The simple infinitive in Quenya is just the uninflected aorist form of the verb: cen- → cene “to see”. Tolkien described the infinitive at length in Common Eldarin: Verb Structure (EVS2) composed in the early 1950s:

This bare tense-stem functioned not only as the stem to which inflexions, mainly pronominal affixes, could be added, but also as the “infinitive” or object of another verb. Cf. English “give” in relation to “I give or gives”, and in such formulas as “I can give”. But this infinitive, or undefined tense-stem, could only be used as an object; it could not be declined as a noun, nor function as a subject. This situation, though arrived at by quite a different historical process, is again like English, “I can give (or give it)”, but “giving (or to give) is a mistake”; I have no “desire to give” or “thought of giving”.

A difference, however, appears between English and Eldarin use in the following cases: (a) English usually employs what is virtually a prefixed infinitive inflexion “to”: “I wish to give (and I mean to)”; (b) and in some cases uses an “ing”-noun, as e.g. in “I avoid giving”. In these types of expression Eldarin always used the bare infinitive: bare, that is, of inflexions defining it in itself; as will be seen below this infinitive, being genuinely verbal, could receive objective pronominal inflexions. The idiom represented above by “and I mean to” was either dealt with by complete suppression of the objective infinitive on its second appearance (as in “and I will”), or by adding a “neuter” pronoun of reference: “and I mean it”. In other cases Eldarin used a genuine full verbal noun made with a suffix comparable to the Latin gerund, or to English “-ing” (PE22/128-129).

In the system described in EVS2, the normal function of the Quenya infinitive was as the object of another verb: merin cene atarinya “I wish to see my father”. Unlike English, Quenya cannot use the simple infinitive as a subject; Quenya would instead need to use either a gerund or the particular infinitive (see below). Thus “to eat would be good” in Quenya would be matie [gerund] nauva mára.

Despite the statements in EVS2, there are examples in Tolkien’s later writing of infinitives used in other syntactical roles:

• Q. kare mára kwí tyare naxa “doing good may cause evil” (PE22/154).
• Q. alasaila ná lá kare tai mo nave mára “it is unwise not to do what one judges good” (PE22/154).

In the first example, the simple infinitive is clearly being used as a subject, and in the second example it appears to be used as the predicate of a “to be” expression. It seems that by the 1960s Tolkien may have relaxed some of the restrictions on infinitive usage.

Forming the infinitive: For the most part, the infinitive is just the uninflected aorist form of the verb. There is one class of verbs where the infinitive form might be different: the u-verbs where Tolkien gave two sets of infinitives (PE22/116): liru, kelu (aorists) vs. lirue, kelue (aorists + e). These examples are from Quenya Verbal System (QVS) written in 1948, which is the last time a complete paradigm of u-verbs appears in the published corpus. For purposes of Neo-Quenya, I would stick to the variants that are uninflected aorists for consistency with other verb classes: liru, kelu.

Particular Infinitives: In Common Eldarin: Verb Structure, Tolkien did not address the statement “this infinitive, being genuinely verbal, could receive objective pronominal inflexions”. However, he discussed a similar construction in some detail in Late Notes on Verb Structure written in 1969:

... the general (aorist) infinitive formed by added -i (not as such capable of any further suffixion; with pronominal affixes it was the stem of the aorist tense); the particular infin[itive] with -ita differing in use from the preceding mainly in being able to receive pronominal object affixes (PE22/154).

Examples elsewhere in this document illustrate the use of this “particular infinitive”:

• Q. la năvin karitalya(s) mára “I do not advise you to do so, (lit.) I don’t judge your doing (it) good”.
• Q. lá karita i hamil mára alasaila (ná) “not to do (in this case) what you judge good (would be) unwise”.
• Q. lá karitas alasaila ké nauva “not doing this may be/prove unwise”.
• Q. lá karitas, navin, alasaila ná “not doing this would be (I think) unwise”.

Thus unlike the simple infinitive, the particular infinitive can be used as subject: merita alasaila (ná) “to wish is unwise”, though for such a simple phrase the gerund is more likely: merie alasaila (ná). Unlike the simple infinitive (and the gerund), the particular infinitive can take both object suffixes (carita-s “doing it”) and subject suffixes, though the subject takes the form of the possessive suffix rather than the normal verbal subject suffix: carita-lya-s “your doing it” = “doing-your-it”. However the “particular” aspect of this infinitive probably means it refers to a specific action. Consider the example:

• Q. lá karita i hamil mára alasaila (ná) “not to do (in this case) what you judge good (would be) unwise” (PE22/154).

