In the basement of the Biblioteca Ambrosiana, in Milan, a conservator named Vito Milo had just applied a small gel strip to the edge of a 500-year-old drawing in order to dissolve the glue that joined it to a larger paper frame. Now, with a scalpel, he worked loose a few millimeters of the drawing. I asked Milo what was in the gel, and after he rattled off a list of ingredients in Italian, I offered a layman’s rough translation: “special sauce.” He smiled and nodded. “Si, special sauce.”

The drawing was a page from Leonardo da Vinci’s Codex Atlanticus, and I had been invited to witness the painstaking process of its conservation. One morning last winter, I descended to the conservators’ laboratory, which occupies a room just outside the steel-and-glass doorway to the Ambrosiana’s gleaming vault. At the bottom of the stairs, I was stopped by an attendant, who took a coffee cup from my hands and placed it out of harm’s way.

The Codex Atlanticus is a 1,119-page collection of da Vinci’s engineering designs and technological dreams—for flying machines, weapons of war, hydraulic devices—along with line after line of commentary in a small, precise hand. It is the largest collection of works by da Vinci in the world. The folio pages, once bound into a single volume, are now preserved as individual sheets. The one Milo was bent over—folio 855 recto, with its design for a parabolic swing bridge—rested on the glass of an LED light box. Da Vinci’s brown ink stood out sharply against a glowing background. Looking closely, inches from the page, I could make out the suggestion of a little man on horseback atop the bridge, rendered in a few flicks—a playful addition for scale.

I was reminded of this visit to the Ambrosiana when I saw the announcement of a da Vinci exhibition, “Imagining the Future,” at the Martin Luther King Jr. Memorial Library, in Washington, D.C. Twelve original folios from the Codex Atlanticus have just gone on display—the first time any of the Codex pages have traveled to the United States. The show, which runs through August 20, has understandably gotten attention: Everyone knows what “da Vinci” signifies—his name recognition is universal.

“Ambrosiana,” of course, is another story.

The Biblioteca Ambrosiana (Piero Cruciatti / Anadolu Agency / Getty)

The Biblioteca Ambrosiana is one of the world’s least-known great museums—to the public, at any rate, if not to scholars. It occupies a handsome 400-year-old building, just a few blocks from Milan’s famous cathedral, but receives only about 180,000 visitors a year. The Vatican Museums, in Rome, welcome that number every week. The Ambrosiana was founded in 1607 by Cardinal Federico Borromeo, the archbishop of Milan, who named it after the city’s patron, St. Ambrose, and endowed it with his own extensive collection of books, manuscripts, and works of art.

The paintings owned by the Ambrosiana are small in number but choice in quality: Botticelli, Caravaggio, Titian, Bruegel, and da Vinci himself. The newly restored preliminary cartoon done by Raphael before he painted The School of Athens—nine feet high and 26 feet long—takes up an entire wall of one gallery. A monumental study in charcoal and lead-white on gray paper, it is emotionally more vivid than the finished fresco. In other galleries, odd relics are preserved behind glass: a lock of hair from Lucrezia Borgia; the gloves worn by Napoleon as he watched his army fall to the Duke of Wellington’s, in 1815.

The books and manuscripts come from all over the world: Borromeo’s collecting sensibility was cultural and cosmopolitan, not religious or provincial. The Ambrosiana opened its doors to anyone who could read and write—one of the first libraries in Europe to do so. It did not chain books in place, as other repositories did, preferring a different kind of security: The penalty for theft, spelled out on a marble plaque that can still be seen, was excommunication.

Over the years, the collection has been augmented, notably by the acquisition of the Codex Atlanticus, in 1637. Da Vinci had died more than a century earlier, leaving his drawings and notes to one of his students. Many of these folio pages were later gathered and bound by the late-Renaissance sculptor Pompeo Leoni into a volume whose dimensions gave the Codex its name. (Atlanticus refers to a large paper size used for atlases.) The Codex then followed a picaresque path into the hands of a Milanese nobleman, who bequeathed it to the Ambrosiana.

The folio pages, which span a 40-year period of da Vinci’s work, are covered not only with sketches and schemata but also with da Vinci’s singular “mirror writing”—he was left-handed, and wrote from right to left. Not all of the exposition is technical. In one place, da Vinci scribbled some words of reminder to buy charcoal, for drawing. The Codex Atlanticus contains his last known dated note, from 1518: “On the 24th of June, the day of Saint John, in Amboise in the Palace of Cloux.” Da Vinci died in Amboise the following year, at age 67.

