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Nowadays, when an amount tabelvorto ("kiom", "tiom", "iom", "ĉiom" or "neniom") is followed by the thing(s) or category to which the amount refers, there's always a "da" between them. (See also Why is "da" used in this question?.)

This goes for countable quantities:

Kiom da gekuzoj vi havas?

... as well as for uncountable ones:

Kiom da akvo vi volas trinki?

As this answer to How to mark accusative for correlatives of quantity? Kiel marki akuzativon ĉe "...iom"-aj tabelvortoj? points out, this though hasn't always been the case:

Actually the tiom/kiom words used to accept the n-ending; Hence you could say "Kiom laboristojn bezonas tiom da laboro?". However it is no longer used and people now use the da-format (kiom da laboristoj).

Is it known when, how and why this changed and "da" became customary and (outside of poetry) seemingly even required?

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  • Not much of an answer, but… There are a lot speakers, who for some reason have hard time to understand other grammatical cases than nominative. (Just see around in any espa forum.) Commented Nov 10, 2019 at 20:21

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The article you linked, mentions that in kiom laboristojn you are using kiom as an adjective, but without ending. While it could be considered correct (mainly because Zamenhof said so), the fact is that it is not very coherent with the rest of the language (where you would expect the adjective to agree with the noun).

At the beginning of the language, as theory and practice met, there were structures that were tried/used but that did not go well with the rest of the language or showed the need for additional elements. An example: kelk- was used to mean plur- because plur- did not exist yet, after plur- appeared kelk/ lost that original meaning (here in PMEG).

Another example: you can find things like la multe da lupoj. It's hard to say those are wrong, since they were used at the beginning by the initiators of the language, but they really feel weird. Today, in that special context you would probably say la multo da lupoj without much thinking (here in PMEG).

The language is alive, and that means users/speakers get to choose among competing forms, sometimes favouring the more coherent form. In this case, since we do use kioma as an adjective, it feels even more strange to use it as an adjective without any ending in just one context.

So all in all, to answer the question on when, why and how: pretty early; because it doesn't play well with the rest of the language; and through normal use as in all living languages.

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    It’s probably worth highlighting that kioma does not have the same meaning as the kiom in kiom laboristojn. Instead it is a question about the position in a sequence rather than about a quantity. Eg, kioma horo estas?. Commented Nov 12, 2019 at 15:38
  • @NeilRoberts kioma car refer to both the quantity and the order. vortaro.net. Commented Nov 12, 2019 at 15:49
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    @Eduaro Trápani, none of the examples in vortaro.net seem to back up that statement. PMEG has this comment: “Rimarku, ke kioma havas vicordan signifon same kiel nombraj vortetoj kun A-finaĵo (unua, dua...), dum la aliaj OM-vortoj (normale) ne havas tian vicordan signifon. Teorie oni povas uzi ankaŭ kioma en ne-vicorda senco, sed tiam oni riskas miskomprenon.”. Commented Nov 12, 2019 at 15:59
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    Interese. Tion vi celis per "vicorda"! Kiam mi legas "kioman fojon ..." mi sentas kvanton kaj ripeton kiel ĉefajn trajtojn, ne vicordon. Sed mi komprenas, vi pravas. Nu, tio iel subtenas la respondon; jen alia nekoheraĵo en la uzo de kiom en tiu frua Esperanto (la menciita en la demando). Commented Nov 12, 2019 at 18:27
  • To me, the fact that "kioma" exists and the ordinal meaning it carries, both indicate that "kiom" is not something adjective-like but rather something number-like, which should support the use without "da" even without agreement to the noun. But of course, I can't argue with history, and this analogy goes only for "kiom", not for all the "...iom"-words, and one would want those to be treated all the same.
    – das-g
    Commented Nov 12, 2019 at 21:35

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