The carita here refers to a particular action in the current circumstances, not a general or habitual action, which requires a different construction (a simple infinitive or a gerund). Compare this to the following phrase with the simple infinitive from the same document, which Tolkien described as being “general advice”:

• Q. alasaila ná lá kare tai mo nave mára “it is unwise not to do what one judges good” (PE22/154).

All the phrases above show the particular infinitive as the subject, but examples elsewhere show it can also function as a verbal object:

• Q. ore nin karitas “I feel an urge/wish/desire to do it”, (lit.) “*[it] urges for me to do it (this specific thing)” (VT41/13).

It’s not entirely clear how the particular infinitive would be formed for derived and u-verbs, but based on the example of the active participle ista- → istaila, I suspect the suffix -ita would be added to the stem: istaitas “to know it”, liruitas “to sing it”.

Infinitive Usage: As the previous example illustrates, the particular infinitive can be used in conjunction with a pronoun in the dative, especially for impersonal constructions, and the same is true of the simple infinitive:

• Q. eke nin kare sa “I can do that”, (lit.) “*[it] is possible for me to do that”.

It seems likely that such dative pronouns can be used with other constructions as well: merin lyen cene atarinya “I want for you to see my father”.

The infinitive is also used with the imperative (positive and negative) and various negative verbs: á care “do it!”, áva care “don’t do it!”, uin care “I don’t”:

Simplest aorist infinitive -i, kare “(to) do”, mostly used after negative verb, uin kare “I don’t” (PE17/68).

Sometimes new nouns are formed by adding a prefix to the infinitive, such as carë “to do” → lacarë “not to do = inaction” or úcarë “bad doing = misdeed”. These derived nouns are sufficiently divorced from their verbal function that they behave as ordinary nouns, can become the subject of sentences, and so forth:

Note that though a verbal derivative such formations as lakare are nouns and not “infinitives”; they cannot take an object anymore than E. “inaction” (PE22/154).

Infinitives with implied subjects: In the Quenya Verbal System (QVS), the governing verb before the infinitive could itself have a direct object (especially a pronoun) if that was also the subject of the following infinitive. This syntax may have remained valid in the 1950s and 60s as well:

Where the second verb also has a subject that subject can be regarded as the object also of the first verb. When this is a pronoun such expressions as the following are permissible in Quenya: ni·merite tule, ni·merite karithe, me·merilte tule (not tulir since the action of tule is sg. belonging to te), me·merilte karithe, me·merilti karilthi: sc. “I wish him to come, I wish him to do it, we wish him to come, we wish him to do it, we wish them to make them (other things)” (PE22/118).

These examples are a bit strange in that “him” is actually the indirect rather than direct object of the main verb in “I wish him to come”, so based on the dative examples above we might instead expect to see: merin sen tule “I wish for him to come” (using the syntax of the 1950s and 60s). A better example might be a transitive verb like cen- “to see”. In later syntax, these examples would become:

• ceninyes tule “I see him come”.
• ceninyes caritas “I see him do it”.
• cenilmes tule “we see him come”.
• cenilmes caritas “we see him do it”.
• cenilmet caritat “we see them do them (other things)”.

In all these examples, the direct object of the first verb acts as the subject of the infinitive. In later syntax, presumably the particular infinitive would be needed if the infinitive had an object, as indicated above. Probably an equally valid alternate construction would be cenilme caritaryas “we see his doing it” with the second subject attached to the particular infinitive. The examples in QVS imply similar constructions are allowed even if the object/subject is technically the indirect rather than direct object of the main verb: merinyes tule or merin se tule, in much that English can say either “I wish him to come” or “I wish for him to come”; such constructions could be a remnant of when the dative was not marked in Ancient Quenya.

In QVS, where the object of the first verb was a noun rather than a pronoun, it was more usual for the object of the first verb to be moved into a subordinate clause (PE22/118):

But in the latter case (with nouns) a clause was far more usual, and could be used in all cases where the subject of the second verb was not the same as that of the first. A clause in such cases is introduced by i, before vowels in [in was rarely used in the 1950s and 60s]. The tense inside the clause depends on that of the first verb: the time of which becomes the present of the second verb.

• ni·mere i Túro tule, in e·tule, in e·karithe “I wish Turo to come, him to come, him to do it.”
• or “[I wish] that Turo come(s), that he come(s), that he do(es) it” [more accurate English glosses].

In the syntax of the late 1960s these would be merin i Túro tule, merin i tulis, merin i carisses or merin i caris sa.

