EKAGGATA - EKAGGA - EKODI

(You can read the notes below first)
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Ekaggatta
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Here, bhikkhus, the noble disciple gains concentration, gains one-pointedness of mind, having made release the object (lit. having undertaken the relinquishing of the support). This is called the faculty of concentration. 

Idha, bhikkhave, ariyasāvako vossaggārammaṇaṃ karitvā labhati samādhiṃ, labhati cittassa ekaggataṃ—idaṃ vuccati, bhikkhave, samādhindriyaṃ. 
SN 48.9

It is indeed to be expected, venerable sir, that a noble disciple who has faith, whose energy is aroused, and whose mindfulness is established, will gain concentration, will gain one-pointedness of mind, having made release the object. That concentration of his, venerable sir, is his faculty of concentration. 
Saddhassa hi, bhante, ariyasāvakassa āraddhavīriyassa upaṭṭhitassatino etaṃ pāṭikaṅkhaṃ yaṃ vossaggārammaṇaṃ karitvā labhissati samādhiṃ, labhissati cittassa ekaggataṃ. Yo hissa, bhante, samādhi tadassa samādhindriyaṃ.
SN 48.50

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Ekagga
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“He whose virtue has no vacillation, who is alert and meditative, whose mind has been mastered, which causes it to become one, well concentrated; 
anuccāvacasīlassa, nipakassa ca jhāyino. cittaṃ yassa vasībhūtaṃ, ekaggaṃ susamāhitaṃ. 
AN 3.58

Develop the mind on foulness, which causes it to become one (undergoing oneness,) well concentrated;
asubhāya cittaṃ bhāvehi, ekaggaṃ susamāhitaṃ.
SN 8.4

The body becomes tranquil and untroubled, the mind becomes concentrated, which causes it to become one.
kāyo asāraddho, samāhitaṃ cittaṃ ekaggaṃ.
SN 35.134

But have established mindfulness, clearly comprehend, are concentrated, with a citta partaking in oneness, and restrained sense faculties. 
upaṭṭhitassatī sampajānā samāhitā ekaggacittā saṃvutindriyā.
AN 2.42

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Ekodi
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With the subsiding of thought and examination, he enters and dwells in the second jhāna, which has internal placidity and transcendence (unification) of mind, and consists of delight (contentment,) and pleasure born of concentration, without thought and examination.
vitakkavicārānaṃ vūpasamā ajjhattaṃ sampasādanaṃ cetaso ekodibhāvaṃ avitakkaṃ avicāraṃ samādhijaṃ pītisukhaṃ dutiyaṃ jhānaṃ upasampajja viharati.
AN 3.58 (+ many same suttas extracts)

But, bhikkhus, there comes a time when his mind becomes internally steady, composed, transcended (trough unification,) and concentrated.
That concentration is peaceful and sublime, gained by full tranquilization, and attained to unification; it is not reined in and checked by forcefully suppressing [the defilements].
Hoti so, bhikkhave, samayo yaṃ taṃ cittaṃ ajjhattaṃyeva santiṭṭhati sannisīdati ekodi hoti samādhiyati.
So hoti samādhi santo paṇīto paṭippassaddhiladdho ekodibhāvādhigato na sasaṅkhāraniggayhavāritagato.
AN 3.101

Steady your mind (make your mind stand still) in noble silence 
ariye tuṇhībhāve cittaṃ saṇṭhapehi, 
Transcend (unify) your mind in noble silence, 
ariye tuṇhībhāve cittaṃ ekodibhāvaṃ karohi, 
Concentrate your mind on noble silence.’ 
ariye tuṇhībhāve cittaṃ samādahā’ti. 
SN 21.1


Bhikkhus, when a bhikkhu’s mind has been subdued, well subdued, regarding the six bases for contact, it then becomes inwardly steady, settled, transcended (throug unification), and concentrated.
bhikkhave, yato kho bhikkhuno chasu phassāyatanesu cittaṃ udujitaṃ hoti sudujitaṃ, ajjhattameva santiṭṭhati, sannisīdati, ekodi hoti, samādhiyati.
SN 35.246

