All 16 Uses of

approach
in
The Scarlet Letter

As night approached, it proving impossible to quell her insubordination by rebuke or threats of punishment, Master Brackett, the jailer, thought fit to introduce a physician.
p. 66.2

approached = got near

They approached the door, which was of an arched form, and flanked on each side by a narrow tower or projection of the edifice, in both of which were lattice-windows, the wooden shutters to close over them at need.
p. 96.6

approached = moved toward

In fact, adown the vista of the garden avenue, a number of persons were seen approaching towards the house.
p. 99.8

approaching = moving nearer

Roger Chillingworth had by this time approached the window and smiled grimly down.
p. 123.9

approached = moved near

His eyes, however, were soon greeted by a little glimmering light, which, at first a long way off was approaching up the street.
p. 138.7

approaching = getting nearer

"Yes; it is Hester Prynne!" she replied, in a tone of surprise; and the minister heard her footsteps approaching from the side-walk, along which she had been passing.
p. 141.2

The thought occurred to Hester, that the child might really be seeking to approach her with childlike confidence, and doing what she could, and as intelligently as she knew how, to establish a meeting-point of sympathy.
p. 166.1 *

approach = speak with someone about something for the first time

But now the idea came strongly into Hester's mind, that Pearl, with her remarkable precocity and acuteness, might already have approached the age when she could have been made a friend, and intrusted with as much of her mother's sorrows as could be imparted, without irreverence either to the parent or the child.
p. 166.6

approached = come near

She heard her mother's voice, and approached slowly through the forest.
p. 190.8

approached = moved nearer

It is singular, however, how long a time often passes before words embody things; and with what security two persons, who choose to avoid a certain subject, may approach its very verge, and retire without disturbing it.
p. 209.2

approach = get near

After parting from the physician, the commander of the Bristol ship strolled idly through the market-place; until happening to approach the spot where Hester Prynne was standing, he appeared to recognise, and did not hesitate to address her.
p. 218.5

approach = come near

Before Hester Prynne could call together her thoughts, and consider what was practicable to be done in this new and startling aspect of affairs, the sound of military music was heard approaching along a contiguous street.
p. 220.1

approaching = getting nearer

And thus much of woman was there in Hester, that she could scarcely forgive him—least of all now, when the heavy footstep of their approaching Fate might be heard, nearer, nearer, nearer!
p. 223.8

As the ranks of military men and civil fathers moved onward, all eyes were turned towards the point where the minister was seen to approach among them.
p. 233.9

approach = get near

They beheld the minister, leaning on Hester's shoulder, and supported by her arm around him, approach the scaffold, and ascend its steps; while still the little hand of the sin-born child was clasped in his.
p. 236.2 *

Near this latter spot, one afternoon some children were at play, when they beheld a tall woman in a gray robe approach the cottage-door.
p. 243.7

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)
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.