?
Horus was the son Isis and Osiris,
who was treacherously slain by by
his brother Seth. In revenge, Horus
sought out his uncle and slew him,
but Seth teared his eye out and
broke it in six parts.
?
But another god, Thot, the eye
doctor, spit on the parts
and the parts came together
again.”
This is why the Eye of Horus
became the heraldic flag of ophthalmology
But is this all about? Thot was also the god of the moon, the
creator of the calender and the master over time for
gods and humans!
The Horus Eye
a glimpse on Egyptian writing
of numbers and dealing with fractions
Balder P. Gloor
Egyptian writing 2900 – 100 ac
Hieroglyphic ≈
typwritten or print
Hyeratic
≈ handwriting  difficult to read
Demotic
=
Ptolemies, Romans
Text from right to the left, numbers variabel
In our time: Usually (!) transposed: from left to right
(transliteration), then translated in Indo-Arabic
4
Indo-Arabic (we) from left to right
We and Egyptians from right to left!
3
In German 13 - 99
1
In English 13 – 19 also r  l
8
But addition and subtraktion:
We and Egyptians from right to left!
7
3
1
8
9
2
2
3
1
6
Egyptian
numerical writing
handle
rope rolled up
decimal system
no zero ( 0 )!
additive
Lotos flower
Raised finger
tadpole
god
To read in the
direction where a
head of a digit is
looking
Egyptian = additive writing of numbers
7 50
7 5
100
20 000 400 000
3000
1
3
2
4
4 2 3 15 7
20 against 6 digits !
Example of
big numbers
prisoners
100 000
20 000
120 000
cows
goats
prisoners
400 000
1 422 000
120 000
Addition
Major difficulties with fractions
Egyptians calculated with unit fractions (1/ n)
the scribes had tables of
important fractions, like 1/3, 2/3,
of the most commun numbers,
e.g.
2/3 of 27 (the month)  18
2/3 of 365 (the year)  243
¾
was written
6/7 was written
½ +¼
½ + ¼ + 1/14 + 1/28
14/28 + 7/28 +
the least
common
multiple
2/28 + 1 /28 = 24/28 = 6/7
The whole eye =
I
hekat
1
1/2
1/4
1/8
1/16
1/32
1/64
The six parts of the Horus Eye are used as hieroglyphs of
fractions for measurement of volumes of grain (Hekat)
Hekat = dry measure
for grain
The whole eye = 1 hekat
1
hekat ≈ 1 gallon ≈ 4,5 l
½ hekat ≈
2,25 l
¼ hekat ≈ 1 quart ≈ 1,125 l
1/8
≈ 1 pint
1/64 hekat = 5 ro
1 ro
= 1/325 Hekat
≈ 1 spoon
Summary: The egyptian scribes
had, with the parts of the eye of
Horus, simple hieroglyphes at hand,
to write, add and handle fractions for
the most important thing in daily life:
FOOD (GRAIN); the story behind a tale or myth to provide an
explanation!
Where my wisdom comes from:
Richard J. Gillings, Mathematics in the time of the
Pharaohs, Dover publications, New York 1972,
1981
Geniève Guitel, Histoire comparée des numérations
écrites, Nouvelle Bibliothèque Scientifique,
Flammarion, Paris 1975
André Pichot, Die Geburt der Wissenschaft,
Campus, Frankfurt, 1991, 1995
Osiris
underneath
the eye of
Horus
Thank you
for your attention
A glimpse on Egyptian writing
of numbers and
handling of fractions
Balder P. Gloor
?
But another god, Thot, the eye
doctor, spit on the the parts
and the parts came together
again.”
Osiris underneath the eyes of Horus
Fractions of the measures
of grain
1 Hekat = ca 4,5 l ≈1 gallon
1 ro = 1/325 Hekat = 1 spoon
Addition
Rind Mathematical Papyrus
Boisseau = scheffel = bushel
Ägyptische Schrift 2900 – 100 ac
Hieroglyphen = „Maschinen- oder Druckschrift“
Hieratisch
= Handschrift, verbunden  wird + unleserlich
Demotisch = Ptolemäer, Römer
Geschrieben von rechts nach links, Zahlen +
Zahlen lesen: Beginn dort wo ein Kopf hinschaut
zum besseren Verständnis umgeschrieben  li nach rechts
(Transliteration), dann noch in indo-arabisch transponiert („übersetzt“)
4
7
3
1
3
8
9
2
Aber Addition Subtraktion:
1
1
auch wir von rechts nach links
8
6
2
3
indo-arabisch (wir) von links nach rechts!
Ägypter von rechts nach links
Big problems with fractions
Egyptians calculated with unit fractions (1/ n)
For 2/3 the scribes
had tables of the
most commun z. B.
27 
9
365  243 1/3
¾
wurde geschrieben
6/7 wurde geschrieben
½ +¼
½ + ¼ + 1/14 + 1/28
Osiris war von seinem Bruder Seth getötet
worden, und als Horus, der Sohn des Osiris
und der Isis, seinen Vater zu rächen versuchte,
riss ihm Seth ein Auge aus und zerriss es in
sechs Teile. Doch ein anderer Gott, Thot, der
“Augenarzt”, spuckte darauf und stellte es so
wieder her”
A. Pichot, Die Geburt der Wissenschaft, Campus Verlag 1995,
S.164
Das Auge des Horus
Wappentier der Ophthalmologie
Und was noch?

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