DOI Page / Citation link:
https://doi.org/10.11588/diglit.6444#0024
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.
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.