Non-Aorist Infinitives: Tolkien’s regular use of the term “aorist infinitive” implies that Quenya can use the bare stem for other verb tenses as the past infinitive, future infinitive, perfect infinitive or present (imperfect) infinitive. In his earlier writings, Tolkien explicitly gave infinitives for different verb tenses (PE14/28), including an explicit present imperfect infinitive kára “(to) be making” in the 1948 QVS (PE22/100). It is not entirely clear how such non-aorist infinitives would be used; in most normal constructions, the main verb carries the tense marker and the infinitive is in the aorist, as in: “I wanted to see my father” mernen cene atarinya. This pattern appears in QVS, though this document follows an earlier paradigm of pronominal subject prefixes rather than suffixes:

The same sort of expression can be used with nouns: e·merne ataretta tule “he wished his father to come”; e·kestane ataretta karithe “he asked his father to do it” (PE22/118).

In the syntax of the late 1960s these sentences would be: mernes atarya tule “he wished his father to come” and cestanes atarya caritas “he asked his father to do it” (particular infinitive).

There is, however, at least one late example of what seems to be a non-aorist infinitive, in the 1960s version of the Markirya poem (hat tip to Findegil for pointing out this example):

• man cenuva fána cirya métima hrestallo círa “Who shall see a white ship leave the last shore” (MC/221).

Here we have two verbs, the first in the future and the second in the present/imperfect, and the object of the first verb is the subject of the second. In more ordinary prose this might be: man cenuva fána cirya círa métima hrestallo “Who will see a white ship [to be] leaving the last shore”. It is conceivable that infinitives of other tenses might be used in other specialized constructions: “I want (now) to have seen my father yesterday (but I didn’t)”, merin (sí) ecénie atarinya noa.

Conceptual Development: In The Qenya Verb Forms of the 1910s, the infinitive was formed in the active voice by adding the suffix -nt or -nqe to the tense stem (present, past, future or aorist); in the medial voice the infinitive suffix was -s(te) and in the passive voice -l(de) (PE14/28-30). This document had distinct gerund forms with similar suffixes: active -nto, medial -sta, passive -ldo (PE14/28-30). The last set of tables in this document suggests that the bare uninflected stem could also be used as an infinitive (PE14/31-33). In the Early Qenya Grammar (EQG) of the 1920s:

-sta for verbal noun or infinitive or gerund. There is no passive infinitive (PE14/56).

It is not clear whether this suffix applied only to the present/aorist or could be used with all verb tenses.

The Qenya Conjugations of the late 1920s or early 1930s gave present, past, future infinitives using the suffix -nt (PE16/128). It also had an “aorist infinitive or gerund” with suffix -u capable of being inflected like a noun, meaning it is probably properly a gerund.

In the Quenya Verbal System (QVS) from 1948 the infinitive was the base stem, but could be inflected with object suffixes. In the 1948 paradigm, subject pronouns were prefixes, and object pronouns were suffixes and could be of any person, 1st, 2nd or 3rd:

The “infinitive” was the same as the basic form and could be similarly inflected: kare “(to) make”; karin “(to) make me” [object pronoun]. This form was only used following and as the direct object of another verb (PE22/99).

As noted above, by this point an infinitive could only be verbal object, never a subject. In QVS any uninflected tense form could be used as an infinitive:

The bare stem of every tense could act as an infinitive, but the Gerund was formed only from the Aorist ... Present ... The infinitive was (as in the Aorist) the bare stem: kára “(to) be making” (PE22/99-100).

In 1948 the infinitive itself could take object suffixes as with karin “to make me” above. The particular infinitive was introduced later. Its first clear mention is in the 1969 Late Notes on Verb Structure, as noted above. However, Tolkien may have conceived of it earlier than this, since -ita was the basis of the Sindarin gerund suffix -ed (PE17/68).

Neo-Quenya: I find the idea of infinitives for other verb tenses to be very intriguing, but we don’t have much information on how they might be used. For now I think it is generally safer and clearer to use a subordinate clause for such constructions: merin (sí) i ecénien atarinya noa “I wish (now) that I had seen my father yesterday”.

Regarding the possible syntactical roles of the infinitive, I recommend limiting the infinitive mainly to the role of verbal objects, as described in QVS and EVS2. This includes serving as the predicate of a “to be” statement where it would function as the “object” of the verb ná. I think the Quenya infinitive is not sufficiently distinct to serve well as a verbal subject, and the gerund or particular infinitive can fill that function as needed. However, given the example kare mára kwí tyare naxa “doing good may cause evil” (PE22/154), there is solid evidence that the infinitive can serve as a subject.