MATHORIGINS.COM_L

 

Home | Color Guide | Abbreviation Guide | Personal Library Master key | Usage Guide | Thank You A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W-X | Y-Z 

Last updated 12/25/05

 

 

 

See images and analysis of ancient mathematical objects: IMAGE GRID

 

LABYRINTHS: (AE) amazing

See also BPAW, [B_200] and LEPSIUS, [B_238]!

 

See Hawara (complex of Amenemhet) Labyrinth info at:

http://www.casa.ucl.ac.uk/digital_egypt/hawara/

This complex was described by Herodotus (II, 148) and Strabo.

 

See also:

Arnold D. Das Labyrinth und seine Vorbilder. MDAIK 35 (1979), p. 1-9.

 

Lloyd A.B. The Egyptian Labyrinth. JEA 56 [B_303] (1970), p. 81-100.

 

Petrie, W. M. F. Hawara, Biahmu and Arsinoe. London 1889.

 

Petrie, W. M. F. , Wainright G. A. , Mackay E. The Labyrinth, Gerzeh and Mazguneh, London, 1912.

 

(as per EEF; J. Gee) see also Eric Uphill’s “Pharaoh’s Gateway to Eternity”, London, 2000.

 

 

LAC MOERIS: (AE, BOTD) papyri

P. Lac Moeris.= Lake Moeris, see WADI.

 

(as per E. G. Turner) See Birket el-Qarun.

 

(as per LEX) Seek work by Ridolfo Vittorio Lanzone, Turin, 1896. [B_273]

 

[B_273,no copies,IGNR]

CATNYP# *OBKQ+++(Lanzone, R. V. Papyrus du Lac Moeris)

“Les Papyrus du lac Moeris, reunis et reproduits en fascimile et accompagnes d’un texte explicatif, par R. V. Lanzone. 9 planches en chromolithographie; figures et carte geographique dans les texte.”

Turin, 1896.

Note CATNYP has this incorrectly listed as *QBKQ!

This is funerary and depicts numerous animal and hunting scenes.

A tome of images of reproductions of an obscure original.

 

 

LACHISH aka LAKISH: (Paleo-Hebrew and Semitic) letters; ostracon

See YADIN. See Amarna. See Arad Letters [800-600 BCE]?

[Biblical Archaeology/evidence from the ruins of Tell ed-Duweir [40 kilometers southeast of Jerusalem]. Some written during the reign of Zedekiah, the last king of Judah, ca. 590 BCE.]

 

http://www.bibarch.com/ArchaeologicalSites/Lachish.htm

[Lachish; a Canaanite Bronze Age Fortress.(Persian territory)]

“These letters consist of the correspondence between the commander of the city of Lachish and an unidentified Judean outpost at the time of Nebuchadnezzar's invasion of Judah in 587 BCE.”

 

http://www.stolaf.edu/people/kchanson/lachish3.html

 

Bibliography of helpful texts:

http://seminary.georgefox.edu/courses/bst550/reports/RHalverson/LachishLet.html

 

Image [faded ostracon]:

http://seminary.georgefox.edu/courses/bst550/reports/RHalverson/LachishOstraca.jpg

 

http://www.bible.gen.nz/amos/glossary/Lakish.htm

 

http://www.us-israel.org/jsource/Archaeology/lachish.html

 

http://www.sbl-site.org/Publications/Epubs/PCHDP/Lachish3.html

 

On Olga Tufnell who unearthed the letters:

http://www.pef.org.uk/Pages/Tuffnell.htm

 

  jhkh

 

LAGASH: (cuneiform) tablets from ancient city of

see UHN. [B_359].

 

 

LAHUN: (AE; Hieratic) papyri

See also KAHUN.

 

(as per AEMT) The Lahun Papyri are associated with

Pharaohs Senusret I and II.

 

(as per AEB) Lahun Studies. Ed. by Stephen Quirke, Reigate (Surrey), SIA Publishing, 1998. [S. Quirke, Curator of the Petrie Museum.]

 

See below

http://www.digitalegypt.ucl.ac.uk/lahun/uc32159.html

LAHUN: [Math] fragments
See link to PETRIE museum item#: UC32114b
http://www.petrie.ucl.ac.uk/search/detail/results/detail.asp?01_objectidentifier=UC32114b
See KAHUN
http://www.petrie.ucl.ac.uk/search/detail/results/detail.asp?01_objectidentifier=UC32118b
http://www.petrie.ucl.ac.uk/search/detail/results/detail.asp?01_objectidentifier=UC32134a
This one above is LV.3; See KAHUN
http://www.petrie.ucl.ac.uk/search/detail/results/detail.asp?01_objectidentifier=UC32159
http://www.petrie.ucl.ac.uk/search/detail/results/detail.asp?01_objectidentifier=UC32160
http://www.petrie.ucl.ac.uk/search/detail/results/detail.asp?01_objectidentifier=UC32162
This one above is LV.4; See KAHUN
http://www.petrie.ucl.ac.uk/search/detail/results/detail.asp?01_objectidentifier=UC54961A-D
http://www.petrie.ucl.ac.uk/search/detail/results/detail.asp?01_objectidentifier=UC62770
These two above not from LAHUN but interesting.

