
6773	UII HI 66UII G666 Uu 111
6774	LI!I
6775	LGGUUUU
6776	L
6777	UUU
6778	GUIII uoull
6779	66UIlI6UUII
6780	-UII
6781	UlUUl UUU U 1I
6782	UUIII
6783	= vll' UUUUI UUUmI
6784	6 UL UDD!l
6785	• . 66UIII
6786	UII
6787	B. M. Facs. Plate IX
6788	evroneous fractional dat.
6789	nnn mnill*
6790	..I 1 П0 9991
6791	!n9993} = 999
6792	"'239333 T
6793	nnn
6794	ші 19% 2333232 1unnn nn,a #ilnon9 llinnn9 nnnđ
6795	I Л 111 Hun HH П
6796	1nn.
6797	-
6798	111!/ Ann
6799	_l!In HII
6800	Innn
6801	Rnn
6802	PI!I
6803	Annn nan lu Hihnn2 nnn^9} !..nnnn
6804	-
6805	HUЛOA !!!!
6806	1ln00 999
6807	minnn 1И0000 999
6808	1A -A
6809	11 n
6810	/ 111 00 10 00 999 11 П00 999
6811	• nnn nn
6812	HInnA s&
6813	шn / SLC "22"Lnn. = SLC
6814	=
6815	HIN
6816	• n() 11n0
6817	!!! IU-
6818	IIIn1 TlIn
6819	- !l
6820	W'III"
6821	STI.
6822	a. With
6823	Tilinen
6824	- =
p. 152
6825	B. M. Facs. Plates X and XI.
6826	b. Dask in evror for dot
6827	a. Îlear in original
6828	11 ППД 99 1пn991 VInAA
6829	I''I nann nnnn
6830	19599 SiC
6831	: 118a0 I!!I II''
6832	14 nn2 12333
6833	il .w-
6834	nnn}
6835	11I
6836	yllIn
6837	=
6838	1119 я Пs што !
6839	LLE n999
6840	!IIAA HInna 141 "Js"
6841	11nnn "JES"
6842	1110 •420 .
6843	7999 \| —IQ II182
6844	IlI=aa "=9" """".
6845	1-OP8e
6846	!!! !!!'
6847	min win 1u0
6848	111
6849	mm2alm=lz 0E HIIN A
6850	1111
6851	34 nZud14ü25
6852	Plate L
6853	= yI
p. 153
6854	=00y- 666У
6855	=#-YYJ -65= UUlI 666UU 666 UU
6856	UUU!!!! U"II UUU'!!! UUU
6857	0LOTYHS_® ue]x--Y,T eIllI 111 1111 UUU''!! UUU 666 UUU 666UUU
6858	UUU
6859	UUU
6860	.. 'II= UOU UUU 14 → 6
6861	-. UII 07 \| \| ULШ
6862	0"1208226= /• U'I.= UIl U
6863	U
6864	07 6-2W- UUU UUU S09 YIlI
6865	111
6866	UU!I UUIn • U1\|E !!I" 111=
6867	1111 U''II •UIlE
6868	U UU-!!! /U UU UU UIl • UIlE
6869	68 01-•7 - !!! •UIle !11 O
6870	=UIISl 1=
6871	→ !!!!!! 50 1y/IWIl
6872	um = yn • •=•
6873	•uU" Uuun UUUIn "66I11EUI "Vull UUU "S"=VIVull Uuull
6874	1 ДıW_inЩ 0-WE ! UmI=! DUUmt DUUM
6875	-010:495 0-609=
6876	13E i UII *I 1EEE UUUU" UUU UUUU UUUU vyll U →Yyl UUU
6877	= 6UUU UUU -Дол
6878	H1 111 "I vUv UUU
6879	-
6880	1555
6881	UUUIII VUUH 1 1
6882	UUUIN UUUl)
6883	666U
6884	U Im o
p. 154
6885	Plate M •
6886	111 I -•
6887	Tl1=l
6888	wn=1I1 wn 1'=, "II..
