?. horus was the son isis and osiris, who was treacherously slain by by his brother seth. in...
TRANSCRIPT
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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 Eyea glimpse on Egyptian writing
of numbers and dealing with fractions
Balder P. Gloor
Egyptian writing 2900 – 100 acHieroglyphic ≈ typwritten or print
Hyeratic ≈ handwriting difficult to readDemotic = 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
Indo-Arabic (we) from left to right
We and Egyptians from right to left!
In German 13 - 99 In English 13 – 19 also r l
But addition and subtraktion: We and Egyptians from right to left!
4 7 3 1
3 8 9 2
1 1
8 6 2 3
Egyptian numerical writing
decimal system
no zero ( 0 )!
additive
To read in the direction where a head of a digit is looking
handle
rope rolled up
Lotos flower
Raised finger
tadpole
god
Egyptian = additive writing of numbers
7 50 100 20 000 400 000 3000
7 5 1 3 2 4
4 2 3 1 5 7
20 against 6 digits !
cows goats prisoners
400 000 1 422 000 120 000
prisoners
100 000
20 000
120 000
Example of big numbers
Addition
Major difficulties with fractions Egyptians
calculated with unit fractions (1/ n)
¾ was written ½ + ¼
6/7 was written ½ + ¼ + 1/14 + 1/28 14/28 + 7/28 + 2/28 + 1 /28 = 24/28 = 6/7
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
the least common multiple
1
1/2
1/4
1/8
1/16
1/32
1/64
I
The six parts of the Horus Eye are used as hieroglyphs of fractions for measurement of volumes of grain (Hekat)
The whole eye = 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
Thank youfor your
attention
Osiris underneath the eye of Horus
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 acHieroglyphen = „Maschinen- oder Druckschrift“
Hieratisch = Handschrift, verbunden wird + unleserlichDemotisch = 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“)
indo-arabisch (wir) von links nach rechts!
Aber Addition Subtraktion: auch wir von rechts nach links
Ägypter von rechts nach links
4 7 3 1
3 8 9 2
1 1
8 6 2 3
Big problems with fractions Egyptians calculated with unit fractions (1/ n)
¾ wurde geschrieben ½ + ¼
6/7 wurde geschrieben ½ + ¼ + 1/14 + 1/28
For 2/3 the scribes had tables of the most commun z. B.
27 9
365 243 1/3
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 HorusWappentier der Ophthalmologie
Und was noch?