 

LALITAVISTARA: Sutra

See CUBIT; BUDDHA; TSS.

 

See an alternate tr.Tarthang Tulku : The Lalitavistara Sutra, the voice of the Buddha. Berkeley, Ed. Dharma

Publishing, 1983, 2 volumes, 714 p. Maha.

Another:

Lalitvistara: Development of the plays, containing the history of the Sakyamuni Buddha, from its birth to its

preaching. Paris, ED Ernest Leroux, 1884, vol. I, translated Sanskrit (Annals of the Guimet Museum, 6).

Reprint. Maha.

 

Another:

Lalita-Vistara Sutra

Edited by: Dr. P.L. Vaidya

Date of Publication: 1958

Publisher: The Mithila Institute of Post- Graduate Studies and Research in Sanskrit Learning, Darbhanga, India.

 

The Lalita-vistara : memoirs of the early life of Sakya Sinha (Chs. 1-15)

http://www.amazon.com/exec/obidos/ASIN/8170305764/atriumA

 

*as per UHN; page 424

*Section on CUBITS; METROLOGY within Lalitavistara sutra: Buddha, age 8 years, in training by Sage Vishvamitra.

See also “Light of Asia / by Edwin Arnold.”

 

[B_558,8.5’s]

CATNYP# *OLWF 88-4510

Title: Tripitaka. S_utrapitaka. Lalitavisara. English.

“The voice of the Buddha, the beauty of compassion / translated into English from the French by Gwendolyn Bays.”

California, Dharma Pub., 1983

From the series: TSS.

Includes Buddha’s [Mahayana Buddhism; pre-enlightenment; legends] discourse on Metrology.

Volume 1 title page: “Lalitavistara / ‘phags-pa rgya-cher-rol-pa zhes-bya-ba theg-pa chen-po’i mdo”

My archives include copies from volume one [of two], pages 210-238.

See chapter 12, “Skill in the Worldly Arts.”

Text of this chapter [12] includes these varied names for Buddha:

Prince / son of King Suddhodana / young Sarvarthasiddha / [potentially godlike] Tathagata Arhat

Buddha / [potentially as successor] Cakravartin King / [one of many] Bodhisattva / the Muni

 

p. 211-212:

O’ Monks. When the Prince had grown still older, King Suddhodana met in the council hall with the assembly of Sakyas. The eldest of the Sakyas spoke thus to King Suddhodana:

“Oh King, you know what has been predicted for the young Sarvarthasiddha by the brahmins who know the signs and by the gods whose knowledge is certain. If the prince leaves his family, he will be a perfect and fulfilled Tathagata Arhat Buddha. But if he does not leave home, he will be a Cakravartin King, a conqueror, a king devoted to the Dharma, posessing the seven precious jewels: the wheel, the elephant, the horse, the mani stone, the queen, the chancellor, and the counselor. He will have a full thousand sons, great heroes, powerfully built and full of courage, conquerors of great armies. Having subjugated this great earth without using weapons or force, he will govern by means of the Dharma.”

“This is why the young prince must be married.Once he is married and surrounded by women, he will know such pleasure that he will never leave his family, and in this way the succession of Cakravartin kings will surely be maintained. The Sakyas will be respected and not subject to the scorn of the frontier kings.”

[Seems inherently illogical doesn’t it. i.e. Sakyas put less faith in the worth of Enlightenment than conquest]

[compare tho Enkidu and the Harlot in the Epic of Gilgamesh. Strength of desire.]

[compare to Homer’s “Odyssey” and Herodotus “Histories” in the development of settings surrounding the interpretation of oracles.]

 

page 213:

All previous wise Bodhisattvas have been shown with a wife and a son…”

[This is not the first Buddha or first incarnation of Buddha?]

(Buddha describing a woman he would marry)

“A common woman who lacked good conduct or qualities such as truthfulness would never suit me. The woman who would truly delight me is modest and very pure, in body and birth, in family and race.”

[Buddha here is antagonistic towards intermarriage of races; xenophobia!]

 

page 215:

(King Suddhodana directing his assembly to find Buddha a good woman

“The prince does not consider the family or the race; he looks only for the virtues.”

[Apparently intermarriage is not common enough to even deserve mention!]

 

page 216:

(Some assemblymen recruiting Buddha’s future wife encounter Gopa, the daughter of Sakya Dandapani.)

[Gopa says]: “Brahmin, I have all the suitable qualitites. May this loving and handsome young man be my husband! The prince has spoken; let there be no delay! With an ordinary woman, he could not live.”

[She does not seem modest here!]

 

page 218:

(Sakya Dandapani, Gopa’s father, says to King Suddhodana)

“Lord, it is the custom of our family to give our daughters in marriage only to men skilled in the arts, and your son has grown up in luxury in the palace. If he does not excel in the arts, does not know the rules of fencing or archery or boxing or wrestling, how then can I give my daughter to him?”

(This discourse troubles the King and sets the stage for a competition)

 

“When the Bodhisattva learned what had transpired, he went to the king saying: “Sire, you are troubled. What is worrying you?” To which the king replied: “Young man, do not ask.”

