
gebieten
to command
To order, command, or demand something with authority. The word is mostly used in a formal or elevated context.
Der König gebot seinen Untertanen, ihm zu gehorchen.
The king commanded his subjects to obey him.
to command
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to command
To order, command, or demand something with authority. The word is mostly used in a formal or elevated context.
Der König gebot seinen Untertanen, ihm zu gehorchen.
The king commanded his subjects to obey him.

to require
Used to express that something is required or appropriate for reasons of politeness, duty, or reason.
Die Höflichkeit gebietet es, sich für das Geschenk zu bedanken.
Politeness requires that one thank someone for the gift.

to rule over
To rule over someone or something; to have power or control over a territory or a group of people.
Der Feldherr gebot über eine riesige Armee.
The general ruled over a huge army.
The verb 'gebieten' (to command) belongs to an elevated, formal style of language. It is rarely used in everyday spoken language.
Der Richter gebot dem Zeugen, die Wahrheit zu sagen.
The judge commanded the witness to tell the truth.
'Gebieten' (to command) is closely related to the noun 'das Gebot' (the commandment, rule, law) and 'der Gebieter' (the ruler, master). All of these words express a form of authority or necessity.
Das oberste Gebot für Ärzte ist es, Patienten zu helfen.
The highest principle for doctors is to help patients.
In the meaning 'befehlen' (to command), the person who is being commanded to do something is in the dative. The instruction itself can be a noun in the accusative or a subordinate clause.
Die Königin gebot ihrem Diener (Dativ) absolutes Schweigen (Akkusativ).
The queen commanded her servant (dative) to maintain absolute silence (accusative).
The expression 'es gebietet' (it requires) is often used with an abstract noun such as 'die Höflichkeit' (politeness), 'die Vernunft' (reason), or 'der Anstand' (decency). The 'es' is a fixed element of the construction.
Der Anstand gebietet es, älteren Menschen seinen Sitzplatz anzubieten.
Decency requires that one offer one's seat to older people.
In the meaning 'herrschen über' (to rule over), 'gebieten' (to rule) is always used with the preposition 'über' and the accusative.
Der Kaiser gebot über ein riesiges Reich.
The emperor ruled over a huge empire.
to rule / prevail
Both words can express a person's power over a territory. Herrschen generally refers to actual political rule, while gebieten über places greater emphasis on command and control and sounds more formal. Herrschen is usual in a neutral statement; gebieten über also fits a formal or power-focused context.

Laut der alten Urkunde gebietet die Königin über das Land.
According to the old document, the queen rules over the country.
Die Königin herrscht seit vielen Jahren über das Land.
The queen has ruled the country for many years.