Sati & Sati

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"Sati" has two meanings:

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First meaning: from the Vedic smṛti स्मृति (√ smṛ), meaning "thinking upon" (calling to mind, ~"mindful") [TĀr. ChUp. MBh.]. It can be being mindful of (thinking upon) the breath. Or being mindful of not letting the external akusala get in, etc. 

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Second meaning: from सति sati = साति sāti = सन्ति santi = gaining , obtaining , acquisition (RV.)

Sati as "obtention", "acquisition". 

Sāti @ http://sanskritdictionary.com

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In Chinese, it is written as 念 . 

As in 安那般那念 = Ānāpānasati = obtention of in & out breath. 

But it can also be written as 想 (ideation), as in "mindfulness of death" (死想) [EA 40.8/AN 6.19]

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Even this might be considered:


Smṛ or Spṛ ? 
स्मृ  smṛ = vario lectio (v.l.) for √ spṛ  
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स्पृ  √ spṛ  (v.l. [ stṛ ] and [ smṛ ] )

- to release , extricate or deliver from (abl.), save, gain, win  RV. TS. Br. TUp. 

- Caus. [ spāráyati ] , to attract to one's self, win TBr. ; to preserve, save, rescue ib. ; 

- to gladden, delight, gratify, bestow  Dhātup.


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The second meaning, viz. "obtention", is seen in the extract:

Intending (paṇidhāya) towards the beginning (parimukhaṃ), and having cared for (upaṭṭhapetvā) the obtention (sati) [of Citta].

Paṇidhāya parimukhaṃ satiṃ upaṭṭhapetvā*. (See note at the end)

OR again in this extract: 

Yet he is covetous - inflamed by lust for sensual pleasance - with a mind (citta) full of enmity - with intentions (mana-saṅkappo) corrupted by hate - negligent about the obtention [of (a free) citta] - lacking clear comprehension - not well set (located, settled [in citta]) - (with a) scatter-mind (citta) - loose in his/her sense faculties.

So ca hoti abhijjhālu kāmesu tibbasārāgo byāpannacitto paduṭṭhamanasaṅkappo muṭṭhassati asampajāno asamāhito vibbhantacitto pākatindriyo.
SN 22.80

The closer one is to samādhi, the closer one is to the second meaning of sati. 
Also, it is remarkable to notice how citta has to be gladdened (as per the Dhātup definition above,) to reach cetaso ekodibhāva and cetovimutti, in ānāpānasati and jhāna.

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Usually, the first meaning of sati is used in the context of seclusion from the external. That is to say, remembering the Teaching to prevent the "attacks" from the external (see SN 35.238 & SN 35.245). 

So, bhikkhus, your citta might also often stray towards the five guṇas that you formerly experienced; which have passed, ceased, and changed; or towards those in the present, or  slightly towards those in the future.

Tasmātiha, bhikkhave, tumhākampi ye te pañca kāmaguṇā cetaso samphuṭṭhapubbā atītā niruddhā vipariṇatā, tatra vo cittaṃ bahulaṃ gacchamānaṃ gaccheyya paccuppannesu vā appaṃ vā anāgatesu.


So for your tranquility, you should practice vigilance, mindfulness, and guarding the citta, regarding the five 
guṇas that you formerly experienced; which have passed, ceased, and changed (been perverted (by lust)).

Tasmātiha, bhikkhave, tumhākampi ye te pañca kāmaguṇā cetaso samphuṭṭhapubbā atītā niruddhā vipariṇatā, tatra vo attarūpehi appamādo sati cetaso ārakkho karaṇīyo.

SN 35.117


Note:

Here guṇa has the meaning of the external fields of sensory experience in pre&post-Buddhist texts (Mn. & MBh.). 

1. ether has sound for its Guṇa and the ear for its organ ;

2. air has tangibility and sound for its Guṇas and the skin for its organ ;

3. fire or light has shape or colour , tangibility , and sound for its Guṇas , and the eye for its organ;

4. water has flavour , shape , tangibility , and sound for its Guṇas , and the tongue for its organ ;

5. earth has the preceding Guṇas , with the addition of its own peculiar Guṇa of smell , and the nose for its organ. 

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Lexical note:


Paṇidhāya parimukhaṃ satiṃ upaṭṭhapetvā

Intending towards the beginning*, and having looked after the obtention (sati) [of Citta].

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Paṇidhāya
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Pali:
Optative of paṇidahati [pa+ni+dhā]
- direct, intend.

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Parimukhaṃ
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Sanskrit:
परि pari
- towards , to (RV. AV.)

मुख mukha
- introduction , commencement , beginning (Br. MBh.)

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Upaṭṭhapetvā
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Pali:
Absolutive of upaṭṭhahati.
Upaṭṭhahati,& °ṭṭhāti [upa + sthā]
- look after.

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* Here, the "beginning" is the first step of ānāpānasati.
So satova assasati, satova passasati. 

But it can also be the assāsapassāsā, (the kāyasaṅkhāro) of the Saṅkhārā nidāna (the second link of Paṭiccasamuppāda) [SN 41.6]   - the immaterial breath. 

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