[Buddha first somehow learned of the problem and then proceeds to nag the king into telling him what he already knows!]

“But the prince persisted: “It is always necessary to explain oneself.” Three times the Bodhisattva questioned King Suddhodana, until the king finally explained the situation. At once the Bodhisattva reassured him: “Sire, is there a single person here in the city who can rival my dexterity and skill in the arts?”

[Buddha seems to boast here.]

“… the king questioned the Bodhisattva still further: “Could you, my son, prove your skill?”

[Odd, the father does not know at all of his own son’s skills and training]

 

Page 219:

“On the seventh day, five hundred young Sakyas came together, and Gopa, the daughter of Dandapani, was promised as the prize for the victorious one; to the one who wins in fencing [1], in archery [2], in boxing [3], and in wrestling [4], she would belong.”

[Seems illogical as four different winners are possible; Bruce Jenner won the decathalon but not all the individual events.]

 

“The young Devadatta [nemesis; wild like Enkidu killing Hawara; see GILGAMESH] … envious and drunk with pride..drunk with his own strength…(kills elephant)”

[This irrational act is softened by the virtuous Sundarananda who drags the elephant corpse outside the city.]

 

Page 220: Bodhisattva is aware of the elephant having been dragged, maybe he saw the path where it had been dragged.

 

Buddha throws the rotting corpse of the elephant far away from the town with one foot.

“Upon seeing this, gods and men by the hundreds of thousands waved scarves and cheered…”

[Gods here seem especially attentive and proud]

 

Page 221:

“First, the young Sakyas skilled in writing [5] contended with the Bodhisattva.”

[A fifth contest]

 

“The Sakyas said: “Let the young man reveal his knowledge of mathematics [6].”

[A sixth contest]

 

Page 222:

“Forthwith Bodhisattva proposed a problem, and …(nobody could solve it).”

[Why was the question not posed by Arjuna, the resident mathematician?]

 

(500 Sakyas compose an unsolvable question and Bodhisattva solves it easily)

 

Page 223-224:

(The multitude of Sakyas declare)

“Victory to the young Sarvarthasiddha!”

 

Buddha’s discourse on metrology

“A hundred kotis is called ayuta;

100 ayutas=niyuta;

100 niyutas=kankara;

100 kankara=vivara;

100 vivaras=aksobhya;

100 aksobhyas=vivaha;

100 vivahas=utsanga;

100 utsanga=bahula;

100 bahula=nagabala;

100 nagabalas=titila;

100 titilas=vyavasthanaprajnapti;

100 vyavasthanaprajnaptis=hetuhila;

100 hetuhilas=karahu;

100 karahus=hetvindriya;

100 hetvindriyas=samaptalambha;

100 samaptalambhas=gananagati;

100 gananagatis=niravaravadya;

100 niravaravadyas=mudrabala;

100 mudrabalas=sarvabala;

100 sarvabalas=visamjnagati;

100 visamjnagatis=sarvasamjna;

100 sarvasamjnas=vibhutangama;

100 vibhutangamas=tallaksana”

 

“Now with the numeration called tallaksana one could take even Meru, the king of mountains, as a subject of calculation and measure it. And next is the numeration called dvajagravati; with the help of this numeration, one could take all the sands of the river Ganges as a subject of calculation and measure them.

Above this is the numeration called dvajagranisamani; and above this is the numeration of vahanaprajnapti; next comes the numeration called inga; above this is the numeration of kuruta.

Again above this is the numeration called sarvaniksepa, with the help of which one could take the sands of ten Ganges rivers as a subject for calculation and measure them all.

[this is ILLOGICAL!; see dvajagravati]. And again above this is the numeration called agrasara, with the help of which one could take the sands of a hundred kotis of Ganges rivers as a subject of calculation and measure them all. And again above this is the highest numeration called uttaraparamanurajahpravesa, which is said to penetrate the most subtle atoms [molecules?]. Except for a [Go to page 225] Tathagata, or a Bodhisattva who has reached the purest essence of enlightenment…”

 

Page 225:

Arjuna [the great mathematician further] said: “Young man, how must one proceed in the numeration which penetrates the dust of the most subtle atoms?”

(Bodhisattva discourse on sub-molecular metrology)

“Seven subtle atoms [molecules?] make a fine particle

7 fine part.=small part.

7 small part.=vatayanaraja

7 vatayanaraja=sasaraja

7 sasaraja=edakaraja

7 edakaraja=goraja

[All above are smaller than dust and most likely conceptual rather than measured [?] ]

[Is any surviving inscription reference to any of these above measures?]

 

7 goraja=liksaraja [7 specks of dust stirred up by a cow=1 poppy seed]

7 liksaraja=sarsapa [7 poppy seeds=1 mustard seed]

7 sarsapa=adyava [7 mustard seeds=1 grain of barley]

7 adyava=anguli [7 grains of barley [must be determinable!]=1 phalange or digit or knuckle!]

