χαῖρε, φίλε Δαυιδ!
1. The accusative of respect is a useful category for English speakers learning Greek, but this is only because the Greek accusative does not act in every way like the English objective case does. In English, we say "I hit him," but we don't say "I am angry him." For the latter, we have to say something like "I am angry WITH him," or "I am angry as far as he goes," or "I am angry in respect to him." But this is largely just an accident of how English developed. If we could say (and there is no reason why we could not have been able to say) "I am angry him" we would not feel so much the need for a category like the accusative of respect.
2. One can say that τὸ βάθος in τὸ τῆς θερμασίας βάθος ἐστιν τριάκοντα is a predicate nominative and means "the depth of the heat is 30," or one can say that τὸ βάθος is an accusative of respect and means "It is 30 in respect to the depth of the heat." Both of these statements are true, and both are false. Whenever you analyze a Greek sentence with meta-language, whenever you provide a translation, what you are doing is stepping away from the Greek and looking at it from a certain angle, and attempting to describe what you see. Looking at τὸ τῆς θερμασίας βάθος ἐστιν τριάκοντα from one angle you see it one way, but it is always possible to shift your perspective and look at it in another way. But the key thing to remember, is that in either case, you are stepping away from the Greek. You are choosing to separate yourself from the Greek text and you are plunging yourself into the realm of analysis. Because, the fact is, τὸ τῆς θερμασίας βάθος ἐστιν τριάκοντα really only means one thing, namely what it says, τὸ τῆς θερμασίας βάθος ἐστιν τριάκοντα. Any other meaning we give it is an abstraction, approximate at best. We do this, presumably, because either we don't know what τὸ τῆς θερμασίας βάθος ἐστιν τριάκοντα means, or because we think that our abstraction will give us a more precise understanding of what τὸ τῆς θερμασίας βάθος ἐστιν τριάκοντα means. It does, and it doesn't. "traduttore, traditore" applies to meta-language as well.
daivid wrote:As Ancient Greeks didn't have thermometers this won't be attested in the sources but, if they did, how would they say it?
One of the things that I have come to believe, through the process of writing a bunch of Ancient Greek and then constantly checking that against actual Greek texts that I read, is that the Greeks loved to say the same thing in a lot of different ways. The question is never "How would you say that in Ancient Greek?" but rather "What are four or five ways of saying that in Ancient Greek?" Maybe I am wrong, but I have come to believe that the Greeks used all this varied vocabulary and overlapping constructions for the same reason that we climb mountains--because they were there.
So, I can easily imagine a Greek saying
τὸ τῆς θερμασίας βάθος ἐν ταύτῃ τῇ γῇ λίαν θερμόν ἐστιν!
The temperature in this land is very hot!
αὕτη ἡ γῆ ἐστιν λίαν θερμὴ τὸ τῆς θερμασίας βάθος.
This land is very hot in respect to temperature!
daivid wrote (on the weather thread:)
τήμερον ὁ ἤλιος ελαμπε αλλα ου ἐπανηλελυτηε, αὐτοῦ εικοσι και δυο τὸ τῆς θερμασιας βάθος ὄντος
I saw immediately what you are doing here, the genitive absolute referring to "it" or "the air," and βάθος being an accusative of respect. "It (the air) being 20 in respect to the depth of the heat." In my humble opinion, you will continue to learn Greek effectively if you continue to do stuff like this, namely experiment with writing Greek, try different constructions and vocab, and then compare them to what you find in actual Greek while you do your reading. In my humble opinion, you cannot really understand stuff like genitive absolutes and accusative of respects unless you attempt to construct them yourselve in actual communication, and then revise your command of these with more reading of actual Greek texts.
My sense is, another (not necessarily a better or "more real") way to say this would be something like
τοῦ ἀέρος ὄντος εἴκοσι καὶ δύο κατὰ τὸ τῆς θερμασίας βάθος...