Two-Way Prepositions: Horizontal / Vertical

Believe it or not, two German accusative/dative prepositions make yet another distinction that English does not! The common prepositions an and auf can both mean "on" or "at" but they differ in how they are applied to surfaces.

If an object is on or near a vertical surface (a wall, a chalkboard, etc.), then usually the preposition an is used. If a horizontal surface (a tabletop, a floor, etc.) is involved, then auf 

is used to express "on" or "at." 

Look at the illustrations below...

Horizontal and Vertical "ON" or "AT" AN (vertical) and AUF (horizontal)

AN > VERTICAL - SENKRECHT  die Wand • the wall

An object approaching a vertical surface. The accus. phrase "an die Wand" answers the question wohin?

An object "on" or "at" the wall. (vertical surface) The dative phrase "an der Wand" answers the question wo?

AUF > HORIZONTAL - WAAGERECHT  der Tisch • the table

An object approaching a horizontal surface. The accus. phrase "auf den Tisch" answers the question wohin?

An object "on" the table. (horizontal surface) The dative phrase "auf dem Tisch" answers the question wo?

Now, if you've been paying attention, can you say what the dative prepositional phrase an dem Tisch or am Tisch means? Unlike auf dem Tisch, an dem Tisch means "at" or "next to" the table. If you are sitting at the table, you are am Tisch. If you are sitting on top of the table, you are auf dem Tisch!

German is being very consistent here.

If you are talking about your location in relation to the vertical part of the table (the legs, etc.), then you use an. If you're talking about your location in relation to the horizontal top of the table, then you use auf. This logic also applies to expressions like an der Donau (on the Danube). The use of an refers to being on the edge of the river.

If we're actually on the Danube (in a boat), then we're auf der Donau.

More Examples (A = accus., D = dative)
Here are some examples of the uses of an and auf:

• wo? an der Ecke D - on/at the corner
• wohin? an die Ecke A - to the corner
  
  
• wo? an der Grenze D - on/at the border
• wohin? an die Grenze A - to the border
  
  
• wo? am Rhein D - on the Rhine
• wohin? an den Rhein A - to the Rhine
  
  
• wo? auf dem Dach D - on the roof
• wohin? auf das Dach A - onto the roof

Idiomatic Expressions

Besides their "normal" uses, an and auf are also used in many idiomatic expressions and verbal phrases. Here are some examples:

• auf der Bank - at the bank
• jemandem auf der Tasche liegen - to live off of someone
• auf der Straße liegen A - to be down and out
• jemanden an der Nase herumführen - to lead someone around by the nose, take them for a fool
• woran liegt das? - what's the reason for that?

Most of the other two-way prepositions are used in idiomatic expressions as well.