12 anguli=parva [handspan or span or half cubit!=12 fingers]

2 parva=hasta [CUBIT=2 spans!] [Greek cubit was also composed of 24 fingers=2 spans]

4 hasta=dhanu [4 CUBITS=1 arc or 1 bow; similar to our fathom=about 2 meters]

1000 dhanu=krosa (of the country of Magadha) [4000 CUBITS =~about 1 mile]

4 krosas=yohana [16000 CUBITS; see Page 231!] ~3 miles? As per translation via this link:

http://www.ralphmag.org/newZH.html

[Again it seems very strange to divide your metrology on base seven!]

[Stranger here than even the AE Royal Cubit]

See UHN page 424.

[How many “subtle atoms= 1 cubit?:]

(7^10) x (12 x 2) = 6,779,405,976. = 1 hasta = 1 cubit

[an inconsistent and difficult base]

A cubit divided by over 6 billion parts!

1 [span] = 3,389,702,988 subtle atoms!=1 parva

1 [finger or knuckle] anguli = 282,475,249 subtle atoms!

 

Cambodian Cubit=~435 mm. = 2S=24F

AE Royal=~535 mm. = 7P=28F

[above] Malayan C=2S=24F=168 B*

See Ziggurat of Babylon [Kus(h)]=30F=180B* [s(h)e or Uttetu]

[Not necessarily actual or any local barley]

Z cubit=36B=1 Sun diameter same as Persian C.

See Mayan Matl and Arabic Pik Belady.

Results from my Barleycorn analysis [American grown, dried barleycorns.]

42 B= 187mm, 210mm, 181mm

which results in a cubit of: 724 to 840 mm! TOO BIG!

 

Page 228:

“And as they continued in their contests – in jumping [7], in swimming [8], in running [9] and all the rest…”

(Bodhisattva demonstrates his superiority)

[seventh, eighth and ninth contests…]

 

“power of love and self denial”

[unique and interesting phraseology]

 

Page 229:

“…yet he travels to all the worlds in an instant”

[transcendental?]

 

“But the Sakyas said: “The people want the prince to show his superiority in feats of strength as well.”

fencing [1],

archery [2],

boxing [3],

wrestling [4]

writing [5]

mathematics [6]

jumping [7],

swimming [8],

running [9]

[1-4; 7-9, seem to be feats of strength already resolved, illogical, this statement is followed by wrestling [4]]

 

Page 230:

[none can defeat Bodhisattva in wrestling]

 

“All the beings in the ten directions,

no matter how fearsome,

he would conquer in a moment…”

[Which 10 directions?; subtle implication of a 4th and 5th axis on a graph; more likely North, East, South, West, and up and down]

 

Page 231:

(Dandapani [Gopa’s father] directs archery competition)

 

Ananda [with Nanda, was first to wrestle with Bodhisattva] sets his target at 2 krosas [8000 cubits of 16-

26 inches? Range is reasonably assumed by myself.];

2 krosas=~2.02-3.28 miles!

[Are these the krosas of the country of Magadha? Setting is city of Kapilavastu; p. 219.]

Devadatta [nemesis/elephant killer] sets his target at 4 krosas

Sundurananda [honorable elephant dragger] sets his target at 6 krosas

Sakya Dandapani [Gopa’s father competes for her - as a wife!] at 8 krosas!

Bodhisattva sets his [closest] target at 10 krosas, ~10.1-16.41 miles!

[Note the arithmetic progression]; [exaggeration of numbers as in SKL; AE barks]

 

Page 232:

[finding a bow of sufficient strength for Bodhisattva]

“Your Grandfather Simhahanu, the Lion’s Jaw, had a bow which is now honored in the temple of the gods..”

[Similar to Odyssey and Gilgamesh, honored / retired weaponry and/or armor set in temples] See HOMER and GILGAMESH.

 

Page 233:

[Buddha’s arrow strikes the Earth and causes a spring to burst forth]

Sarakupa=Spring of the Arrow

Like the area defined by the elephant Buddha tossed with one foot, legend here gives deeper meaning to geography, a universal theme.]

 

“Without any training, he has such skill in every worldly art!”

[How could the king’s son have no training?]

 

“The former Buddha Ksitigarbha previously sat just so,

shooting the arrows of egolessness and emptiness

through the sky of tranquility..”

[Former Buddha? Phrasing is lovely. Can this offer a reasonable chronology?]

 

P. 234-235:

[Poorly constructed and conflicting list of skills/contests in which Buddha excelled.]

See Archery and separate Use of the Bow

Game of dice?

Joking?

Mime?

Explanation of dreams?

The action of throwing forward, backward, and taking away? [wrestling or math?]

The science of tending the fire?

Decorating the body?

Business? [what kind of test?]

Knowledge of the riches? [a shopping test?]

Silk manufacture [a worm race?]

In dyes [a tie-dye contest?]

Working with wax [what kind of test?]

Extracting oil [what kind of test?]

Cutting of palm leaves [what kind of test? Basketweaving?]

And things. [still further skills not specified; an olympic suprathon]

 

Buddha wins hand of Gopa; Buddha betrothed.

 

[complaints from the masses of Gopa’s behavior]

“This young woman has far too lax a manner! Always she goes about unveiled!”

[Is Gopa vain or humble or both?]