6889	CUm UII
6890	ZÍPLa n=" -
6891	UUUG!! nn0
6892	11 Л
6893	IInaAn
6894	1nAn •n \|m ш= D= IIIAnA :U.U" 11Л 111 111(0 11l1 - !'' 1999a nnnnf nnn nan se nin nnao nnna
6895	Tisic ynona 11 —
6896	nnn д299
6897	-• SoSTE
6898	38
6899	11 їїi/ ¡Til1 a
6900	ш!-mZ її їg
6901	"=UI
6902	Hnnn yin
6903	666 U In llng9 T!II winh 111 +0II- 77-Y*
6904	UHII U1 Uullcull
6905	1GIДU e uun -"6GIl1E UI UUUI Uull! mOnn *=lI!
6906	°=•ДU " =!!! #0999=
6907	Hnan ШЛ0О mnnn i00 lncn
6908	lunon
6909	UuU!!! 111000
6910	I11
6911	68
6912	O.-
6913	0 ~III1 D
6914	• FeeE 0"19 -826→
6915	/U »S "
6916	EE
6917	= /1111 111
6918	UIl U'''II UUI11I UUIH =
6919	UII= • Ulle • UIl= • UIE
6920	111 = • 1 m
6921	olg
6922	nnn nnn
6923	=!! In (11 /'00 ='II'n•
6924	-IIn 2 me toi
6925	202-21 SªJI•—a
6926	='II./ IIN =!!! nnn nnaz\|.-
6927	=3200 PI21Q
6928	IIN →!!!
6929	nnn non
6930	#Tn.
6931	nnn330
p. 155
6932	+U:0 07661°
6933	U 6666UUU 6G6 UU U 5-y-UllI
6934	UVU H
6935	UUUUTI
6936	→ u 103 5-7166
6937	U
6938	UUU 1
6939	6 1666
6940	U 6 = 666 y 6vuu U 6666 UUU 666 UU - ull
6941	U • : 666 6G UUUU11 UUU
6942	6666uili
6943	47"10 6"IIL 66UII = Um UUI =Й
6944	H11 • UД • 6lLД • 6666 UUII L UUUII Я1gU"G=''sr4"
6945	0y6666I07
6946	ПYLS
6947	UU!= UUUU!!! UUU DUUII
6948	U!!I !II LШ U
6949	-III vuu I ''I Uuull (I UUU 666 Yul
6950	TE0090
6951	UMUUIII
6952	• UUU !!I
6953	OUUU!!!
6954	UU! lil
6955	UUU!!! -
6956	GUIIII=
6957	1 nann 9} 11 n0ng
p. 156
6958	B. M. Facs. Plates XII to XIV.
6959	"!Bna- e Д' -"'-ЛоЛ2GE!
6960	99 nnn nn nnn nn
6961	99
6962	299
6963	→2 021200
6964	nn 999 'l!n-m 1&-9=-9
6965	11 П00 _..
6966	HInAOn
6967	Пonon#F9
6968	Snodlnnn
6969	3 п
6970	7 Innnno 1 nnn n- 9993 •25-7-T
6971	9 nnng- nn П00 9999 999 !n n-9
6972	-
6973	933- HInOAO " AA0 nnn
6974	•20-322-04002=92 2323EAotnoa 111c699
6975	Tn=T"!
6976	Tllo n- Tàn = 'ii I1 n0
6977	CPD .- H11 Tn. i Tuing. Н0 2299 m nan "ISI.=''nM1
6978	ö{200
6979	¡5RRIDnle
6980	2{Т→T2=11R-081[„∞L10=11
6981	lnnc
6982	RTIII Mn iiii B9" =
6983	#n111 1 m i!1 n00 !11/
6984	2. Ligature: nct like &
6985	ПАДШЕА"'
6986	S/l'ng
6987	1l nann92
p. 157
6988	01Lhn
6989	>1084E
6990	, sie o
6991	I-ДК-.
6992	UUU 1111-
6993	Written like 60.
6994	Plate O
6995	»"<n →ODiPEEA 47
6996	"s 5I< \|•ö10 ASD180
6997	T,fs01l< "li<
6998	48
6999	11
7000	111 aT!"I
7001	-!1I 11 111 1111 !!!/
7002	C111l
7003	49
7004	IRAMO
7005	B1-9-T
7006	1-%Д20050 R 9
7007	#A-IL-A 50
7008	" %Ek0m→"mnl-o-0
7009	100
7010	1n0n 111
7011	unnG
7012	"K''''=0ge 1 ERD -ela-a 51
7013	1I1EO Ene aDadErEll
7014	140000 1Ta2tEPZ
7015	"01"-92".00- •ДP$∞1-IЁ1a
7016	2999
7017	99
7018	b. Distinct from the sign for cubit.
