The so-called accusative-infinitive construction means the same as a construction involving the possessive pronoun and the gerund (-ing form). The pronoun-equivalent replaces the article of (i) and (ii) above and is "possessive" by juxtaposition:

Mi dicte petitio an acte re
I asked him to do it
(I requested his doing it)

Briefly the rule is that u(n) or de before an operator is equivalent to the empty word to (German zu, Swedish att, French a), and tendo u is equivalent to in order to (German um zu, Swedish för att). As above, a pronoun in its possessive sense may replace the article u(n). Hence the possessive gerund construction and the accusative-infinitive are both indistinguishable from a noun clause, as when we say in English:

I saw he did it = I saw him doing it
I know he is right = I know him to be right

Participial Usage

Since a verboid has no flexion, date means give, gives or giving, and we can use it (or any other verboid) as an adjective-equivalent, i.e. as the present active participle.

U geo, kine peri heli
The earth, moving round the sun¹

In contradistinction to participial expressions, including operative constructions with an amplifier, the simple verboid as epithet takes the usual position:

U kine dactyli acte grapho
The moving finger writes

Unlike Russian and the Scandinavian languages, English, German and French have no separate active and passive participial forms for the past. As adjectives, the present and past participles are respectively active and passive. In fact, the so-called past (more properly, passive) participle need not

¹ Without a pause in speech or a comma to mark it in print, un avi, kine in aero might mean a bird, moving in air (a bird in flight) or bird motion in air (the flight of a bird). We can sharpen the distinction beyond possibility of doubt. Thus un avi; su kine in aero (a bird which is moving in air) can mean only a bird in flight; and u kine de avi in aero (motion of a bird in air) can mean only the flight of a bird.