Pratītya (paṭicca) is a gerund or absolutive, a verbal form indicating an action occurring before the action of the main verb.  The form of the gerund for verbs with prefixes is different from verbs without prefixes, and probably originated in Indo-European as an instrumental singular of a verbal noun in -i, which form instrumentals by substituting -i with -yā.  The verb in this case is pratyeti (pacceti) which we can analyse as prati + √i. The root √i is related to the Latin eo,  and the cognate is only rarely found in English words like ‘iterate’ (meaning ‘to go again’). The form pratītya is regular and arises out of some sandhi changes along the way. √i is a second class verb in Sanskrit (first class in Pāli) that undergoes guṇa (strengthening) and forms a stem by adding the vowel ‘a’. The guṇa grade of i is e. Sandhi rules say that e + a > e,  and we’re left with a stem e- The 3rd person plural is eti. When we add the prefix prati- there is another sandhi change i + e > ye: so the final stem is pratye-; 3rd person singular pratyeti. When this devolves to Pāli we get some phonetic changes in the conjunct consonants: pra > pa; tye > cce: this gives us pacceti.
The root √i ‘to go’ is the same in Pāli and Sanskrit. The suffix prati- (paṭi-) gives a sense of towards, near; or opposition. Prati-√i, then, should mean something like ‘go towards, go near, go back’. The affect of combining a prefix and a root is not always predictable from the parts but this is what we get more or less: patyeti means ‘to come on to or back to, to fall back on’, as well as ‘to go towards, go to meet’.
To form the gerund in the case of a verb with a prefix, in both Pāli and Sanskrit, one adds a suffix -ya to the weakest grade of the root (simply ‘i’ in the case of √i), or in this case because the stem vowel is short: -tya.  So we get prati + i + tya. Sandhi applies here so i + i > ī giving pratītya. In Pāli pra > pa, tya > cca, and we find that tī > ṭi (with retroflexion of the consonant, and shortening of the vowel).  The meaning of the gerund should be something like ‘having come to, having fallen back on’ but in application it means more like ‘grounded on, on account of’.
One very common form of use for paṭicca in Pāli Buddhist texts is in the twelve-fold formula of paṭiccasamuppāda which is sometimes written like this:
avijjāpaccaya paṭicca saṅkhārā...
grounded on unknowing as a condition, there are the processes...
Samutpāda (samuppāda) is a verbal noun from a root with two prefixes: saṃ + ud + pāda. The root is √pad which primarily means ‘to go, to walk’ (but also ‘to fall’). The prefix ud- ‘up, upwards’ becomes ut- with the unvoiced ‘p’ of √pad to give the present stem utpada- ‘to arise, originate, come forth, be produced’. From this we get the past-participle, utpanna (uppanna) ‘arisen, originated’. The causative form of the verb has the stem utpādaya (with the addition of ‘-ya-’ and the lengthening of the root vowel) meaning ‘to produce, beget, generate’. There’s not a great deal of difference between here the indicative and the causative - the difference between ‘to arise’, and ‘to produce’. From utpādaya- we get the verbal noun utpāda (uppāda) ‘coming forth, birth, production, arising’. And in Pāli the tpā conjunct devolves to ppā. Perhaps, given that utpāda seems to derive from the causative, we should favour translations which retain that flavour – ‘arising’ is something that just happens, whereas if something is ‘produced’ we get the sense of a definite process causing the arising.
The suffix sam- gives the sense of ‘completed’ or ‘together’ (it is cognate with the English suffix ‘com-’). The word samutpāda (samuppāda) means ‘appearing with, arising together’. It is only infrequently used as a stand-alone word in Pāli. 
The two parts (pratītya and samutpāda) are usually understood as forming a compound, and should therefore be written as one word pratītyasamutpāda, though we often find it written with a hyphen for readability: pratītya-samutpāda. The last thing is to discuss what type of compound they form, and the relationship between the two parts. In fact it is unusual to find a compound with gerund as the first member. This type of compound where one part retains the syntactical form it would have in a non-compounded sentence is called a ‘syntactical compound’.  Philologists suggest that this type of compound was originally a gerund and verb form which has become lexicalised.  We do find this kind of construction with the verb utpadyate (uppajjati) in the Pāli phrase: paccayaṃ paṭicca uppajjati - (‘arising in dependence on a condition’). 
In the case of pratītya-samutpāda the compound is formed from the gerund and the verb as a past-participle or verbal noun. Because the words retain their syntactical relationship, i.e. ‘having depended [on a condition] it is produced’, we do not need to analyse them in terms of the nominal compound paradigms. If we did do such an analysis we could take the gerund in its archaic the sense as an instrumental, and treat the compound as an instrumental tatpuruṣa meaning ‘produced through depending on’.