The most traumatic event in the Ambrosiana’s life was the arrival of Napoleon. He crossed the Alps in 1796, and as he made his way down the Italian peninsula, he sent wagonloads of plunder back to Paris. The hundreds of paintings and statues taken from Italy—Laöcoon and His Sons, from Rome; Venus de’ Medici, from Florence; the bronze horses atop St. Mark’s, from Venice—would by themselves constitute a world-class museum. In fact, they did: the Louvre. Napoleon took books and manuscripts too. Much of the Vatican archives made its way north. So did the Codex Atlanticus.

After Napoleon’s defeat, the plundered treasures of Europe were supposed to be returned to their places of origin. Some were; some weren’t. The Vatican couldn’t afford to cart back all of its archives; many documents were sold for scrap and used in Paris to make paper or to wrap meat and cheese. France held back many items. In the end, only about half of what was lost to le spoliazioni napoleoniche—“the Napoleonic looting”—was actually returned. The Codex Atlanticus was one of those items. It has been lodged safely in the Ambrosiana ever since.

Two da Vinci folios from the Codex Atlanticus (Mondadori Portfolio)

Safe from marauders, but not from everything. During the 1960s, specialists took apart the massive single volume of the Codex and reframed each of the 1,000-plus folios with a modern paper support, leaving both sides of each folio visible when necessary. When that was done, the pages were rebound into 12 smaller volumes. Then, in 2006, a conservator from the Metropolitan Museum of Art, in New York, raised an alarm. Examining the Codex, she had discovered black spots on the pages, possibly caused by mold.

An investigation began. The spotting, it turned out, was caused not by mold but mainly by mercury salts, probably in the adhesive attaching each folio to its paper support. Fortunately, the spotting hadn’t affected the da Vinci folios themselves—only the paper around them. The Codex volumes were taken apart. Each affected folio had to be detached from its old paper frame and given a new one. Henceforward, the folios would be preserved as single sheets.

Which brings the story back to Vito Milo, working outside the Ambrosiana’s vault. He wore a white lab coat and white latex gloves. His features were bottom-lit by the golden glow from the box. As he worked, he spoke about the intimacy of this connection to da Vinci: how you can see his erasures, his mistakes, the little notes he wrote to himself. It would take about a month, he said, before this particular drawing was free of its old paper support, cleaned of the old glue, and reaffixed with a new kind of adhesive to a new support. Then he would be onto the next folio.

One consequence of unbinding the Codex is that the folios could be digitized. Another is that individual sheets can travel and be displayed, making possible exhibitions such as the one now in Washington. At the Ambrosiana itself, a rotating selection of a dozen pages is now always on public view in display boxes, climate-controlled and bulletproof. The protocols are strict: To prevent deterioration brought on by natural light, a folio can be exhibited for only three months. Then it must rest in darkness for three years.

The Ambrosiana remains an ecclesiastical institution, and Alberto Rocca, the director of its picture gallery, is a Catholic priest. I met with him for an hour in a Baroque ground-floor office, its ceiling high, its bookshelves sagging. A member of the Ambrosiana’s governing College of Fellows, Rocca oversees not only the picture gallery but also a network of programs for far-flung scholars. He is trim and professional. Take off the Roman collar, and he would be at home among the staff at the Rijksmuseum or at Christie’s.

Our conversation ranged over many topics. Looking back: how unusual Borromeo’s cross-cultural outlook was at the time, and also how unusual his wish to make books freely available to the public. Looking forward: the difficulty of sustaining an institution of this kind. The Ambrosiana’s art gallery can support itself; the research library, with its 1 million books and 40,000 manuscripts, cannot. Europeans, Rocca noted, don’t have the philanthropic tradition that Americans do.

It is said that Napoleon himself walked out of the library with Petrarch’s own copy of Virgil under his arm. (It was eventually returned.) It is certainly true that some material by da Vinci did not come back, and likely never will. Rocca did not wish to dwell on history, even if Napoleon clearly had a lot to answer for. On the plus side, Rocca said, “at least we have the gloves he had when he was defeated at Waterloo.”