Is there a good historical/etymological explanation why 大きい and 小さい can take the な ending in attributive position?
Also, is there a good historic/etymological explanation why 多い in attributive use turns into 多くの-?
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大きな is the 連体形 (attributive form) of an old na-adjective おおきなり, and only the attributive form is used in the present day. 小さな, おかしな are also the same thing. They are analyzed as pre-noun adjectivals.
The attribute form of 多い is 多い, but it alone isn't commonly used such as 多い車. However 多い with a modifier can be used as the attribute form such as 外国人の多い学校. 多く is a noun, so when it modifies a noun, の is needed after a noun such as お菓子の家.
I can answer your first question. If you think of it from a grammatical perspective,
is used in sentences such as
大きいです。(It is large.) or 大きく書きます。(I will write it large.)
the word 大きい can be used at the end of the sentence or be connected to a verb.
On the other hand, 大きな can only be used to be connected to a Noun.
There is another difference that exists. The previous example does not quite explain the difference, so this might help in that perspective. I will use these two sentences to compare.
大きい木 (Large Tree) and 大きな木 (Large Tree)
The Japanese dictionary gives examples of 大きな.
大きな政府 (Large Government)
大きな影響を与える (Give a large effect)
大きな意味がある (t has a big meaning.)
If you look at the 大きい part of the dictionary, you will get:
大きい服 (Large clothes)
大きい体 (Large body)
大きい字 (Large words)
It looks like most Japanese use 大きな with more abstract concepts, and 大きい with more objective or literal concepts.
I could not find much information about the second question, but here is a grammatical explanation, if it helps.
多い and 多くの, is a special case adjective since it cannot be used before the noun it describes. This sentence would not work:
多い 人(ひと[people]) が います。
Instead, you can use it after the noun.
人が 多い です。
So if you want to say many+noun in Japanese you use 多くの. 多くの人
I hope this helps. Please tell me if I can help by clarifying anything.