We’ve now looked at each of the separate elements – (prati+√i+tya) + (saṃ+ud+√pad) - and how they go together (morphology); and we’ve looked at how the individual parts contribute to the meaning (semantics). However it is not enough to know the etymology in order to understand a word. We have to look at how it is used in context. Even then we must accept that we have only an imperfect understanding since in the case of Buddhist texts we are far removed in time and culture from the authors or composers. Not being a native speaker of a language means we never really have the same facility as someone who is. When we hear a foreigner speaking our mother tongue we almost always hear words being used incorrectly, idioms being misunderstood, sentences oddly constructed. We need to keep this in mind when reading a Sanskrit or Pāli text, even when we think we understand the words. Back in 1966 the Dutch philologist Jan Gonda wrote a 165 page essay on the uses of the single word ‘loka’ in Vedic literature in which he suggests that the most common translation – ‘world’ – is actually the least likely to apply in any given situation.
By far the most common use of our term is with reference to the twelvefold nidāna chain. The links in the chain are called ‘dependently arisen elements’; in Pāli ‘paṭicca-samuppanne dhamme’.  And the whole system of one thing arising with the previous one as a condition (paccaya) is known as ‘dependent arising’ – paṭiccasamuppāda.
We can see how the English Translations get at the meaning, but only as long as we already know what is being said. The phrase ‘dependent arising’ is probably now the most popular translation of pratītya-samutpāda but it does not communicate very much to the uninitiated. Even if we choose a more descriptive translation such as Conze’s ‘conditioned co-production’ this isn’t much help. In any case the form of the syntactical compound tells us that pratītya-samutpāda is a short-hand way of referring to a longer description: ‘the process by which something is produced because the necessary conditions for its production are in place’. Even then it leaves many questions: what type of ‘something’ we are referring to? Does the formula constitute a general theory of causation, or only apply to the production of mental states? To this extent Buddhism is esoteric and much of our jargon is opaque to outsiders.
- Coulson, Michael. 2003. Sanskrit. 2nd Ed. Teach Yourself Books.
- Gonda, J. 1966. Loka : World and heaven in the Veda. Amsterdam, Noord-Hollandsche U.M.
- Hamp. Eric P.1986. ‘On the Morphology of Indic Gerunds.’ Indo-Iranian Journal 29 (2), p.103-107
- Macdonell. A.A. 1926. A Sanskrit Grammar for Students. 3rd Ed. D.K. Printworld (2008)
- Norman, K.R. (trans.) 2001. The Group of Discourses (Sutta-Nipāta). 2nd. Ed. Pali Text Society
- Norman, K. R. 1991. ‘Syntatical Compounds in Middle Indo-Aryan’ in Middle Indo-Aryan and Jaina Studies, Leiden, p.3-9. Also in Collected Papers, 1990-2001, Vol.4, p.218-25.
- Whitney, William Dwight. 1885. The Roots, Verb Forms and Primary Derivatives of the Sanskrit Language. Motilal Banarsidass. (2006 printing)
Plus a range of Pāli, Sanskrit, and English dictionaries and other reference works both printed and online
 The gerund is used extensively in Buddhist texts. We might read for instance that someone approaches the Buddha, and having approached the Buddha, they salute him; and having saluted him, they sit off to one side; and having sat off to one side they respectfully asked a question. The Gerundsindicated here in italics – in English they are usually rendered as a perfect participle (having approached), or as a present participle (approaching).
 Authorities are divided on the origins of the gerund in –tvā, though seem to agree on it being an instrumental singular of a verbal noun. See Coulson Sanskrit, p.67, Macdonell 163 (p.137-8) derive it from a verbal noun in -tu; and for a dissenting view Hamp On the Morphology of Indic Gerunds who argues that –tvā must derive from a verbal noun in –tva, especially as nouns in –tu usually require guṇa and we don’t see this in gerunds.
 Fans of Monty Python's Life of Brian will recall that Brian misuses the verb eo in his slogan 'romanes eunt domus' and is forced to conjugate the verb while having his ear twisted by the centurion. He is looking for the third person plural imperative ite - 'romani ite domum'.
 If we have for instance ete aśvāḥ (these horses) we would write it ete śvāḥ or we can use an apostrophe to indicate the missing letter ete 'śvāḥ; in Devanāgarī we might use the avagrāha एतेऽश्वाः
 The addition of -t- for roots with short vowels is regular: cf Macdonell A Sanskrit Grammar for Students. 182.a (pg.160).
 Sanskrit prati- can become either pati- or paṭi- and it's not clear in each case why. Maybe due to the influence of different dialects? E.g. Vin i.96, S v.374, A iii.405, A v.201.
 K.R. Norman has adopted this term coined by G.V. Davane in 1956. They are also called ‘unregelmässige’ (irregular) by J. Wackkernagel, and ‘anomalous’ by Whitney – see Norman 'Syntactical Compounds', (in collected papers) p.218.
 See note 72 in Norman The Group of Discourses, p.175; and Norman 'Syntactical Compounds'. I'm grateful to Dhīvan Thomas Jones for pointing out Norman's note in the Sutta Nipāta.
 M i.259. This appears to be the only occurrence of this phrase in the Pali Canon. The shorter phrase, paṭicca uppajjati, occurs a number of times throughout the nikāyas. I cannot find the obvious precursor: paṭicca samuppajjati.The Verb samuppajja- appears to occur only once in the Nikāyas at SN 36:12 (PTS S iv.219) in verses which accompany prose using uppajja-.