A section of the exhibition explores the artist’s first dated drawing, a landscape from Aug. 5, 1473, that pays witness to his fascination with nature. The original, (a copy is displayed), which belongs to the Uffizi Galleries, has been lent to the Louvre show, along with Leonardo’s Vitruvian Man — a work whose fame almost matches the Mona Lisa’s — on loan from the Accademia Galleries in Venice.

The museum focuses on Leonardo’s interests in science, architecture and engineering, and includes several models — including war and flying machines — created in 1952 for an exhibition commemorating the 500th anniversary of his birth. Other sections focus on optics, anatomy, mechanical clocks, the study of water, and geometry.

Sometime in the 1460s, Leonardo left Vinci for Florence, where his father lived. Because he was illegitimate, he could not become a notary, the family business, so he was first sent to learn math at what was known as abacus school. (Vasari wrote that Leonardo very quickly outwitted his teacher.) In his early teens he became an apprentice in the workshop of the artist and engineer Andrea del Verrocchio.

There, in the mid-1470s, Leonardo painted the figure of an angel on the far left of Verrocchio’s “Baptism of Christ.” Leonardo’s panel of “The Annunciation” for the Church of Monte Oliveto also dates to that time. Both hang in the Uffizi, next to the “Adoration of the Magi,” which Leonardo abandoned when he moved to Milan in 1482. The Uffizi declined to lend these works to the Louvre because of their fragility.

Leonardo’s first stay in Milan lasted 17 years, when the city state was ruled by Ludovico Sforza, a prince who enlisted Leonardo for various tasks in his court, including the production of elaborate pageants. A draft of an introductory letter Leonardo wrote to Ludovico is on exhibit in Milan’s Ambrosiana gallery in which he presents himself as an expert military engineer, able to design weapons that “will cause great terror to the enemy.”

He mentions his other skills, sculpture and painting, almost as an aside. He also promised to cast a bronze horse “to the immortal glory and eternal honor” of the house of Sforza. Five hundred years later, a modern version of the horse was installed at Milan’s racetrack, though some citizens would like it to be moved to a more well-trodden site.