# | Indogermanic | Proto-Gmc. | Gothic | Old English | Old Norse |
1 | *oinos | *ainaz | ains | ân | einn, ein, eitt |
2 | *d(u)wôw | *twôu | twai | twœyen (twâ, tû) | tveir (tvær, tvau) |
3 | *treyes | *þrejiz | þreis | þrîe (þrîo, þrîo) | þrîr (þrjâr, þrjû) |
4 | *kwetwôres | *fedwôr(iz) | fidwor | fêower | fjôrir (fjôrar, fjogur) |
5 | *penkwe | *femfi | fimf | fîf | fimm |
6 | *s(w)eks | *sehs | saíhs | siex | sex |
7 | *septm > *sepunt | *sebun(þ) | sibun | siofun | sjau |
8 | *oktôw | *ahtôu | ahtau | eahta | átta |
9 | *newn > *newunt | *newun(þ) | niun | nigun | níu |
10 | *dekmt > *dekunt | *tehun(þ) | taíhun | tîen(e) | tíu |
11 | *oin- + *likw- | *ain-lif | ainlif | endleofan | ellifu |
12 | *dwôw + *likw- | *twôu-lif | twalif | twelf | tólf |
13 | *þreji-tehun(þ) | *þreitaíhun | þrîetîene | þrettán | |
14 | *fedwôr-tehun(þ) | fidwortaíhun | fêowertîene | fjórtán | |
15 | *femf-tehun(þ) | fimftaíhun | fîftîene | fimmtán | |
16 | *sehs-tehun(þ) | *saíhstaíhun | siextîene | sextán | |
17 | *sebun-tehun(þ) | *sibuntaíhun | siofuntîene | sjaután | |
18 | *ahtôu-tehun(þ) | *ahtautaíhun | eahtatîene | átán | |
19 | *newunþ-tehun(þ) | *niuntaíhun | niguntîene | nítján |
Indogermanic forms of the decades 20-90 were based on the unit number (1-9) plus a variant (d)komt- of the word for "10" (*dekmt):
Early Developments: Indogermanic to Proto-Germanic ("*" alone means "was lost")
# | Indogermanic | Early Proto-Germanic | Late Proto-Germanic | Pre-Gothic | West Germanic (Pre- Old High German) |
20 | *wîkmt | *wî-hund (*wî- < *dwî- "2") |
* | * | * |
30 | *tríkomt | *þrí-hand | * | * | * |
40 | *kwetwrkomt | *fedwur-hand | * | * | * |
50 | *penkwêkomt | *fimfê-hand | *fimfê-hund | * | * |
60 | *s(w)ekskomt | *sehs-kand | *sehsê-hund | * | * |
70 | *septmkomt | *seftun-hand | *sebuntê-hund | *sibun=têhund | *sebun=tô(hund) |
80 | *oktôkomt | *ahtô-hand | *ahtô-hund | *ahtô=têhund | *ahtô(hund) |
90 | *newnkomt | *newun-hand | *ne(w)un-hund | *niun=têhund | *niun=tô(hund) |
100 | *(d)kmtóm | *hundan | *hund | *tehunþ=têhund | *hund-tehunþ-tiy |
Later Developments: Proto-Germanic to Gothic, Old English and Old Norse
(Note: The Proto-Germanic plural of *tehun "10" is *tigus "10s.")
20 through 60:
# | Indogermanic | Proto-Germanic | Gothic | Old English | Old Norse |
20 | *dwôw + *dekús | *twôu *tigus | twai tigjus | twœn-tiy | tuttugu |
30 | *treyes + *dekús | *þrejiz *tigus | þreis tigjus | þrî-tiy | þrír tigir |
40 | '4' + *dekús | *fedwôr *tigus | fidwor tigjus | fêower-tiy | fjórir tigir |
50 | '5' + *dekús | *femfi *tigus | fimf tigjus | fîf-tiy | fimm tigir |
60 | '6' + *dekús | *sehs *tigus | saíhs tigjus | siex-tiy | sex tigir |
70 through 90 with different pattern-levelings:
# | Proto-Germanic | Gothic | Old English | Old Norse |
70 | *sibun=têhund | sibun=têhund | hund-siofun-tiy | sjau tigir |
80 | *ahtô=têhund | ahtau=têhund | hund-eahta-tiy | átta tigir |
90 | niun=têhund | niun=têhund | hund-nigun-tiy | níu tigir |
100:
# | Indogermanic | Proto-Germanic | Gothic | Old English | Old Norse |
100 | *dekmkómt > *(d)kmkóm(t) > *kmkóm > *kmtóm |
*hundan "120" | taíhun=têhund (once) taíhun=taíhund (3x) |
hund hund-red hund-têon-tiy |
tíu tigir tí-rætt hund-rað (pl.: hund-ruð) |
110 | ellifu-tigir | ||||
120 | *hundan "120" | *hund | hund-twelf-tiy | tólf-rætt hund-rað | |
200 | twa hunda | twa hund, tu hund |
hund-rað ok átta tigir (= 120 + 80) |
||
240 | tvau hund-ruð | ||||
300 | þrija hunda | þrîe-hund | |||
360 | þrjú hund-ruð | ||||
400 | fidwor hunda | fêower-hund | |||
480 | fjogur hund-ruð | ||||
500 | fimf hunda | fîf-hund | |||
600 | fimm hund-ruð | ||||
600 | saíhs hunda | siex-hund | |||
720 | sex hund-ruð | ||||
700 | sibun hunda | siofun-hund | |||
840 | sjau hund-ruð | ||||
800 | ahtau hunda | eahta-hund | |||
960 | átta hund-ruð | ||||
900 | niun hunda | nigun-hund | |||
1,080 | níu hund-ruð | ||||
1,200 | tíu hund-ruð | ||||
1,320 | ellifu hund-ruð | ||||
Et cetera |
1000:
# | Indogermanic | Early Proto-Germanic | Late Proto-Germanic |
1000 | *tûs-(d)kmtóm | *þûs-hundan | *þûs-hundi |
# | Gothic | Old English | Old Norse |
1,000 | þûsundi | þûsend | |
1,200 | þúsund, þús-hund, þús-hund-rað | ||
2,000 | twos þûsundjos | twa þûsend | |
2,400 | tvær þûsundir | ||
3,000 | þreis þûsundjos | þrîe þûsend | |
3,600 | þrjár þûsundir | ||
