Here, bhikkhus, the noble disciple gains establishment and one-pointedness of citta having made release the object (lit. having undertaken the relinquishing of the support). This is called the faculty of establishment. 

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 who has arrived at the obtention (sati), will gain establishment, will gain one-pointedness of citta, having made release the object. That establishment of his, venerable sir, is his faculty of establishment. 
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



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

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

The body becomes tranquil and untroubled, the citta becomes established, which causes it to become one.

kāyo asāraddho, samāhitaṃ cittaṃ ekaggaṃ.
SN 35.134

But have arrived at the obtention, clearly comprehending, established with a citta partaking in oneness, and restrained in sense faculties. 

upaṭṭhitassatī sampajānā samāhitā ekaggacittā saṃvutindriyā.
AN 2.42


With the subsiding of thought and examination, he enters and dwells in the second jhāna, which has internal placidity and transcendence of citta, and consists of pīti & sukha born from its establishment; without thought and examination*.
vitakkavicārānaṃ vūpasamā ajjhattaṃ sampasādanaṃ cetaso ekodibhāvaṃ avitakkaṃ avicāraṃ samādhijaṃ pītisukhaṃ dutiyaṃ jhānaṃ upasampajja viharati.
AN 3.5 (+ many same suttas extracts)
* Vicāra (विचर् vicar [ vi-√ car ]) : the "thought-concretisation" (the outcome of investigation, pondering & choice, that ensues thinking in different directions) - the "mental" undertaking that results (viz. the wish to act or conduct one's self after examination).

But, bhikkhus, there comes a time when his citta becomes internally steady, composed, transcended and established.
That establishment is peaceful and sublime, gained by full tranquilization, and attained to transcendence; 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 citta (make your citta stand still) in noble silence
ariye tuṇhībhāve cittaṃ saṇṭhapehi,
Transcend your citta in noble silence,
ariye tuṇhībhāve cittaṃ ekodibhāvaṃ karohi,
Establish your citta in noble silence.’
ariye tuṇhībhāve cittaṃ samādahā’ti.
SN 21.1

Bhikkhus, when a bhikkhu’s citta has been subdued, well subdued, regarding the six fields of experience through contact, it then becomes inwardly steady, settled, transcended, and established.
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 expression-less (manifestation-less) establishment of ceto. Steady your citta in the expression-less establishment of ceto, transcend your citta in the expression-less establishment of ceto, establish your citta in the expression-less establishment of ceto.
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, fetch apart (distinctively) the noticeable body (breath) among the body, ardent, clearly discerning, having transcended , with a serenely distinctive citta, established and partaking in oneness*; in order to know the body according to how 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

* Note: "oneness" of citta :
The noun "citta" is derived from the participle of the verbal root √ चित् cit.
Citta means "the 'thing' that has intended and designed (RV.), that has appeared and be conspicuous (RV. TS.), that has thought and reflected upon (TS. ŚBr. ChUp. MBh.), and comprehended.
Citta is a past participle. It is something "of the past". It is the first elemental and "pristine" stage of the cit. Citta appears first in the saṅkhārā nidāna. Then the more it descends (avakkanti) in the subsequent links (nidānas) of paṭiccasamuppāda, the more it gets"polluted", so to speak.
The "oneness" of citta is about recovering this primary dimension. Although one knows that this is not an end in itself. For the citta had, as its primary motive, the intention, the aim, the wish (RV. VS. AV. TBr.) and the longing for (ChUp.) making things to appear (RV.), so they could be comprehended.
Once one's citta/ceto has comprehended (in the saḷāyatana nidāna) - one must stop thinking & reflecting - one does not need to make things conspicuous (to his/her citta) any longer; and one does not need to wish, or intent, or desire anything anymore.
One just goes back to the original "oneness" of the citta, and abandons it as well (withdrawal from citta = cittavūpakāsena - SN 46.3).

Cetaso (ceto) ekodibhāva is just transcending the ceto, towards the superior established (samādhi) citta (free from wordly sensory stimuli and intentions).





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

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

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).


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.

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.


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.)



Eka: See above

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



The conundrum of Ekaggata and Ekagga. 

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


* √ 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.)


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.


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

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?


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). 




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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