7019	B. M. Facs. Plates XIII and XIV.
p. 158
7020	Plate P
7021	52
7022	1RETIYAETTOLTMEPZIERMOa
7023	1∞ß=∞ї½Ê~g∞ngğÑДŸД*Ț∞§_»l
7024	41∞01A∞0110-20=®
7025	„-"Б20128 11 999
7026	.- 53
7027	÷×9me
7028	2\|\|l sic
7029	SLC
7030	Sik sic
7031	× "Ъ
7032	SIc
7033	xL° 51
7034	11E × = 11/ nI-92-
7035	11
7036	*a ™ !!!!-
7037	"= ''' •
7038	→TET " 911 • =
7039	=IEXT'.'- = 7
7040	#2-5Д24
7041	b.. Hieratic 3 c. All figures in red except the '!!' d. Read "li
7042	B.M. Facs. Plate XIV, bottom half.
p. 159
7043	B. M. Facs. Plate XV.
7044	Traces. Not i
7045	I row lost.
7046	aces : notok or s
7047	nusual. fom
7048	1'=28-"0/210=33 Patch here.
7049	59B #REn-A29e
7050	11 mí 2=Aff
7051	1111 > 20202 S11= 0 8\|
7052	111→x=00= 111• SRTZMOE
7053	IBARAZIPAREO"RAAPEDPREDAEI
7054	42opof
7055	/'!9# a
7056	#И? #
7057	T lIIAn I AN >\|lI
7058	nnn
7059	•
7060	=0"1T"mZ""m2'0=84mm24o
7061	ЕEA-RI
7062	PRPEDDRIDER
7063	PPRPEOMRADERO BMRMIRARIZM ARI
7064	100
7065	>\|II=
7066	99
7067	Plate Q
p. 160
7068	U"!
7069	#11=
7070	11'=
7071	U'.I
7072	UUU
7073	sia j
7074	Plate R
7075	=9-PI2mn-=2"2-0 60
7076	- •I4'''3-2 104nn-R40'1'0→='''1
7077	11 PPAtTEm
7078	61
7079	Aofa-to #"2T-P
7080	SEPHİLE #2T-I
7081	П-TEIa
7082	нілл i WI-P
7083	9mP!l'"→
7084	--t12 1008 =
7085	81-bIt-t •BEŞM
7086	„1=12 LE b.
7087	пnnn lit milinT-I
7088	About 5 lines lggt
7089	Пn 2-'
7090	Sie
7091	n m P in
7092	SeltmmTaDo-a 62
7093	a 1I /s
7094	0 111/0
7095	OffD 050mcl < !/a
7096	somla #=llll
7097	I1t A0
7098	ces do not suit à s eraseo I1 П. 1'".
7099	ver a vertical stroke
7100	nnnd
7101	B. M. Facs. Plates XV to XVII.
p. 161
7102	b. Clear in öriginal. c. Orin d.Or an erroneous
7103	66UU VU!II'
7104	I6666 UUU UUU —!II
7105	666
7106	G666UU
7107	666UUUI U 1H
7108	UUUI UU!I=
7109	1006010608-
7110	-13→166UU UUUI103
7111	uuu mn
7112	UHII UUIU!!! UUU I1
7113	LUU 11H
7114	UU00mi
7115	ulI ogy=
7116	4D 1D S0
7117	=-6666—.1• 66 6666 666
7118	1-6666m.1.66UuumI L →-6660 •1• 6
7119	= VI'I' 6666 "- 6666 —1.Gll'''
7120	=810 966660 0→6666
7121	=-66667/66 #-6666YGUulI""
7122	718010=
7123	111 GG6
p. 162
7124	Plate T
7125	F→OLL-ÁAEiB-→EE
7126	—-?R=E→*BÉMFEEX(EESP
7127	• e. 1.
