“It is by presence of mind in untried emergencies that the native metal of a man is tested.”

Dijkstra (1969) J.N. Buxton and B. Randell, eds, Software Engineering Techniques, April 1970, p. 16. Report on a conference sponsored by the NATO Science Committee, Rome, Italy, 27–31 October 1969. http://homepages.cs.ncl.ac.uk/brian.randell/NATO/nato1969.PDF Possibly the earliest documented use of the famous quote.
1960s

Introductory Lecture on Experimental Physics held at Cambridge in October 1871, re-edited by W. D. Niven (2003) in Volume 2 of The Scientific Papers of James Clerk Maxwell, Courier Dover Publications, p. 241; this has sometimes been misquoted in a way which considerably alters its intent: "in a few years, all the great physical constants will have been approximately estimated, and … the only occupation which will then be left to the men of science will be to carry these measurement to another place of decimals."
Context: This characteristic of modern experiments — that they consist principally of measurements — is so prominent, that the opinion seems to have got abroad, that in a few years all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry on these measurements to another place of decimals. If this is really the state of things to which we are approaching, our Laboratory may perhaps become celebrated as a place of conscientious labour and consummate skill, but it will be out of place in the University, and ought rather to be classed with the other great workshops of our country, where equal ability is directed to more useful ends.
But we have no right to think thus of the unsearchable riches of creation, or of the untried fertility of those fresh minds into which these riches will continue to be poured. It may possibly be true that, in some of those fields of discovery which lie open to such rough observations as can be made without artificial methods, the great explorers of former times have appropriated most of what is valuable, and that the gleanings which remain are sought after, rather for their abstruseness, than for their intrinsic worth. But the history of science shews that even during the phase of her progress in which she devotes herself to improving the accuracy of the numerical measurement of quantities with which she has long been familiar, she is preparing the materials for the subjugation of the new regions, which would have remained unknown if she had been contented with the rough methods of her early pioneers. I might bring forward instances gathered from every branch of science, shewing how the labour of careful measurement has been rewarded by the discovery of new fields of research, and by the development of new scientific ideas. But the history of the science of terrestrial magnetism affords us a sufficient example of what may be done by experiments in concert, such as we hope some day to perform in our Laboratory.

Ayala's Angel (1881), Ch. 41

Dijkstra (1970) " Notes On Structured Programming http://www.cs.utexas.edu/users/EWD/ewd02xx/EWD249.PDF" (EWD249), Section 3 ("On The Reliability of Mechanisms"), corollary at the end.
1970s
Variant: Program testing can be a very effective way to show the presence of bugs, but it is hopelessly inadequate for showing their absence.

Asked of a driving instructor in Scotland, as quoted in "Long line of princely gaffes" http://news.bbc.co.uk/1/hi/uk/1848553.stm, BBC News (1 March 2002)
2000s

Napoleon : In His Own Words (1916)

Part 1.3 Rights of Man
1790s, Rights of Man, Part I (1791)

Source: Island Beneath the Sea

Introduction
Bards of the Bible, 1850