Udāna 1: Bodhivaggo
The Chapter (including the Discourses) about the Awakening (Tree)The chapter titles in the Udāna are principally named after one or, as here, more of the main discourses that occur in the chapter; the only exception to this being the 7th chapter Cullavagga, the Chapter (including) the Short Discourses. Book, chapter, and discourse titles in Pāḷi are normally quoted in the nominative, which is the so-called label-use of the nominative; see Perniola pg. §245d. But note that in the manuscript editions of the texts the end-title is the rule, quoting the title at the beginning of a text is a modern felicity.01

Reverence to him, the Gracious One, the Worthy One, the Perfect Sambuddha

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1: The First Discourse about the Awakening (Tree) Bodhi in the title here and in the next two discourses refers to the Tree of Awakening, not to the Awakening itself, as the events described herein took place some time after that momentous event. Compare 1.4 Nigrodhasuttaṁ (The Discourse about the Banyan Tree).02

 

Thus I heard:
at one time the Gracious One was dwelling near Uruvelā, Most of the discourses open with the same formula: Evam me sutaṁ: ekaṁ samayaṁ Bhagavā....viharati. Notice the use of the historical present, literally: ...at one time the Gracious One...dwells. The locative in the place name which precedes the verb in these formulas is proximate, and usually means near (not at or in), which is more specifically stated in what follows the verb.03 on the bank of the river Nerañjarā, at the root of the Awakening tree, in the first (period) after attaining Awakening.

Then at that time the Gracious One was sitting in one cross-legged posture for seven days experiencing the happiness of freedom. Then with the passing of those seven days the Gracious One, after arising from that concentration, for the first watch of the night, applied his mind thoroughly to conditional origination in forward order: Anuloma literally: along the hair (or grain); as opposed to paṭiloma (see next discourse), against the hair (or grain).04

“This being so, that is; from the arising of this, that arises, Locative absolute construction, giving conditional sense, Syntax §184b.i. 05

that is to say: with ignorance as condition there are (volitional) processes, The Commentary takes sambhavanti which occurs at the end of the passage as applying to all the terms but it seems to me that this part of the formula corresponds to the first part of the statement in brief, made above: This being so, that is, being parallel to: with ignorance as condition there are (volitional) processes; with honti being understood. 06
with (volitional) processes as condition: consciousness,
with consciousness as condition: mind and bodily form,
with mind and bodily form as condition: the six sense spheres,
with the six sense spheres as condition: contact,
with contact as condition: feeling,
with feeling as condition: craving,
with craving as condition: attachment,
with attachment as condition: continuation,
with continuation as condition: birth,
with birth as condition: old age, death, grief, lamentation, pain, sorrow, and despair (all) arise,
and so there is an origination of this whole mass of suffering.”

Then the Gracious One, having understood the significance of it, on that occasion uttered this exalted utterance:

“When (the nature of) things becomes really manifest
To the ardent meditating brāhmaṇa,
Then all his doubts disappear,
Since he knows (the nature of a) thing and its cause.”