7128	nana nand
7129	nnn o nan
7130	',1999 nAЛ
7131	199 T
7132	'!!? wI
7133	68
7134	IIN E •
7135	""90•22 T11
7136	T'b0o''Ii:182e
7137	nn =1
7138	T'tsto!lI T'pao1l {a÷inohe
7139	""AS!!! ""SI.II oll !" .
7140	T't0'') T'pao'") 0=
7141	HЦASalI 11!!- 1 -
7142	y0... 7'ROIII
7143	""V!!! ""S!II
7144	T'pe0''1 11'I/ Tit so 'II "'i
7145	patch
7146	Vi7 →0''1.05ae 11•8 = 20
7147	nn
7148	'!\|x: "Q Effi7z2
7149	T''n ""Ox. 1I 8 11
7150	11 • !II
7151	I !IID T'7A0.I
7152	01.
7153	Patched. Extra stroke in Facs. is vemains of original do. ar tof in next line. 2. Fractioncl dot omittea e. Long form?s. b. Trace in original; nict shown in Facs. I. Tha two strakes in tacs. ave the c, Ligature, sim
7154	mains ot the originat D. The whole fage is much patched
7155	B. M. Facs. Plates XVII and XVIII.
p. 163
7156	Plate U
7157	TMTHRAAE =\|II . 69
7158	mnn20-83090 1100 II n
7159	ñº7-14- nAnA
7160	50PP* 111 nm22os"2'0=18 nanno
7161	#\| 7<
7162	"..
7163	"= " = M/
7164	• TIS "''I nand nana
7165	!.I! N299 9929 9999
7166	"=S In nn ggg ПП997 "/ nnn9
7167	"bo "n nAn nnn? > П999 •\|I/
7168	#20ia
7169	•.a(#9070
7170	.... '1II 70
7171	I='!'n
7172	→ ,nn ~∞ 1A128
7173	111000 nnA 11 / 9.-42oli *="\|A0=8
7174	T-
7175	#oAE"
7176	10=43090
7177	• • in
7178	-2c00p •n ii Tin !!II-
7179	BEU ofu n- 111
7180	SNOs n Tg iies in ai
7181	71
7182	0°=x\|0=
7183	OI24OSN SOR IAU
7184	• on patch, but no trace of o on original. b. Hieratic 3. c. A trace. d. Ulear in criginal
7185	B. M. Facs. Plates XVII and XVIII.
p. 164
7186	Plate V
7187	→ll@ GN-BAEngelnSEnS"mo
7188	99998418908mno9 Saleoo do9.age
7189	SAPTRE
7190	nn d n öene genmaffaRmi fRSMERe
7191	∞K*ФAE
7192	LONELA
7193	900>'I'
7194	On000
7195	sieappolhe 2A80
7196	oDllll " nn
7197	ОD''!!
7198	RMÖ8A=AREnDEP
7199	291. RITERASSE
7200	11 M П-
7201	nn 111
7202	a!s foRofsnTs >\|'∞
7203	H!E sui -ft9ln.8e #1110 77
7204	a Perhaps a mere separater wather ter an a b. Probably an erased vertical strcke. (Hieratic 3
7205	B. M. Facs. Plates XVIII and XIX.
p. 165
7206	acs. Plates XVIII and XIX.
7207	90'!!! sic . 20П= ¡—!!i!!!
7208	90]\|!I
7209	20=1. -!!!! • 900
7210	90'\|8 20= -
7211	→5,y 0 90
7212	— ІiI
7213	190 < →\|l•
7214	1 113
7215	!I=.e sii
7216	21.r L111 •!1: I1 11E
7217	→\|1• 6 lin=lll:
7218	!1 • • F 90='!'l
7219	81 -malla 1020'
7220	- I 1.
