We’ll never have Paris here in New York. But we could have . . . if not for Aaron Burr.

The Manhattan we know today is laid out on a great rectilinear street grid conjured up two centuries ago: hundreds of parallel streets crossed at right angles by a dozen or so parallel avenues. Many grid users love its predictability, its rational, orderly power. Essayist Phillip Lopate calls the grid “a thing impossible to overpraise.”

The grid inspired Mondrian, thrilled Corbusier, and architect Rem Koolhaas pronounced it “the most courageous act of prediction in Western civilization.”

Others see a dull, repetitive, unbeautiful, un-green, congestion-inducing act. Columbia’s Peter Marcuse: “one of the worst city plans of any major city in the developed countries of the world.”

Edgar Allan Poe was horrified: “In some thirty years every noble cliff will be a pier, and the whole island will be densely desecrated by buildings of brick, with portentous facades of brown-stone.” That was in 1844, when the grid plan had been reducing naturalistically varied Manhattan to a right-angled flatland.

But it would not have been that way if Joseph Francois Mangin had gotten his way.

In 1797, Mangin, a French-born surveyor-architect and protégé of Alexander Hamilton, got a contract (with a partner, Casimir Goerck, who soon died) from the city to make its first accurate map since the Revolution. New York then was a haphazard town of 60,000 people packed south of Chambers Street on mostly Colonial-era streets.

When another surveyor asked to have a look at Mangin’s progress, Mangin refused, with the incredible assertion that he was making “not the plan of the City such as it is, but such as it is to be.”

That wasn’t what Mangin had been hired to do. Nevertheless, when he presented his map — six feet square, handsomely engraved — to the city government in February 1803, it was immediately and officially considered “the New Map of this City.”

Mangin’s map — formally, the Mangin-Goerck plan — did two remarkable things. In the settled part of the city, Mangin straightened and widened streets and envisioned new ones on river landfill. Out in the country, up to what today is about 22nd Street, Mangin laid out a pastiche of grids, of varying densities, at acute angles to each other, sensitive to natural contours.

In the irregular meetings of the grid segments were countless opportunities for small parks, prominent buildings or other urban display and public space. It was a layered picture of order and ornament, urban function and natural form: the complexity and grace of a European capital adapted to the limits of a narrow island. It was, one might say, beautiful.

And it was not to be.

In late 1802, Mangin (with a partner) had won the design competition for what is our now landmark City Hall. Mangin was not supposed to win. English-born, Philadelphia-based and future “Father of American Architecture” Benjamin Latrobe was. His competition sponsor had guaranteed it. His sponsor was the dominant force in city politics and the nation’s vice president, Aaron Burr.

Mangin’s design was better, but Latrobe was furious, and Burr was vengeful. Conveniently, the city’s top (and only) street official was one Joseph Browne, recently appointed through the influence of Burr. Oh, and Browne was Burr’s brother-in-law and willing partner in a lifetime of schemes. By November 1803, after relentless trashing by Browne, Mangin’s “New Map of this City” was the discarded map of the future city.

Then, wistful, the city government realized that having a plan for the future was actually a good idea. A three-person commission was appointed in 1807, dominated by cranky Founding Father Gouverneur Morris, owner of the vast country estate that is now the Morrisania section of The Bronx. Morris was a practical man, who wanted “Convenience and Utility,” without “supposed Improvements by Circles, Ovals, and Stars.”

Morris got exactly what he wanted: “A City . . . to be composed principally of . . . strait sided and right-angled Houses [that] are the most cheap to build and the most convenient to live in.”

Adapted from “City on a Grid: How New York became New York” by Gerard Koeppel. Reprinted courtesy of Da Capo Press. Koeppel will appear at 6:30 p.m. Tuesday at the Museum of the City of New York for a Q&A and book signing.