 

Page 236:

[Gopa justifying her behavior]

“Those who speak sweet words with malice in their hearts are like a pot of poison covered over with ambrosia, like the bitter pith of wild fruit.

Drawing near such hardhearted people is like carressing the head of a serpent.”

[Beautiful phrasing]

 

Page 237:

[Gopa still justifying her behavior]

“The magnanimous rsis [who?],

skilled in penetrating the thoughts of others [omniscient, ESP?],

know my intentions, just as the assemblies of the gods know my conduct,

my virtues, my restraint, and my modesty. Why should I veil my face?”

 

Page 238:

[Gopa exhonorated by King Suddhodana; king speaking to community]

“My son is adorned with great virtues,

and his bride has qualities like his own;

the union of these two pure beings

is like the union of butter and ghee.”

[A happy ending with moral and purpose.]

 

http://www.borobudur.tv/survey_1.htm

"A standard cubit in Cambodia would range roughly between .40 and .50 m. I used this range to divide axes and circumferences at Angkor Wat until finally, after four months of trial and error, a very precise unit of .43545 m yielded the most consistent results." (2)

(2) Angkor Wat: Time, Space and Kingship by Eleanor Mannikka. University of Hawaii Press, copyright 1996, pp. 17-18.

 

http://www.ralphmag.org/newZH.html

[Buddha] names all the atoms in a yojana (a league roughly three miles):

seven of the finest atoms make a grain of very fine dust,

seven of which make a little grain of dust.

seven such grains make a mote you can see in a sunbeam,

seven of these a rabbit's grain,

seven rabbit's grains a ram's grain,

seven ram's grains an ox's grain,

seven ox's grains --- a poppy seed!...

he continues on to mustard-seed

and barleycorn

and knuckles, twelve of which make a span

two spans a cubit,

four cubits a bow,

a thousand bows a cry in the land of Magadha.

 

(as per V. Gupta; 082904; personal correspondence)
On pp 135 of "The Wonder That Was India" by A.L. Basham, it states that:

"The Yojana, like the medieval English league is an uncertain measure of distance varying from four to ten miles; but internal evidence shows that the author of Arthasastra had in mind a Yojana of about 5 miles."

On page 503, under Appendix VII, the same author gives the weights and measures as follows:

8 yavas (barleycorns) = 1 angula (finger's breadth, 3/4 inch)
12 angulas = 1 vitasti (span, 9 inches)
2 vitastis = 1 Hasta or aratni (cubit, 18 inches)
4 Hastas = 1 danda (rod) or dhanus (bow, 6 ft.)
2000 dhanus = 1 krosa (cry) or gruta (cow-call, 2 1/4 miles)
4 Krosas = 1 yojana (stage, 9 miles approx.)

Though most sources give krosa as of 2000 dandas the Arthasastra gives it as of only 1000, the yojana, which was the commonest measure of long distance in ancient India, being thus of only 4 1/2 miles. It is therefore clear that there were at least 2 yojanas, and the distances as given in the text are thus very unreliable. It would seem that for practical purposes the shorter yojana was more often used than the longer, especially in earlier times.

…note that the finger breadth is given as 3/4 inch.
So based on that a yojana will be = 4 (krosas)* (1000 dhanus)*(4 hastas)* (2 parvas)*(12 angulas)
Or
1 yojana = 384,000 angulas
= 384,000 (3/4 in./angula)/(12 in./ft.)(3ft/yd*1760)= 4.545 miles

On Index page the same author says Yojana = 4 1/2 to 9 miles.

This is the measure in Lalitavistara. If you use this measure then there is no ambiguity. Number of atoms per angula will be 282,475,249. Since 1 angula is about 3/4 in (approx. 20 mm), number of atoms per millimeter will be 14.2 millions. Modern estimate is about 3 to 10 million atoms per mm length. So Buddhists were extremely close to modern estimate...

 

(as per V. Gupta; 083104; personal correspondence)
Ancient Indian mathematics websites:
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Indian_sulbasutras.html

 

http://www.geocities.com/dipalsarvesh/mathematics.html

 

[*] pursue the tr. by Bijoy Goswami.

 

…[more correspondence from this date]
Please use the following Sanskrit names for the size of the atoms. A parmanu in Sanskrit means an atom. Yava or Adyava means barley corn. Here it means width of a barley corn. An anguli means finger and anguliparvan may mean finger breath (also translated as finger-joint). A finger joint is about 3/4 inch. Liksa means a louse and liksarajah may mean egg of a louse (or a small particle of dandruf or something like that). I do not think Liksarajah means a poppy seed. Dhanu or Dhanuh means a bow. Hasta means a length from elbow to the tip of middle finger. [CUBIT]

 

7Parmanus =1anu7anu=1truti7trutis=1vatayanarajah7vatayanarajahs=1sasarajah7sasarajah=1edakerajah7edakerajahs=1gorajah7gorajahs=1liksarajah7liksarajahs=1sirsapa7sirsapas=1yava7yavas=1anguliparvan 12anguliparvans=1vitasti2vitastis=1hasta4hasta=1dhanuh1000dhanuhs=1krosa4krosas=1
yojana

 

Number of atoms (parmanus) in a yojana = 1.0847 x 10^14
Number of millimeter in a yojana = 7,314,468
Number of atoms/mm = 14,829,580

Actual No. of atoms/mm = 3 to 10 millions

 

See RGVEDA and INDUS VALLEY SCRIPT.