7221	==
7222	<
7223	80 #EmAfPPE ELooP '''DLS
7224	1992**
7225	119991*
7226	Í[ •' 11: J. 'I39991 1119999
7227	"999121"
7228	19999 = 9a0 = пn299
7229	• [a1$
7230	79
7231	111
7232	101=LAN06
7233	9na80"2M·R→A
7234	78 9•nAEARMÕA
7235	Plate W
7236	B.M.i
7237	90.MI
7238	32mm
7239	20=. 5 0200
7240	-!LL
7241	0.90-
7242	?T!II
7243	920 m=
7244	,078
7245	1I.5 900
7246	9050 1207
7247	9018
7248	In...I
7249	g. ALbnormal form
7250	f.Is ro crossed out in back
7251	e. Clear in origural.
7252	S. Lisueto etuear io original.
7253	Ked smloge or erasuure. b.
7254	a. Unintelligible signs.
p. 166
7255	a. Cross stroke is part
7256	erroneous (:b
7257	like è C. Lincertai
7258	urusuaL. d. Abro
7259	E. Memeral made lik
7260	J. Red , not. black as in
7261	g. Lncerrain : fold in
7262	h. Made Like 60. k.
7263	2. Not convincing; but u
7264	sic
7265	cos. -
7266	85
7267	Plate X
7268	Over ve a sign of 9 Reas ar •ę[1-"&?12 82
7269	i. Form very
7270	mal form.
7271	5 hk3t
7272	Facs. • ПЕ
7273	papyrus.
7274	Hieratic 3 П •090L -
7275	hat ebe bonible?
7276	• 0 9
7277	""IE1! •u xbe az
7278	-
7279	T'tzolliola
7280	alts"al. DÍARO
7281	o1. 82 B
7282	sö..Il no a e
7283	-
7284	nn
7285	H0"8i. 41i:1800
7286	H°DSRO:ge 83
7287	""NE2t f ş —
7288	"ENE -l
7289	"4Eon
7290	"*8ш 15n900
7291	."F*1EAAДAP
7292	'''h #1"
7293	h "FX! •ERtIHf
7294	111
7295	..= ''!lii= n° (11
7296	'I!I! = 87-
7297	11C 1 1111 "*•\|=
7298	B. M. Facs. Plates XIX to XXI
p. 167
7299	101-enn
7300	12111.72*3
7301	3..
7302	-
7303	# >01•ї= H11
7304	Ả =
7305	??
7306	Af
7307	1844111M D8 sx 110 1111
7308	$, 1111 < 6k 10S0l
7309	0, 111 < • 110 =0
7310	ЩHI 4 •111 =0,1
7311	9. 1111 < • 110=21
7312	19 111 < • 11 #=0;1
7313	eolfoi
7314	090RE11E
7315	Z4"EM=#TnE) 1 - 6c
7316	The i - Ї bath dear in oniginal. b. Orsimply if
7317	Prabably blank in criginal d Perhaps mo loss. e. Probably
7318	10 not 5 as in facsimile § Traces g. Clear in original.
7319	Not convincing on original coin, despile facsimile. First stroke doubttul. k. Certain is here obscured by dis-
7320	coloured gelatine. m. Stroke shown by farsimile accos
7321	This sign is not there
7322	B. M. Facs. Plate XXI.
7323	Plate Y
7324	86
7325	87
7326	B
7327	ULLE
p. 168
7328	RIBLIOTHEAL LILLE
7329	UMVERS
p. 169
7330	1.Erc Peet- THE RHIND MATHEMATICAL PAE
7331	1923
7332	ZA 22504

Provenance

Full provenance, licence and citation: part 1.

What the layers are

L0 witness
The text as its witness or edition has it, original spelling; its dialect is a description and is never standardized.

L0.5 transliteration
For Egyptian texts: the transliteration with the editors' marks turned into the symbols ° * < > _ ^ (ruled 2026-09-10). For papyri: the edition's Leiden marks as the same symbols, and the editors' readings beside the scribe's as ‹scribe→editors› (ruled PAP-3).

L1 Cairene
Standardized Greco-Bohairic spelling and grammar, generated by code from the layer above under the rulings of the project.

L2 Kemetic
The Kemetic alphabet, generated by code from L1.

English
Quoted translations where they exist, credited; otherwise model drafts, marked as drafts.