Moggāllana, do not be negligent, brahmin, regarding the attribute-less concentration of mind. Steady your mind in the attribute-less concentration of mind, unify (and transcend) your mind in the attribute-less concentration of mind, concentrate your mind in the attribute-less concentration of mind.
Moggallāna, moggallāna. Mā, brāhmaṇa, animittaṃ cetosamādhiṃ pamādo, animitte cetosamādhismiṃ cittaṃ saṇṭhapehi, animitte cetosamādhismiṃ cittaṃ ekodiṃ karohi, animitte cetosamādhismiṃ cittaṃ samādahā’ti. 
SN 40.9

Come friends, dwell contemplating the body in the body, ardent, clearly comprehending (discerning), transcending (through unification), with a limpid mind, concentrated, with a citta partaking in oneness, in order to know the body as it has come to be. 
Etha tumhe, āvuso, kāye kāyānupassino viharatha ātāpino sampajānā ekodibhūtā vippasannacittā samāhitā ekaggacittā, kāyassa yathābhūtaṃ ñāṇāya.
(Idem for the other khandhas)
SN 47.4

 

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NOTES
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EKAGGATĀ
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GATA

Pali:
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
As in ekaggatā > eka + gata = arrived at one - directed to one.

Gata [pp.of gacchati ] 
- arrived at, directed to. [PTS]


Sanskrit:
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
Gacchati = third present of √ गम् gam.

गत gata [pp. √ गम् gam]

√ गम् gam

- to cause to go to any condition (RV. AV.), cause to become - (TS. ŚBr.) 
- to strive to obtain - (ŚBr. ChUp.) 
- to wish to bring (to light) - (TS.)
- to go with the mind , observe - (RV.)
- to go to any state or condition , undergo , partake of , participate in , receive , obtain - (RV. AV.) 
- to go , move , go away , set out , come - (RV.) 
- to go to or towards , approach - (RV.) 
- to cause to go or come, lead or conduct towards , send to - (AV.) 
- bring to a place - (RV.)
- to cause to understand , make clear or intelligible , explain - (MBh.)

From these meanings of √ gam, I would privilege the three first ones & the last one. First, because the three firsts, pertain to shakhas close to the Buddha. Then because of the continuity of one of the meaning in pre and post Buddhist times.

In other words, I would go for some meaning like that: 
"caused to go to - (obtain an understanding of) - (or become) - (or undergo)" .... ([the] one).


EKA:

Pali [PTS]
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
1. “one” as number, either with or without contrast to two or more; often also “single” opp.to nānā various, many.
2. one, by oneself, one only, alone, solitary.
3.a certain one, some one, some.


Sanskrit:
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
एक Eka: 
- one of two or many, the one - the other, some, some - others - (ŚBr. KātyŚr. MBh.) 
- the same , one and the same , identical - (ŚBr. KātyŚr.)
- One -(RV.)
- alone , solitary , single , happening only once , that one only - (RV.)

Again privileging the first definition.

"Eka-g-gachati" in sanskrit, would then take the somewhat meaning of: "caused to obtain an understanding of one (of two)".

Trying to get to Eka-Udi.
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EKODI
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Sanskrit:
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
Eka+udi (transcend - escape)
उदि udi [ ud-√ i ] 
See उद् Ud: (var. uc, uj, un, ut) - particle and prefix to verbs and nouns. (As implying superiority in place , rank , station , or power) up , upwards upon , on over , above. - and √ इ i : appear (BṛĀrUp.), arise from (ChUp.), escape (RV. AV. ŚBr.)

- to come out or arise from - (RV. AV. ŚBr.) 
- to escape - (ChUp.) 
- to go up to , proceed or move up , proceed - (RV. AV. VS.)
- to rise (as the sun or a star ) - (RV. VS. ŚBr. ChUp.) 
- rise up against , march off - (AV. MBh.)


Pali
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
Ekodi

Eka-Udi

Eka: See above

Udi (or udī) - artificial adj.form. fr.udeti, meaning “rising, excelling”.