 

LANGUAGE: origins

http://www.friesian.com/trees.htm

http://members.aol.com/rmallott2/origin.htm

 

See FONTS.

 

See this link to an alternate language construction proposed by Omar Rumi:

http://www.mcn.org/2/sesame/

 

LANSING: (AE; Hieratic) papyrus

(as per AEMT) See P. Lansing in the British Museum 2nd Series.

 

(as per LEX) Seek work by E.A. Budge.

 

(as per S. Lorber) Seek ZAS 62, 1927.

 

As per [note 3] the following link:

http://sondmor.tripod.com/index-html

 

3. Papyrus Lansing (4.10) continues with the observation that "the ship's crews of every house (per) they take up their freights. They depart for Syria." It is well known that, for good reason, the terms "family," "house," and "firm" overlapped in antiquity (ESoA, Chap. 2.D). Obviously, then, there were nonroyal trading "houses" operating in Egypt, Perhaps, the reference includes trading enterprises under the auspices of temples, but there is no reason to exclude independent firms. Another text (Pap. Bibl. Nat. 211.18) locates a merchant in the "house" of the scribe of contracts Mery (Janssen). Sike, chantress of (the god) Thoth, instructs her correspondent to go to the "merchant" (shewty) and have his oath annulled (Caminos, p.26). The point of Sike's letter is obscure but the merchant has no named institutional connection.

 

(as per M. Tilgner; EEF)

Papyrus Lansing = BM 9994 is named after Reverend Gulian Lansing (1825-1892) acquired from him by the British Museum in 1886. Alan H. Gardiner published this papyrus again in

“Late-Egyptian Miscellanies.”

[LEM], Bruxelles, 1937 (Bibliotheca Aegyptiaca, VII), pp. 99-116. Gardiner only remarked in the introduction, p. XX: "The papyrus was acquired by the Trustees of the British Museum in 1886 through the agency of the American missionary Dr. Lansing."

The original Hieratic text was published in: Ernest Alfred T. Wallis Budge (ed.), Facsimiles of the Egyptian Hieratic Papyri in the British Museum, 2nd series, London, 1923, pls. XV-XXX. According to Erman/Lange cited above the papyrus had been in a small pot, which also contained "some kind of salt" causing the papyrus to be soaked in salt, especially at the margins, and the text to be faded A German translation is provided by Erman and Lange; English translations

can be found in Ricardo A. Caminos, Late-Egyptian Miscellanies, London, 1954, pp. 373-428 and more accessible in Lichtheim II, pp. 168-175.

See also:

LAe IV, 718, s.v. "Papyrus Lansing"

LAe V, 737-739, s.v. "Schuelerhandschriften" [apprentice texts]

 

(as per F. Rocchi; EEF)

[P. Lansing is] dated to the end of 20th dynasty by various elements (name of the scribe, names of private persons, names of gods, hieratic palaeography etc.), and doesn't come from Akhenaten's reign. It measures 4.65 m in length and 20.5 cm in height. The Theban provenance is inferred from various titles of persons relating them to the temple of Amun-Ra. It has palimpsest traces (accounts) but these again should be of 20th dyn.

A rather long article about the papyrus was

written by Blackman and [Thomas Eric] Peet in JEA 11 (1925), 284.

 

 

LARSA: (ancient) city

See UHN: p. 150: re LARSA/SENKEREH town source of mathematical cune text [Louvre, AO 8862, side IV] ZERO as a blank space. See URUK.

 

 

LATIN: collections

[B_564=Y_014,rvw] CATNYP# *GBI+ (Lowe, E. A. Codices Latini antiquiores) [Sent to the ANNEX; a scary NYPL procedure that requires a minimum of 24 hours notice for access; as of 042003; this can wait]

SUMMIT# BT1390 .C7 1955 [always could request this but 12 volumes is a lot to ask.]

“Codices latini antiquiores : a palaeographical guide to Latin manuscripts prior to the ninth century /..”

Germany, 1982.

All items [in 12 comprehensive volumes] 900 BCE or prior.

 

LAURENZIANA: (Greek) papyri

P.Laur.: Dai Papiri della Biblioteca Medicea Laurenziana

P.Laur. 1.1. Copy of a petition to the prefect:

(Greek; AD 192; Arsinoite)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0147

 

[B_503=O_071,OS,IMG]

CATNYP# *OC+ 86-2145

BOBST# PJ2196 .B53 1984 Oversize

“Papiri Laurenziani copti (P. Laur. V) / [a cura di] Gerald M. Browne.”

Firenze, 1984.

From the series: Papyrologica Florentina, v. XIII.

Greek letters, contracts, Orders, receipts, leases, lists.

See plates.

Only one piece [item 193] can be dated with any degree of accuracy to ~708-9 [C.E.]

