to climb / board
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to climb
To climb up or ascend something, especially a mountain, a tower, or another elevated place.
Die Alpinisten wollen morgen den Gipfel des Mount Everest besteigen.
The mountaineers want to climb the summit of Mount Everest tomorrow.
'Besteigen' (to climb/board) is an inseparable verb made up of the prefix 'be-' and the verb 'steigen' (to climb/rise). The prefix 'be-' makes the verb transitive, so it requires a direct object in the accusative.
Er hat schon viele hohe Berge bestiegen.
He has already climbed many high mountains.
After 'besteigen' (to climb/board), there is always an accusative object without a preposition. Say 'den Berg besteigen' (to climb the mountain), not 'auf den Berg besteigen'.
Wir wollen am Wochenende den höchsten Turm der Stadt besteigen.
We want to climb the tallest tower in the city this weekend.
In this meaning, 'besteigen' (to climb) is typically combined with high places. Common objects are: einen Berg (a mountain), einen Gipfel (a summit), einen Felsen (a rock), or einen Turm (a tower).
Nur erfahrene Kletterer sollten diesen Felsen besteigen.
Only experienced climbers should climb this rock.
When the object is a means of transport or a riding animal, 'besteigen' (to board/mount) means something like 'einsteigen' (to get in/board) or 'aufsteigen' (to mount). It is a somewhat more formal variant.
Die Reiterin bestieg ihr Pferd und ritt davon.
The rider mounted her horse and rode away.
The phrase 'den Thron besteigen' (to ascend the throne) is a fixed expression. It means that a person becomes king or queen.
Prinz Charles hat nach dem Tod der Queen den Thron bestiegen.
Prince Charles ascended the throne after the Queen's death.
to cover / to set
'decken' and 'besteigen' can both refer to reproduction in the context of animals. In animal breeding, 'decken' is the usual word for a male animal mating with a female animal. 'besteigen' more strongly describes the physical action of one animal mounting another; in technical biological language, it can also mean mating. The words can be confused because they are close in meaning in this specific area. In conversations about breeding, 'decken' is usually more natural. 'besteigen' sounds more technical or describes the visible movement.
Der Tierarzt beobachtet, ob der Bulle die Kuh besteigt.
The veterinarian observes whether the bull mounts the cow.
Der Züchter lässt den Hengst im Frühling die Stute decken.
The breeder has the stallion cover the mare in the spring.