“There is nothing in this world that does not have a decisive moment,” wrote the 17th-century cleric and memoirist Cardinal de Retz, “and the masterpiece of good ruling is to know and seize this moment.”

Today, the idea of the decisive moment is synonymous with a certain kind of photography, exemplified by the great European master Henri Cartier-Bresson. He used the phrase as the title of his – and European photography’s – most famous book, published in America in 1952. (The simultaneous French edition was, intriguingly, called Images a la Sauvette – Images on the Run.)

Now, having long been out of print and beyond the financial reach of all but the most serious collectors (a French first edition will set you back £2,750) The Decisive Moment has finally been republished. Sixty-two years on, it still carries the weight of its initial importance – even if the notion of the decisive moment no longer holds sway as it once did; staged photography, conceptual strategies and digitally manipulated images have all but rendered it old-fashioned except to purists, photojournalists and street photographers.

That The Decisive Moment belongs to a different time is immediately apparent from its cover, which is not a photograph but a signature cut-out by Henri Matisse, who offered to design the cover when Cartier-Bresson showed him a dummy copy. (The cultivated Cartier-Bresson was also friends with Jean Cocteau and Joan Miró, who designed the cover for his book The Europeans three years later.)

Extraordinarily, given that he had taken up photography seriously in the early 1930s, The Decisive Moment was Cartier-Bresson’s first self-conceived and edited book – 1947’s The Photographs of Henri Cartier-Bresson was a catalogue for an exhibition at the Museum of Modern Art in New York.

Having co-founded the now-famous Magnum photo agency in 1947 with Robert Capa and David “Chim” Seymour, Cartier-Bresson had travelled widely on assignments, most productively to India and China, by the time it was published. He was also more aware of the value of his extensive archive, which he meticulously trawled to select the 126 images included in the book.

It is divided into two chronological and geographical sections: the first spans the years 1932 to 1947 and is made up of photographs taken in the west; the second spans 1947 to 1952 and was shot mostly in the east. Today, a photographer is more likely to make the move from photojournalism into art (not least because that’s where the big money lies), but Cartier-Bresson took the opposite tack. As the curator Clément Chéroux points out in his essay for the new edition, the pre-Magnum Cartier-Bresson was obsessed with form, and creating his now signature style. Post-Magnum – and post second world war – he was driven to make images that mattered more in terms of their social and political rather than aesthetic import.

What The Decisive Moment did above all was enshrine the term in the collective photographic consciousness, shaping several ensuing generations of photographers. What Cartier-Bresson understood by the decisive moment is best explained by the famous quote from his lengthy introduction to the book: “Photography is the simultaneous recognition, in a fraction of a second, of the significance of an event as well as of a precise organisation of forms which give that event its proper expression.”

France. Paris. Place de l’Europe. Gare Saint Lazare. 1932. Photograph: Henri Cartier-Bresson/Magnum Photos

Cartier-Bresson always emphasised the importance of composition, and liked to “instinctively fix a geometric pattern” into which a chosen subject fitted. The idea that he lay in wait for someone to walk into a precomposed frame may explain his extraordinary hit rate – but it runs contrary to the French title, Images on the Run, which suggests exactly the opposite.

The decisive moment has come to mean the perfect second to press the shutter. In this context, it might be better applied to, say, Garry Winogrand or Joel Meyerowitz, photographers who pounded the streets in search of the right convergence of light, action and expression rather than patterns and geometry.

In a thought-provoking essay in the London Review of Books last year, Gaby Wood wrote, “The reason his photographs often feel numbly impersonal now is not just that they are familiar. It’s that they’re so coolly composed, so infernally correct that there’s nothing raw about them, and you find yourself thinking: would it not be more interesting if his moments were a little less decisive?” Perhaps, but then he would not be the Cartier-Bresson we know – and his influence would not have been so widespread. Wood’s impatience may also be concerned with that lingering influence. Cartier-Bresson continues to cast a long shadow in the public, if not the contemporary photographic, consciousness. I would go so far as to say that, for many people with a passing interest in photography, he almost single-handedly represents photography: what it is meant to do and – more problematically for a generation of younger artists relentlessly questioning its meaning in an over-mediated world – what it is.

For me, what is interesting about the republishing of The Decisive Moment is that it has happened too late. The book is now a historical artefact. It cements an idea of photography that is no longer current but continues to exist as an unquestioned yardstick in the public eye: black and white, acutely observational, meticulously composed, charming. Colour and conceptualism may as well not have happened, so enduring is this model of photography outside the world of contemporary photography itself.

That Cartier-Bresson is historically important is not in question: he was a master, if not the master as his champions insist. But The Decisive Moment, despite its beauty and excellence, belongs to another photographic time in a way that, say, Robert Frank’s The Americans or even William Eggleston’s Guide does not. Whereas Cartier-Bresson confirmed the traditional with his painterly eye, Frank and Eggleston signalled the future, their photographs informed by some deeper, darker narratives guided by their outsiders’ eyes. From where we are now standing – and looking – these are the decisive moments in 20th-century photography, their iconoclastic ways of seeing and shaping photography as we now understand it. Can we really say that about The Decisive Moment?