 

LAUSANNE: (AE; Hieratic) papyrus; University of

[B_180a,8.5,IMG, v. 1] CATNYP# *OBQ+ 73-2731 t. 82, “Hommages Serge Sauneron, Cairo, 1979, v. 1.

See work by Michael Valloggia, “Le P. Lausanne No. 3391”.

Hieratic, parallels P. Louvre 3284.

University of Lausanne.

http://www.unil.ch/philo/

 

 

LAW: You know who you are.

See CONSTRUCTION. HAMMURABI; TALMUD; TORAH…

 

[B_368,HOUSE,alt via TAPS,RARE] CATNYP# *KGW 1799 (United States. Constitution of the United States of America)

“The constitution of the United States of America, with all the amendments; and Gen. Washington’s paternal address to the people of the United States, on his resigning the presidency…”

Baltimore, Printed for Thomas Henry, by Warner and Hanna, 1799.

At rare books; NYPL.

See alternate pamphlet by TAPS.

 

[B_368] original (1799) includes:

[No copying permitted from the RARE collection at NYPL]

“…the acceptance of, and continuance hitherto in, the office to which your suffrages have twice called me, have been a uniform sacrifice of inclination to the opinion of duty, and to a deferance for what appeared to be your desire.  I constantly hoped, that it would have been much earlier in my power, consistently with motives, which I was not at liberty to disregard, to return to that retirement from which I had been reluctantly drawn.”

“The disorders and miseries, which result, gradually incline the minds of men to seek security in the absolute power of an individual; and sooner or later the chief of some prevailing faction more able or more fortunate than his competitors, turns this disposition to the purposes of his own elevation, on the ruins of public liberty.”

“As a very important source of strength and security cherish public credit. One method of preserving it is to use it as sparingly as possible; avoiding occasions of expense by cultivating peace, but remebering also that timely disbursements to prepare for danger frequently prevent much greater disbursements to repel it; avoiding likewise the accumulation of debt, not only by shunning occasions of expense, but by vigorous exertions in time of peace to discharge the debts which unavoidable wars may have occasioned, not ungenerously throwing upon posterity the burthen [burden] which we ourselves ought to bear.”

“Can it be that Providence has not connected the permanent felicity of a nation with its virtue?”

“17 September 1796”

 

Internet copyright LAW:

http://www.unc.edu/~unclng/public-d.htm

 

Ancient law:

Required Reading

Robert Wenke, "The Origins of Cultural Complexity in Africa", in Patterns in Prehistory 475-487 (1980)

John A. Wilson, "Authority and Law in Ancient Egypt", Journal of the American Oriental Society (1959)

Aristide Theodorides, "The Concept of Law in Ancient Egypt", in The Legacy of Egypt (John Richard Harris, ed., 2nd ed., 1971)

"Edict of Harmheb", in James H. Breasted, 3 Ancient Records of Egypt (1935)

"Tomb of Rekmire", in James H. Breasted, 2 Ancient Records of Egypt (1935)

"Records of the Royal Tomb-Robberies", in James H. Breasted, 4 Ancient Records of Egypt (1935)

"The Protests of the Eloquent Peasant", in Ancient Near Eastern Texts (J.B. Pritchard, ed., 1950)

Recommended Reading

Cyril Aldred, "More Light on the Ramesside Tomb Robberies", in Glimpses of Ancient Egypt (John Ruffle et al., eds., 1979)

S. Allam, "Legal Aspects in the Contendings of Horus and Seth'", in Studies in Pharaonic Religion and Society in Honour of J. Gwyn Griffiths (Alan B. Lloyd, ed., 1992)

Rudolf Anthes, "The Legal Aspect of the Instruction of Amenemhet", 16 Journal of Near Eastern Studies 176 (1957)

John Baines, "Literacy in Ancient Egyptian Society", 18 Man 572 (1983)

Ellen Dailey Bedell, Criminal Law in the Egyptian Ramesside Period, unpublished Ph.D. dissertation, Brandeis University, 1973

Aylward M. Blackman, "Oracles in Ancient Egypt", 11 Journal of Egyptian Archaeology 249 (1925)

G.P.F. van den Boorn, "Wd-ryt and Justice at the Gate", 44 Journal of Near Eastern Studies 1 (1985)

G.P.F. van den Boorn, The Duties of the Vizier: Civil Adminstration in the Early New Kingdom (1988)

A. de Buck, "The Judicial Papyrus of Turin", 23 Journal of Egyptian Archaeology 152 (1937)

J. Capart, A.H. Gardiner and B. van de Walle, "New Light on the Ramesside Tomb-Robberies", 22 Journal of Egyptian Archaeology 169 (1936)

Jaroslav Cerny, "The Will of Naunakhte and the Related Documents", 31 Journal of Egyptian Archaeology29 (1945)

Robert C. Ellickson and Charles DiA Thorland, "Ancient Land Law: Mesopotamia, Egypt, Israel", 71 Chicago-Kent Law Review 321 (1995)

C.J. Eyre, "Crime and Adultery in Ancient Egypt", 70 Journal of Egyptian Archaeology 92 (1984)

Alan H. Gardiner, "A Lawsuit Arising from the Purchase of Two Slaves", 21 Journal of Egyptian Archaeology 140 (1935)

