21.2.4 embaixo de, debaixo de, abaixo de (prepositions)
The use as a preposition is more complicated that the use as an adverb, because there is an endless amount of possible relationships between two objects, an endless amount of mouvements in a three dimensional space, an endless amount of positions an object can be placed in space and an endless number of metaphorical meanings. This not a speciality of Portuguese, the same problem we have in English and any other language. Some example may illustrate the problem.
mouvement from one point to another: He passed the letter underneath the door.
mouvement from one point to another: The birds flew beneath the bridge.
mouvement without goal: The dove flutters under the canopy.
mouvement passing an object: He passed by the door downstairs.
mouvement with the indication of a direction: He came down.
vertical placement of two objects: He was sitting under the bridge.
horizontal placement of two objects: Below the castle are the vineyards.
description of a direction: There is nothing down there.
description of a position: He was looking for his shoes under the table.
description of a final position: He threw his shoes under the table.
With embaixo de, debaixo de, abaixo de we can't express all these different relationships. It make a big difference whether a bird passes beneath a bridge and continues his trip or if he flies there to find shelter from the rain. Furthermore there is the problem that in some circunstances these prepositions are interchangeable and other contexts there are not.
Portuguese native speakers tend to use embaixo de, debaixo de if one object is placed vertically under another object. (The shoes are under the table.) There is a preference for abaixo de if an object is placed at a lower level than another, but not in a vertical sense. (Below he saw the people in the street.)
abaixo de below
O hotel está situado abaixo do Castelo.
The hotel is situated below the castle.
embaixo de, debaixo under
~O hotel está situado debaixo do Castelo.
~O hotel está situado embaixo do Castelo.
~ The hotel is under the castle.
It is quite obvious that the sentences marked with ~ are not correct. In theory it is possible that the castle dungeon has been converted into a hotel, for some people with strange romantic ideas, but common sense would say that the hotel is in another building below the level of the castle.
Furthermore in a metaphorical sense, below 20 degree, below 18 years, below 2 percent etc.. the use of abaixo de is more common than the use of debaixo de / embaixo de. The question rises how to find out whether a thesis concerning the use of a preposition is wrong or right. By correct and right we understand the use of the majority. (These criteria is sometimes questioned by some oficial institutions but they end up in accepting the use of the majority because at the end there is no choice.) When defining the appropriate use traditional grammars base their conclusions from examples taken from literature and therefore their conclusions are based on a very small amount of examples. Much more meaningful are site like www.reverso.net or www.linguee.de with thousands of examples. Obviously these sites embrace as well spontaneous contributions, where the speaker / writer gave little attention to correctness, but it is easy to find examples from more conscious speakers.
It is indeed difficult to find examples wer embaixo de, debaixo de is used in a metaphorical context, whereas it is easy to find examples where it is used in a metaphorical sense. Furthermore in most cases the correct translation is below. (Although the distinction between under and below is not always made in English.)
abaixo de metaphorical / below
Está abaixo de nosso processo cognitivo de pensamento.
It is below awareness.
No entanto, manteve-se abaixo de 50 %.
However it remained below 50 percent.
Metade do nosso território situa-se abaixo do nível do mar.
Half of our territory is below sea level.
Ainda está bem abaixo do recorde francês.
It is well below the French record.
In the case of a vertical position it seems that there is a preference for debaixo de, although it is not very difficult to find examples where debaixo de is used in a metaphorical sense and the vertical position is irrelevant.
debaixo de under
Escondeu a pistola debaixo de seu casaco.
He hided his piston unter his jacket.
Vivíamos debaixo de uma ponte.
We lived under the bridge.
Descobriram algo enterrado debaixo do pátio.
They discovered something buried in the yard.
A gata está debaixo da cadeira.
The cat is under the chair.
Seu pai foi encontrado morto, debaixo de um trem.
His father was found dead under a train.
Temos a situação debaixo de controlo.
We have the situation under control.
Estiveram debaixo de investigação durante três anos.
The were under surveillance for three years.
Portuguese native speakers often say that there is no difference between debaixo and embaixo, what very probably is true, in any case it is difficult to illustrate the difference by examples. If embaixo de can be used in a certain context to describe a certain relationship, debaixo de can be used as well.
Estaremos aqui embaixo se precisarem de nós.
In case you need us, we are down here.
Ela tem uma bolsa embaixo do braço.
She has a bag under her arm.
Mando alguém aí embaixo logo que possível.
I send someone down as soon as possible.
Por que não olha embaixo da cama?
Why you don't look under the bed?
However in case of a mouvement, "to pass under the bridge", it seems that there is a difference. If on takes a verb of mouvement with por debaixo, caminar / voar / andar + por debaixo and a verb of mouvement with + por embaixo the construction with por embaixo yields so little results in comparison to por debaixo that we can assume that the construction with por embaixo doesn't comply with the standard.
"Passar por debaixo" for instance, with quotation marks, otherwise google will find any pages were these words show up in any order, will yield more than 100 000 results. The same construction with por embaixo yields only 10 results, from which 10 of poor quality, in other words from non Portuguese native speakers. "Voar por embaixo" doesn't yield any result, "voar por debaixo" yields 20 results.
debaixo por under
Mas muita água ainda vai passar por debaixo dessa ponte.
Al lot of water will still pass under this bridge.
Ainda hoje é considerado mau agouro andar por debaixo da escada.
Still today it is considered bad omen to pass under a stairway.
Um avião tratando de voar por debaixo de uma ponte se espatifou nas águas geladas.
An aircraft that tried to pass under the bridge smashed in the icy waters.
Although in this case, in a context of "pass under", going from one point to another, por baixo is possible as well. (At least google yields a lot of results.)
Muita água terá ainda de passar por baixo da ponte antes que elas se concretizem.
A lot of water still has to flow under this bridge until they become more concret.
Não vamos voar sobre as nuvens, vamos voar por baixo delas.
We well not fly above the clouds, but below them.
However one cannot only pass under a bridge. It is possible as well to go under a bridge and remain there. In this case it is para debaixo, but we get the same situation as before. With a google research we get so few results for para embaixo that it is to suppose that it doesn't comply with the standard. There is very strong preference for debaixo in this context.
Se não conseguir um aluguel social vou ter que ir para debaixo da ponte.
If I don't get a council appartement, I have to go under a bridge.
Vamos para debaixo de uma arvore.
Let's go under a tree.
The construction "para embaixo" shows up several thousand of times, but the para it 3rd person singular of the verb parar (to land, to get into, to end up) in this case and completely different story.
Moto para embaixo de caminhonete em acidente.
A motorcycle ended up under a picup in an traffic accident.
Sob is a synonym for embaixo de, por baixo de and debaixo de and can be used in a metaphorical sense and to describe relationships in space, can be used to describe a fix position and to describe a mouvement, but is never an adverb.
Não consigo trabalhar sob pressão.
I can't work under pressure.
A situação está sob controle.
The situation is under control.
Passamos sob a ponte.
We passed under the bridge.
O livro está sobre a mesa.
The book is on the table.
(In opposite to sobre, upon, sob can be used as well in a methophorical sense, see 20.7.)