And let vs conſider one another to prouoke vnto loue, and to good workes: Not forſaking the aſſembling of ourſelues together, as the manner of ſome is: but exhorting one another, and ſo much the more, as ye ſee the day approching.
It beckoned Scrooge to approach, which he did. When they were within two paces of each other, Marley's Ghost held up its hand, warning him to come no nearer. Scrooge stopped.
1947 January and February, O. S. Nock, “"The Aberdonian" in Wartime”, in Railway Magazine, page 7:
The descent continues, still more steeply to Dundee (Tay Bridge), and approaching from the bridge itself this sharp descent gives the curious appearance that the station is below the level of the firth.
Without these incentives to industry the Norwegian would be like the Laplander, without industry and civilisation; and the nearer he approaches to the beau idéal of those political economists—to the state of being without a taste for these foreign and expensive luxuries—the nearer he approaches to the condition of the Laplander in the comforts and enjoyments of life.
Approch the Chamber, and deſtroy your ſight With a new Gorgon.
a.1700, William Temple, “Some Thoughts upon Reviewing the Essay of Antient and Modern Learning”, in Miscellanea. The Third Part. [...], London: […]Jonathan Swift,[…] Benjamin Tooke,[…], published 1701, →OCLC, page 223:
He [Empedocles] was an admirable Poet, and thought even to have approachedHomer, in a Poem he writ of Natural Philoſophy; [...]
[…] I ſtuck all the Ground without my Wall, for a great way every way, as full with Stakes or Sticks of the Osier-like Wood, which I found ſo apt to grow, as they could well ſtand; inſomuch, that I believe I might ſet in near twenty thouſand of them, leaving a pretty large Space between them and my Wall, that I might have room to ſee an Enemy, and they might have no ſhelter from the young Trees, if they attempted to approach my outer Wall.
When one approaches the nest of this species, the male exhibits the greatest anxiety respecting its safety, passes and repasses, fluttering and snapping its bill within a few feet, as if determined to repel the intruder.
Mr. Brownlow adopted Oliver as his own son, and removing with him and the old housekeeper to within a mile of the parsonage house, where his dear friends resided, he gratified the only remaining wish of Oliver's warm and earnest heart, and thus linked together a little society, whose condition approached as nearly to one of perfect happiness as can ever be known in this changing world.
The secular cooling that must some day overtake our planet has already gone far indeed with our neighbour [Mars]. Its physical condition is still largely a mystery, but we know now that even in its equatorial region the mid-day temperature barely approaches that of our coldest winter.
If a variable takes on successively a series of values that approach nearer and nearer to a constant value in such a manner that [Footnote: To be read the numerical value of the difference betweenand] becomes and remains less than any assigned arbitrarily small positive quantity, then is said to approach the limit , or to converge to the limit . Symbolically this is written .
(transitive) To bring (something) near something else; to cause (something) to draw near.
1987, Dinesh Vaghela, “Publisher’s Note”, in Uppaluri Gopala Krishnamurti, edited by Terry Newland, Mind is a Myth: Disquieting Conversations with the Man Called U. G., Vallabhvidyanagar, Gujarat: Crest Associates, →OCLC, page 7:
"Why bother publishing my conversations. It has not helped you, and it is not going to help anybody else", said U. G. when I approached him with the idea of publishing excerpts from his conversations with the constant stream of people who go to visit him.
Regarding the use of sense 5 (“to come near to (someone or something) in place, time, character, or value”) in discussing convergence in mathematical analysis, modern rigorous formulations avoid using the words approach and converge. However, the terms are used informally when rigour is not required.
From Middle Englishapproche(“approach, arrival”), from approchen, aprochen(“to come or go near, approach; to adjoin, be close by; to enter (someone’s) presence; to be or become involved; to reach (a certain state); to arrive; to befall, happen to; to become similar to, resemble; to be a match for (someone)”); see etymology 1.
Theſe Things, and the Approach of Night, called us off, or elſe, as Friday would have had us, we ſhould certainly have taken the Skin of this monſtrous Creature off, which was worth ſaving; but we had near three Leagues to go, and our Guide haſten'd us; ſo we left him, and went forward on our Journey.
The approach of summer, says our Lord, is not more surely indicated by the first appearances of spring, than the final destruction of the wicked by the beginnings of vengeance on this impenitent people.
There is quite a concert of noises: the great bull-dog, chained against the stables, is thrown into furious exasperation by the unwary approach of a cock too near the mouth of his kennel, and sends forth a thundering bark, which is answered by two fox-hounds shut up in the opposite cow-house; […]
1859 May 10, Richard Owen, “Appendix B. On the Orang, Chimpanzee, and Gorilla, with Reference to the ‘Transmutation of Species.’”, in On the Classification and Geographical Distribution of the Mammalia,[…], London: John W[illiam] Parker and Son,[…], →OCLC, page 85:
The canine, judging from the figures published by M. [Édouard] Lartet, seems to be less developed than in the male chimpanzees, gorillas and orang. In which character the fossil, if it belonged to a male, makes a nearer approach to the human type; but it is one which many of the inferior monkeys also exhibit, and is by no means to be trusted as significant of true affinity, supposing even the sex of the fossil to be known as being male.
[…] he ſaw As of the ſun or moon illuming clear The palace of Phæacia's mighty King. […] Maſtiffs, in gold and ſilver, lined the approach On either ſide, by art celeſtial framed Of Vulcan, guardian of Alcinoüs gate For ever, unobnoxious to decay.
1900, A[lfred] T[hayer] Mahan, “The Opening Campaign in Natal to the Investment of Ladysmith (October 11–November 2)”, in The War in South Africa: A Narrative of the Anglo-Boer War from the Beginning of Hostilities to the Fall of Pretoria, New York, N.Y.: Peter Fenelon Collier & Son, →OCLC, page 31, column 2:
It was, therefore, natural to expect that the main attack would come from the north along the railroad, and from the east, where the approach from the Transvaal boundary, which is there marked by the Buffalo River, is over a country much more practicable than the western mountain range.
1980 May 2, “In the Matter of Amendment of Section 64.702 of the Commission’s Rules and Regulations (Second Computer Inquiry): Final Decision”, in Federal Communications Commission Reports: Decisions and Reports of the Federal Communications Commission of the United States (Docket no. 20828; FCC 80-189), volume 76 (2nd Series), Washington, D.C., published 1982, →OCLC, section IV (Comments), paragraph 41, page 402:
Our proposed definitional approach to the data processing-communications dilemma evoked considerable discussion. There is uniform disagreement and confusion as to the regulatory implications of the proposed definitional terms.
The functional approach [to separation of powers issues] emphasizes the core functions of each branch and asks whether the challenged action threatens the essential attributes of the legislative, executive, or judicial function or functions. Under this approach, there is considerable flexibility in the moving branch, usually Congress acting to make structural or institutional change, if there is little significant risk of impairment of a core function or in the case of such a risk if there is a compelling reason for the action.
Nor, though placed amongst a ruthless crew and every hour passed by ruthless hands, and through the livelong nights shrouded with thick darkness which might cover any pilfering approach, nevertheless every sunrise found the doubloon where the sunset left it last.