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to come near or nearer to:
The cars slowed down as they approached the intersection.
to come near to in quality, character, time, or condition; to come within range for comparison:
As a poet he hardly approaches Keats.
to present, offer, or make a proposal or request to:
to approach the president with a suggestion.
to begin work on; set about:
to approach a problem.
to make advances to; address.
to bring near to something.
to come nearer; draw near:
A storm is approaching.
to come near in character, time, amount, etc.; approximate.
the act of drawing near:
the approach of a train.
nearness or close approximation:
a fair approach to accuracy.
any means of access, as a road or ramp:
the approaches to a city.
the method used or steps taken in setting about a task, problem, etc.:
His approach to any problem was to prepare an outline.
the course to be followed by an aircraft in approaching for a landing or in joining a traffic pattern:
The plane’s approach to the airport was hazardous.
Sometimes, approaches. a presentation, offer, or proposal.
approaches, Military. works for protecting forces in an advance against a fortified position.
Also called approach shot. Golf. a stroke made after teeing off, by which a player attempts to get the ball onto the putting green.
Bowling.

the steps taken and the manner employed in delivering the ball:
He favors a four-step approach.
Also called runway. the area behind the foul line, from which the ball is delivered.

Contemporary Examples

He spoke in a “proper, polite” way he feels a cop should on approaching someone.
Alphonza Bryant, the Slain Bronx Teen Who Did Everything Right Michael Daly May 1, 2013

The approaching Islamic revolution caused the family to be evacuated in 1978.
The First American Casualties of our Iraq “Adventure” Michael Daly March 19, 2013

Rogue female knights and emancipated Wildlings are approaching the center of the story.
Daenerys Goes to Washington: The Modern Politics of ‘Game of Thrones’ Jedediah Purdy April 7, 2014

A new report released by the New York Federal Reserve reveals total student loan debt is approaching $1 trillion.
The University of Debt Ilana Glazer February 28, 2013

Yes, Boehner was demanding more spending cuts, but the two sides seemed to be approaching split-the-difference territory.
Parties Resort to Finger-Pointing as U.S. Heads Over Fiscal Cliff Howard Kurtz December 27, 2012

Historical Examples

He was approaching Aminta, who, when she saw him, hurried to meet him.
The International Magazine, Volume 2, No. 3, February, 1851 Various

We had left the Boulevard, and were approaching the white-domed library.
The Bacillus of Beauty Harriet Stark

The big ship was approaching rapidly; I felt as if we were caught in a trap.
Peter Biddulph W.H.G. Kingston

“I think I’ll stay for the meeting,” said Yates, approaching him and patting the horse.
In the Midst of Alarms Robert Barr

“Perhaps you’d like some water,” said Varbarriere, rising and approaching the bell.
Guy Deverell, v. 2 of 2 Joseph Sheridan Le Fanu

verb
to come nearer in position, time, quality, character, etc, to (someone or something)
(transitive) to make advances to, as with a proposal, suggestion, etc
(transitive) to begin to deal with: to approach a problem
(transitive) (rare) to cause to come near
noun
the act of coming towards or drawing close or closer
a close approximation
the way or means of entering or leaving; access
(often pl) an advance or overture to a person
a means adopted in tackling a problem, job of work, etc
Also called approach path. the course followed by an aircraft preparing for landing
v.

c.1300, from Anglo-French approcher, Old French aprochier “approach, come closer” (12c., Modern French approcher), from Late Latin appropiare “go nearer to,” from Latin ad- “to” (see ad-) + Late Latin propiare “come nearer,” comparative of Latin prope “near” (see propinquity). Replaced Old English neahlæcan.
n.

mid-15c., from approach (v.). Figurative sense of “means of handling a problem, etc.” is first attested 1905.