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EKAGGA
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The conundrum of Ekaggata and Ekagga. 
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As far as ekagga is concerned, the Sanskrit (in fine compositi) ग ga [agt. √ गम् gam]; whose general meaning is: "who goes in, or who is in", seems to be the (only?) real solution to a long lasting conundrum.

Maybe that agent stuff exists also in the Pali. (check the different grammars for that particular case).

Sticking to the Sanskrit grammar, which is very close to the Pali,  and looking at the first definition of √ गम् gam below, the following extract would translate thus:
Samāhitaṃ cittaṃ ekaggaṃ 
The mind becomes concentrated, which causes it to go to (the) one. 
SN 35.134

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* √ गम् gam
- to cause to go to any condition (RV. AV.), cause to become - (TS. ŚBr.) 
- to strive to obtain - (ŚBr. ChUp.) 
- to wish to bring (to light) - (TS.)
- to go with the mind , observe - (RV.)
- to go to any state or condition , undergo , partake of , participate in - (RV. AV.) 
- to go to or towards , approach - (RV.) 
- to cause to go or come, lead or conduct towards , send to - (AV.) 
- bring to a place - (RV.)
- to cause to understand , make clear or intelligible , explain - (MBh.)

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Additional note:

Ekagga seems to be the result of several factors.
It is the result of developing the citta on a specific object, like foulness (SN 8.4) - or mastering (vasī) the citta (AN 3.58) - or of not striving with the mano (amanasikārā) to perceptions of manifoldness as below (although not specifically mentioned):


Here, with the complete overstepping of perceptions of form (matter), with the vanishing of perceptions (based) upon the organs of senses (viz. ajjhattikāni āyatanāni & mano), not striving with the mind (manasa/mano) to perceptions of manifoldness (lit. (what is) differently (than one)), aware that ‘space is boundless,’ he attains and seizes distinctively, the field of boundless space.
Idhānanda, bhikkhu sabbaso rūpasaññānaṃ samatikkamā, paṭighasaññānaṃ atthaṅgamā, nānattasaññānaṃ amanasikārā ‘ananto ākāso’ti ākāsānañcāyatanaṃ.
MN 59

Note that sañña (perception) does indeed mean: "inquiry & assumption". Not just perception.
Vedanā means a "felt experience" (that requires more inquiry) - Sañña is the inquiry and assumptions - and Viññāṇa is the last "knowledge" (the final decision taken among these assumptions" - might it be several of them). 


Nānatta, [Sk.fr.nānā] (opp.ekatta).
- diversity, variety, manifoldness, multiformity.
नाना nānā
- differently , variously , distinctly , separately.

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There is also the possibility of ekaggatā/ekāgratā; in which ekagga/ekāgra could be the following:

Ekāgra-tā 
Ekāgra [agra]
अग्र agra [√aṅg] 
The late (post-Buddhist) meaning of "prominence" (foremost, chief,) for agra, is quite dubious. It seems to have an origin to the root √aṅg, that would itself be linked to √ aṅk, which has the meaning of a hook in RV. "Hooked to (the) one"!?! - That seems a bit far fetched. For one can see that agra, in pre-Buddhist texts means:
- from - up to (ŚBr.)
- before (in time) (AitUp.)

॰ता -tā forms suffixes of state; quality of.

Why this dubious and complicated √aṅg; and not just the plain √ gam?

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If one retains the √ gam option, which is "historically" the most probable explanation for ekaggata in SN 48.9 and SN 48.50 above, is a new noun (not existing in Sanskrit or Pali,) made out from eka and the pp. of √ gam.


Here, bhikkhus, the noble disciple gains samādhi, gains the state of oneness of mind, having made release the object (lit. having undertaken the relinquishing of the support). This is called the faculty of samādhi (SN 48.9). 

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Ekatta and Puthutta:

Ekatva and pṛthutva in Sanskrit, give rise to ekatta and puthutta in Pali.

√ प्रथ् prath [linked to pṛth]
- to spread , extend, become larger or wider , increase (RV.)
- to throw , cast ; to extend (Dhātup.)
√ पृथ् pṛth [linked to prath] 
- to extend (Dhātup)

॰त्व -tva 
- forms neutral substantive of state; essence of.

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