Griffith, Francis Ll. [Editor]
The Petrie Papyri: hieratic papyri from Kahun and Gurob ; principally of the Middle Kingdom (Band 1): Text — London, 1897

Page: 15
https://digi.ub.uni-heidelberg.de/diglit/griffith1897bd1/0024 0.5
1 cm 15

PLATE VIII.

MATHEMATICAL FRAGMENTS.

On the autotype plate are shown two small
papyri found together, one containing an
arithmetical table, the other a calculation, and
several fragments of mathematical papyri, be-
sides one fragment the interest of which
consists in its containing high numerals. On
the plate of transcription is given a facsimile
of some additional fragments of LV. 3 and 4.

Kahun, IV. 2.

[PL VIII., 11. 1-10.]

Found at Kahun, April, 1889. Length, 8 in.
= 20 cm. Width, 6 in. = 15 cm., originally
more (?).

Recto.—Bears some trace of a text washed
off : a narrow and inconspicuous strip of

papyrus is pasted upon this side to mend a
hole.

Verso.—Table of the division of 2 by odd
numbers 1 : a palimpsest trace on the left-hand
edge.

The table shows the values of the division of
2 by odd numbers from 1 to 21; in other words,

it is a table of the fractions f, f, f...... n,

expressed according to the Egyptian method,
which admitted the " radical" fractions ^,

\, j...... ioooj &c. (with numerator unity, and

denominator of any magnitude), but excluded
f, f, &c, i.e. all fractions with numerator
exceeding unity, except only §—but even in
this case the hieroglyphic sign clearly indicates
the conception of f as When re-arranged
for clearness, the table is :

2+ '3 = | (proof)

1 of 3

2 "T- 5—3 + 15

i of 5

2 -r 7 = 4 +

i of 7

2+9=^+^

* of 9

2 + 11 = i + *

* of n

2 • 13 — 8 + 52 + 104

| of 13

2 -r- 15 = To + -30

To of 15

2-5-17 =12 + 5t + 6~8

iVof 17

2 -r- 19 =fx + T^g + yyj

A of 19

2 -r 21 =t4+ "jV

rVof 21

The papyrus expresses this"very briefly :

2 3 f 2

5 3 If

1

1 5

i

3

7 j* in

1

1

' 4 x2 4

28

4

&c. &

C.

= 2

= If* rV of 5 = i (total If + i = 2)
= H;i of 7 = i (total 2)
= Hi -rs = \ (total 2)
= 1* % -h = i (total 2)

— 1^ lb = 4, t^j = 1 (total 12"i" + i + ^ = 2)
= H, = i (total 2)

= 1^ 1^9 ~h\ = \> = \ (total l"g""r2 + ¥ + T = 2)
= ltA.^ = i. Th[=i] (total 2)
= 11, 4T = i (total 2)

The E/imii Mathematical Papyrus (Hyksos
period), pis. i.-ix., gives the same table extended

1 The use of this table is explained Proc. Soc. Bill. Arch.,
xvi., pp. 201 et seqq. 