We hear several variations from the suttas of dependent origination (pitacca-sam-uppada). By that name, it begins by answering the problem of aging and death. Before enlightenment, Bodhisatta Gotama asked himself “what are aging and death dependent upon?” Obviously birth.
He worked out a chain of dependencies down and up “with the cessation of what, ceases this?” Sometimes he stops/begins at birth (jati), or thirst (tanha), or name-form/consciousness, or the ultimate origin: ignorance (a-vijja). Typically of the form:
avijja (ignorance) > sankhara > vinnana (consciousness) > nama-rupa > … tanha (thirst, craving) … > bhavo (becoming, existence) > jati (birth) > aging and death … and dukkha (pain, suffering, etc)
The Buddha does not say that one-to-one birth causes pain. Rather, the Buddha only asserts that pain is dependent upon birth. There must be at least one instance of birth for any amount of pain.
From what I remember, birth (jati) is always included in dependent origination by that name (pitacca-samuppada). However, the four noble truths are the preeminent diagnoses of the problem of pain (dukkha) dependent upon thirst (tanha) as its origin (sam-udaya) and answers the same question as the pitacca-samuppada: “with the cessation of tanha, ceases dukkha”. There are numerous individuals who, in a moment, without rebirth, cease ignorance (no-vision, a-vijja), cease sankhara, cease tanha, cease dukkha, and realizing nibbana, know with clear dustless vision that there is no further birth.
Thus have I read…
Bhikkhus, before my enlightenment, while I was still a bodhisatta, not yet fully enlightened … ‘When now will an escape be discerned from this suffering [headed by] aging-and-death?’
Then, bhikkhus, it occurred to me: ‘When what exists does aging-and-death come to be? By what is aging-and-death conditioned?’ Then, bhikkhus, through careful attention, there took place in me a breakthrough by wisdom: ‘When there is birth, aging-and-death comes to be; aging-and-death has birth as its condition.’
– Nagaram SN.2.12.65 (trans Bhikkhu Bodhi)
“And what is dependent co-arising (paticca-samuppado)? From ignorance (avijja) as a requisite condition come fabrications (sankhara) … consciousness (vinnanam) … name-and-form (namarupam) … six sense media (salayatanam) … contact (phasso) … feeling (vedana) … craving (tanha) … sustenance (upadanam) … becoming (bhavo) … birth (jati) . From birth as a requisite condition, then aging and death, sorrow, lamentation, pain (dukkha), distress, and despair ((originate)) (sam-bhavanti)… Such is the origination (sam-udayo) of this entire mass of stress and suffering (dukkha-kkhandhassa ) ((This, is co-arising)) (sam-uppado) … And what is birth (jati)? Whatever birth, taking birth, descent, coming-to-be, coming-forth, appearance of aggregates, and acquisition of [sense] media of the various beings in this or that group of beings, that is called birth.”
– Paticca-samuppada-vibhanga SN.2.12.2 (trans Thanissaro Bhikkhu)
“If, Ananda, there were no being born at all of any sort, by any being of any sort, whatever, however; that is: of gods to godhood, … man to manhood, … snakes to snakehood, if there were no being born by any being of thus and such a sort at all, with the non-existence of all birth, with the eradication of birth, could there then be any discerning of aging and death?”
Such could not be, bhante…
“If, Ananda, consciousness having entered the mother’s womb, were to be revoked from there could named-form develop there in such and such a way so as to arrive at birth?”
Such could not be, bhante.
– Maha Nidana DN 15 (trans Michael Olds)
Now this, bhikkhus, is the noble truth of suffering (dukkham ariya-saccam): birth is suffering (jati pi dukkha), aging … illness … death is suffering; union with what is displeasing is suffering; separation from what is pleasing is suffering; not to get what one wants is suffering; in brief, the five aggregates subject to clinging are suffering.
"Now this, bhikkhus, is the noble truth of the origin of suffering (dukkha-samudayo ariya-saccam): it is this craving (tanha) which leads to re-becoming (pono-bhavika), accompanied by delight and lust, seeking delight here and there; that is, craving for sensual pleasures (kama-tanha), craving for becoming (bhava-tanha), craving for disbecoming (vi-bhava-tanha).
"Now this, bhikkhus, is the noble truth of the cessation of suffering (dukkha-nirodho ariya-saccam): it is the remainderless fading away and cessation of that same craving (tanha-ya), the giving up and relinquishing of it, freedom from it, non-reliance on it…
The knowledge and the vision arose in me: 'Unshakeable is the liberation of my mind. This is my last birth (jati). Now there is no more re-becoming (punab-bhavo)." …
And while this discourse was being spoken, there arose in the Venerable Kondanna the dust-free, stainless vision of the Dhamma: “Whatever is subject to origination is all subject to cessation.” (Yam kinci sam-udaya-dhammam sabbantam nirodha-dhamman ti)
– Dhammacakkappavattana SN 5.56.11 (trans Bhikkhu Bodhi)
From the PTS Pali-English Dictionary:
Sambhava [sa.m+bhava] 1. origin, birth, production; maataapettikas-sambhava born from father and mother; n’atthi sambhavaµ has not arisen; 2. semen virile; aaabraa-esin seeking birth.
Samudaya [sa.m+udaya] 1. rise, origin. dukkha- the origin of ill, the second ariya-sacca; (sam+u+aya); 2. bursting forth, effulgence (pabhaa); 3. produce, revenue.
Samuppaada [sa.m+uppaada] origin, arising, genesis, coming to be, production.