4,000 | fidwor þûsundjos | fêower-þûsend | |
4,800 | fjórar þûsundir | ||
5,000 | fimf þûsundjos | fîf-þûsend | |
6,000 | fimm þûsundir, fimtán tigir hundruð | ||
6,000 | saíhs þûsundjos | siex-þûsend | |
7,200 | sex þûsundir | ||
7,000 | sibun þûsundjos | siofun-þûsend | |
8,400 | sjáu þûsundir | ||
8,000 | ahtau þûsundjos | eahta-þûsend | |
9,600 | átta þûsundir | ||
9,000 | niun þûsundjos | nigun-þûsend | |
10,800 | níu þûsundir | ||
10,000 | taíhun þûsundjos | têon-þûsend | |
12,000 | tíu þûsundir | ||
20,000 | twai tigjus þûsundjo | twœn-tiy þûsend | |
24,000 | tuttugu þûsundir | ||
Et cetera. |
Note: In the Germanic numeric vocabulary, there are three separate numbering systems:
Alphabetic Character |
Numeric Value |
Note |
A | 1 | ahsa "axis, axle" |
B | 2 | bairkan "birch seedling" |
G | 3 | giba "giving; that which is given, gift, present" |
D | 4 | dags "day" |
E | 5 | aíhvs "horse" |
Q | 6 | qaírþra "lure, bait, decoy" |
Z | 7 | azêti "ease, comfort, pleasureableness" |
H | 8 | hagl "hail" |
Þ | 9 | þiuþ "(the) good, something good." The Gothic letter “thorn” was written like the Greek “psi”, Y, not runic þ |
I | 10 | eis "ice" |
K | 20 | kusma "boil, tumefaction, infected swelling" |
L | 30 | lagus "lake, sea, open water, ocean" |
M | 40 | manna "man, human being" |
N | 50 | nauþs "necessitation, compulsion, force, constraint; duress" |
J | 60 | jêr "year." Written something like “G,” but pronounced as English “y” in “year” or the “K” in “OK” when slurred as “Ogay.” |
U | 70 | ûrus "urus, aurochs," extinct European bison |
P | 80 | paírþra "dice cup, dice box, cup for throwing dice" |
q | 90 | Koppa; used only as a number, never as a letter |
R | 100 | raida "ride, journey; riding vehicle, wagon" |
S | 200 | sáuïl sun |
T | 300 | Teiws "Tew, Tyr, Tiu or Ziu," before Wodan's time, the highest divinity, the one-armed god of the sky and war (and god of "Tue's day"); = Roman Mars. |
W | 400 | winja "pasture, grazing meadow." Written like a capital “Y” |
F | 500 | faíhu "movable goods, chattels; property, possessions; wealth, riches; money" |
X | 600 | Iggws [Originally NG-rune] "Ingw," a Germanic demigod, myhical progenitor of the Anglo-Frisian Ingwaeones |
Hv | 700 | hvaír "cauldron." Written like the Greek “theta,” Q |
O | 800 | ôþal "patrimony, ancestral inheritance" |
á | 900 | Teiws "Tew" The RUNE Teiws or Tyr (see "T," above); written as an upward-pointing arrow. Not used as a letter. |
The key concept in the development of modern arithmetic and mathematics was the concept of zero.
The philosophical preparation for the concept of zero was laid in the Middle Ages by the Christian schoolmen who, following Aristotle, viewed the world as being composed of “form” (forma) without “substance” (materia). During the crusades, the Latin West borrowed not only Greek philosophy from the Mohammedans (who had translated it into Arabic), but also the Sanskrit numbering system. That is, the numerals we currently use came from the "Indo-" part of the Indogermanic-speaking peoples. For the Muslims had conquered northern India and adopted the mathematics originally invented and used there, whence they took these numerals to the west. Europeans came in contact with them during the crusades. As a result, the “Arabic” numerals 0 1 2 3 4 5 6 7 8 9 are in actual fact not Arabic at all, but Sanskrit and Indic. Europeans then took this Arabic-overlayed Sanskritic mathematics (“algebra,” “zero” and “algorithm,” like “alchemy” and “chemistry,” are Arabic words) and, combining it with Graeco-Roman philosophy which viewed the universe as essentially rational, began to develop mathematics as we know it in the West today - a mathematics which is the foundation of science. “Zero” (same word as “cipher”) was viewed as pure “form” without substance, whereas the other digits were thought of as various levels of form with substance. This made modern calculations possible (Imagine having to multiply and divide with Roman numerals!). Our history, thus, is a history of the synthesis of ideas. We take the best ideas from any and every source and combine them with the best ideas from elsewhere, thereby creating new intellectual structures much more powerful than any of its components. No other branch of man has come anywhere close to us in this respect. |
— Þeedrich = (reachable at theedrich@harbornet.com) |