In the summer of 1504, one commission pitted two titans of the Italian Renaissance against each other. On a single wall of Florence’s Great Council Chamber, inside what is now the Palazzo Vecchio, Leonardo da Vinci and Michelangelo were set to work cheek by jowl, both painting battle scenes nearly 60 feet wide.

The two men were natives of Florence who had recently returned to their home city, Leonardo from Milan and Michelangelo from Rome. Leonardo was the elder statesman. A genial and urbane painter and scientist, aged 52, he possessed a large following of friends and students, as well as a reputation for wearing flamboyant satin gowns and velvet capes. A contemporary doctor named Paolo Giovio said he was “by nature affable, sparkling, generous, with an extraordinarily beautiful face.” Michelangelo was the young pretender. A petulant sculptor and poet, aged 29, he had a crooked nose and a reputation for living in solitary squalor, rarely removing his dogskin shoes. “Rough and uncouth” is how Giovio described him.

The Virgin and Child with the Infant Saint John (The “Taddei Tondo”), by Michelangelo, circa 1504–5.

Leonardo had been working for months on the designs for his Battle of Anghiari, a whirling mêlée of horsemen mid-combat, when Florence’s ruling gonfaloniere, Piero Soderini, decided to turn the assignment into a contest. Right next to Leonardo’s wall space, he tasked Michelangelo with the Battle of Cascina, a depiction of half-naked soldiers who are ambushed while bathing. It would be the battle of the Battles.

But neither work was ever realized. Leonardo attempted to use oils, which failed to stick to the wall; he eventually gave up and returned to Milan. Michelangelo did even less, departing for Rome at the request of Pope Julius II without ever having put brush to plaster.

Fortunately for the curators of “Michelangelo, Leonardo, Raphael”—which opens at London’s Royal Academy next Saturday—both murals can be imagined from surviving preparatory sketches and fragmentary copies of each artist’s full-size design, or “cartoon.” The works the Royal Academy has managed to assemble, largely from the collections of the British Museum, Oxford University, and King Charles, make one thing clear: had the artists finished, these would have been masterpieces.

The Virgin and Child with Saint Anne and the Infant Saint John the Baptist (“The Burlington House Cartoon”), by Leonardo, circa 1506–8.

The idea for an exhibition with a laser-tight focus on the events of one febrile year in Florence, says co-curator Per Rumberg, stemmed from Michelangelo’s Taddei Tondo, a circular marble relief of the Madonna and Child in the R.A.’s own collection, which was left unfinished when the artist discovered a crack in the stone. It too was begun in 1504—at the same time the toiling artist was putting the finishing touches on his triumphant David. In January of that year, Leonardo, who had just started the Mona Lisa, sat on a committee charged with deciding the placement of the behemoth nude sculpture. His suggestion? Tuck it away in an inconspicuous location among some tapestries and add a leaf for modesty.

In late 1504, another genius arrived in the city—the 21-year-old Raphael, who, according to Giorgio Vasari, seized a chance to see the battle cartoons in the flesh. The exhibition explores his impressions of the elder artists’ work, including his Bridgewater Madonna (circa 1507–8), on loan from the National Galleries of Scotland, which is indebted to Michelangelo’s tondo.

Raphael’s Virgin and Child with the Young Saint John the Baptist (“The Esterhazy Madonna”), circa 1508.

Just four years later, Michelangelo and Raphael would enter into their own, equally fierce rivalry, further inflamed when Julius II commissioned Michelangelo to decorate the Sistine Chapel ceiling and Raphael to paint, mere yards away, a suite of frescoes for the papal apartments. “What he knew of art,” a surly Michelangelo declared following Raphael’s tragic death, in 1520, “he learned from me.” Arguably true.

“Michelangelo, Leonardo, Raphael” will be on view at the Royal Academy, in London, from November 9, 2024, to February 16, 2025

Harry Seymour is a London-based art historian and writer