Alan H. Gardiner, The Inscription of Mes: A Contribution to the Study of Egyptian Judicial Procedure (1905)

J. Gwyn Griffiths, "Isis as Maat, Dikaiosune, and Justitia", in Hommages a Jean Leclant, vol. 3 (etudes isiatiques) (Catherine Berger et al. eds., 1994)

T.G.H. James, Pharoah's People: Scenes from Life in Imperial Egypt (1984) (esp. chapters 2,3)

David Lorton, "The Treatment of Criminals in Ancient Egypt", 20 Journal of the Economic and Social History of the Orient 2 (1977)

A. McDowell, Jurisdiction in the Workman's Community of Deir el-Medina, unpublished Ph.D. dissertation, University of Pennsylvia, 1987

Richard A. Parker, A Saite Oracle Papyrus from Thebes (1962)

T. Eric Peet, The Great Tomb-Robberies of the Twentieth Egyptian Dynasty (1930)

P.W. Pestman, "The Law of Succession in Ancient Egypt", 20 Journal of the Economic and Social History of the Orient 2 (1977)

P.W. Pestman, Marriage and Matrimonial Property in Ancient Egypt (1961)

Kurt Pfluger, "The Edict of King Haremhab", 5 Journal of Near Eastern Studies 260 (1946).

J. Pirenne, Histoire des institutions et du droit prive de l'ancienne Egypte (1932-5)

J. Pirenne and A. Theodorides, Droit egyptien (1966)

Gay Robins, "The Economic and Legal Position of Women", in Women in Ancient Egypt (1993)

Nili Shupak, "A New Source for the Study of the Judiciary and Law of Ancient Egypt: 'The Tale of the Eloquent Peasant'", 51 Journal of Near Eastern Studies 1 (1992)

Diodorus Siculus, On Egypt (Edwin Murphy, trans., 1985)

H.A. Szubin & Bezalel Porten, "Royal Grants in Egypt: A New Interpretation of Driver 2", 46 Journal of Near Eastern Studies 15 (1994)

Stephen E. Thompson, "The Anointing of Officials in Ancient Egypt", 53 Journal of Near Eastern Studies 15 (1994)

Vincent Tobin, "Ma'at and Dike: Some Comparative Considerations of Egyptian and Greek Thought", 24 Journal of the American Research Center of Egypt 113 (1987)

Raphael Ventura, "More Chronological Evidence from the Turin Papyrus", 42 Journal of Near Eastern Studies 271 (1983)

Russ VerSteeg, "Law in Ancient Egyptian Fiction", 24 Georgia Journal of International and Comparative Law 37 (1994)

S.P. Vleeming, "The Days on Which the Knbt Used to Gather", in Gleanings from Deir el-Medina (R.J. Demaree and J.J. Janssen eds., 1982)

John A. Wilson, "The Oath in Ancient Egypt", 7 Journal of Near Eastern Studies 129 (1948)

All the above and more as per this link:

http://www.law.pitt.edu/hibbitts/egypt.htm

 

[B_598, alt HOUSE]
CATNYP# **QDM (Dostoyevski, F. M. Crime and punishment. 1957)
“Crime and punishment.”
London, Folio Society, 1957.
In house copy is a Harper’s Publishing edition.
Fyodor Dostoyevsky b. 1821, d. 1881.

LAW: and the AE amt-pr

(as per Y. Muffs) See [W_012***=B_191,JH], ELEPHANTINE.

See Papyrus Kahun II, I (MK; XII dynasty, 2000-1788 BCE.)

Legal content. See DJE I, pp. II ff.

Some of the legal documents included the amt-pr, a deed which recorded the transfer of property from one individual to another. One such will by a man named Mery transferred his priestly office and title of his property, house and contents, to his son, who would take on his office.

Other wills refer to members of one family. For example, the will of Sahu, an architect, leaves all his property and his slaves to his brother Uah, also an architect and priest of Sopdu, the falcon-god. Uah in turn left a will, mentioned above, which transfers this property to his wife, giving her the freedom to pass it on to any of their children.

http://www.touregypt.net/featurestories/kahun.htm

 

79. I. ORIGINAL WRITINGS.

The legal and official documents may be classed according to their titles: the amt-per or deed recording the transfer of property from one person to another either prospectively or immediately, and those from Kahun, which, though sometimes as fragile

 

http://www.reshafim.org.il/ad/texts/illahun/47.htm

 

http://www.reshafim.org.il/ad/texts/illahun/c.htm

 

LAW: resources

See:

http://www.library.uiuc.edu/lax/

 

http://web.library.uiuc.edu/resource/catalog.asp

 

LDG: (Libyan) desert glass

(as per EEF; G. Negro)

-Boccazzi A., V. de Michele e G. Negro, 1991. Un'esplorazione

geo-archeologica nel Great Sand Sea (Egitto). Sahara, 4: 89-102.

 

-Bokelmann K., 2002. Einige Libyan-Desert-Glass-Artefakte des Atérien

aus der Glass Area in Südwest-Ägypten. In: Tides of the Desert - Gezeiten der Wüste, Köln: Heinrich-Barth-Institut, p. 67-73.