All 5 Uses

approach
in
The Lightning Thief
(Auto-generated)

Luke approached the fire, bowed his head, and tossed in a cluster of fat red grapes.†
Chpt 7
Approach, seeker, and ask.†
Chpt 9
But she let me approach-twenty feet, ten feet.†
Chpt 11 *
I didn't have to be told who the two gods were that were sitting there, waiting for me to approach.†
Chpt 21
I approached the fisherman's throne and knelt at his feet.†
Chpt 21

Definitions:

(1) (approach as in: approached the city)
to get closer to (near in space, time, quantity, or quality)
(2) (approach as in: use the best approach)
a way of doing something; or a route that leads to a particular place
(3) (approach as in: approached her with the proposal)
to begin communication with someone about something -- often a proposal or a delicate topic
(4) (meaning too rare to warrant focus)
More rarely (and typically only in classic literature), the phrase nearest approach to as used in "her nearest approach to an apology" or "her nearest approach to a smile" typically means that "something is as close to something else as it ever gets." "As near an approach to" can have a similar meaning.