Dear teachers,

Would you please tell me if my analysis is correct ?

They considered the sunny sandy beaches a property of theirs.

They = subject
Considered = transitive verb
The sunny sandy beaches = direct object
A property of theirs = object complement

All the best,
Looks good to me, Hela. You could go on to call it a 'nominal object complement', I suppose.
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Thanks Mr Micawber,

And what do you think of "She is very proud of her looks"

She = subject
is = intensive verb

(by the way how would you qualify "intensive / transitive / intransitive" is is the NATURE of the verb, its GRAMMATICAL CLASS rather than its functions? What do you call this exactly in linguistics ?)

very proud = subject complement
of her looks = ? / adverbial ? if yes, of what ?

Many thanks,
(1) 'Intensive verb' is not a common denomination in English; 'intensive' is normally used of adjectives and adverbs like 'utter' ('utter nonsense') and 'extremely' ('extremely dense'). I recommend that you stick with 'copular' or 'linking' verb for clear communication.

(2) Hopefully grammatical class and function will be the same, but in cases where it is not, the verb would be classified according to its function, as with or example:

I hurt my Achilles tendon. (transitive 'hurt')
My sacroiliac hurts. (intransitive 'hurt')

(3) What do you call what in linguistics?-- I'm sure of neither your question, nor the answer. Sorry

(4) 'Of her looks', it seems to me, is not an adverbial, but a prepositional complement of the adjective 'proud'.
Thanks Mr Micawber,

3) I think that the function of a verb (part of speech) is to be a "verb". But when we say that it is copular, transitive and so on, we probably talk about its "syntactic nature" or "verb type", right ?

Kind regards,
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Ah yes, I see. The basic 'function' of a verb is to 'express an action, thought or state of being'-- or something to that effect.

But I don't think that the word 'function' is used linguistically-- or in linguistics-- to separate 'part of speech' from subdivisions of same ('syntactic nature'). One could do so in e.g. an academic paper if one defined them as such, I suppose.

However, I don't converse a lot with linguists, so I don't really know how they use this nomenclature popularly. 'Function' is a relatively superordinate word/concept, though.