What is the difference between 越える and 越す and are they truly transitive verbs?

Question

My question arose when I was trying to rationalise the first two sentences below. I wondered if these two verbs (越すand 越える） formed a pair with one transitive, one intransitive (like 消える &　消す）with を　acting as a "spatial object marker" for the intransitive form (as in the sentence 「飛行機が空を飛ぶ」, 飛ぶ being an intransitive verb) but the dictionary entries and examples 3-5 below suggest they are both transitive verbs of similar meaning. (越す　possibly has wider use.)

Could somebody familiar with these answer my question above and rationalise the sentences with these verbs below?

1. 駅を乗り越す| go/ride past the stop

2. 彼は門を乗り越えて庭に入ってきた｜He climbed over the gate into our garden.

3. 川を越す｜cross a river

4. 国境を越える｜cross the border

5. 球はライトの頭上を越えた｜The ball sailed over the right fielder's head.

Bonus: what is the difference between these two verbs and 超える?

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My answer to the bonus: I think that where as 越える　is used for "crossing over/going past" when referring to tangible actions (and possibly compound verbs) such as those in the examples above, 超える refers to non-tangible abstract events such as exceeding a limit or crossing/transcending a generation:

1. 支出が収入を超えた｜My expenses exceeded my income.
2. 彼の作品は世代を超えて愛読されている｜His works are loved by people of all generations.

but confusingly the word for transcend is 超越　which used both!

Please correct me if I am wrong.

Answer 1

Interesting question as it brings up some Japanese particularities.

First, please notice that 乗り越す/乗り越える and 越す/越える are different verbs (like go and overgo in English) and thus a little out of the scope of the question.

As a notice, I am basing the following on the 明鏡国語辞典(第二版), others dictionaries might have different nuances.

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越す intransitive verb ([自動詞]{じどうし})

pass over -place- (sharing the meaning with 越える)

山を越す。 (Pass over the mountain.)

exceed -quantity- (sharing the meaning with 越える、超す、超える)

熱は38度を越しています。 (The fever exceeds 38 degrees.)

pass over -time-

日本で年を越す。 (Pass the new year in Japan.)

[敬語]{けいご} form of 行く and 来る

オフィスにお越しください。 (Please come at the office.)

to move in

山田さんは東京に越しました。 (Mr. Yamada moved to Tokyo.)

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超す intransitive verb ([自動詞]{じどうし})

exceed (sharing the meaning with 越える、越す)

熱は38度を超しています。 (The fever exceeds 38 degrees.)

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越える intransitive verb ([自動詞]{じどうし})

pass over -place- (sharing the meaning with 越す)

山を越える。 (Pass over the mountain.)

exceed -quantity- (sharing the meaning with 越す、超す、超える)

熱は38度を越えています。 (The fever exceeds 38 degrees.)

exceed -normality-

年齢を越えた健康。 (An impressive health for the age.)

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超える intransitive verb ([自動詞]{じどうし})

exceed -quantity- (sharing the meaning with 越す、超す、超える)

熱は38度を超えています。 (The fever exceeds 38 degrees.)

exceed -normality-

年齢を超えた健康。 (An impressive health for the age.)

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Considerations on usages

こす and こえる can both be used for pass over and exceed a quantity, but こえる is usually preferred.

For the "exceed a quantity" meaning, 超える is preferred when a certain quantity or criteria is exceeded.

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Consideration 越す/越える being intransitive verbs

One could legitimately think that as 越す/越える are used with を most of the time (eg: 山を越える。), they should be transitive verbs.

But the trick is about how を is used, in case it is used as an action marker the verb is transitive, in case を is used in a non-action role the verb is considered intransitive.

You can read more regarding this topic at this link.