“Botticelli’s Secret” isn’t really about a secret. To prove the point, I’ll spoil it right away. The Florentine painter illustrated a Florentine poet’s poem, a project that went into political and cultural eclipse for centuries until sharp-eyed connoisseurs spotted it through the clouds of a shifting zeitgeist. If there is no secret, there is something more interesting; a fraternity of genius that stretched across centuries and hustled across piazzas.

At the heart of Joseph Luzzi’s story are Sandro Botticcelli’s illustrations of nearly every one of the 100 cantos that make up Dante Alighieri’s “Commedia.” The charm of “Secret,” however, is not so much those drawings — we get reproductions of just a few, and sparing analysis of method — as their utility as a pretext to gain temporary Florentine citizenship between its covers. This is art history for the many via focus on the inspired few.   

Dante, who lived two centuries before Botticcelli, was already Florence’s poet by the time the painter was commissioned to illustrate him by a relative of the Medicis, the ruling banking family that Mr. Luzzi calls “the Kennedys of Renaissance Italy.” Dante was not always thus revered, and Mr. Luzzi is adroit at charting the uncertain course of his early fame, where Giovani Boccaccio and Francesco Petrarch contended over his legacy. 

Botticelli was master at combining aesthetic splendor with commercial acumen. He was both an auteur and a savvy businessman. His “The Birth of Venus” and “Primavera” still draw throngs to the Uffizi Gallery. At the same time,  Mr. Luzzi sees in his “Adoration of the Magi,” no mean feat, the “nexus of money, power, and influence that the Medici family had come to exercise over both Florence and Botticelli’s burgeoning career.” 

Mr. Luzzi gives attention to the way art was made, sketching how Florence’s botteghe, or “workshops,” comprised a network of training, apprenticeship, and labor. He notes that “by the late fifteenth century, Florence had more woodcarvers than butchers, suggesting that creating beautiful objects was considered as essential as eating meat.” Hungry for commissions and trained from youth, the men who would become Old Masters were first handy artisans.

The notion of a unified Italy was still nearly half a millennia away when Dante began writing — radically, in his native Tuscan dialect — and Mr. Luzzi is attuned to the terroir of art. Florence was founded as a remote military camp by Julius Caesar, and as Mr. Luzzi puts it, “its collective gaze was always turned inward.” Dante would prende ‘l cappelo, or seize the poet’s crown, but only after exile from Florence would make him macro, or lean.

Mr. Luzzi is a fair appraiser of Botticelli’s achievement, observing his “beauty, grace, and purity of line” and how his sustained success made him into a “brand,” with even his (relatively) mediocre work fetching heaps of ducats. He’s also alert to when the painter coasts, noting that Botticcelli “seemed to lose interest in quality control, leaving his unevenly talented assistants with major responsibilities.” His star was hitched to the Medicis, and tracked their fortunes. 

Botticcelli himself is a bit of a cipher off the canvas. He was adept at meeting the “stone-cold criteria of a patron’s demands,” but left not a single written word, a stark contrast with Michelaneglo’s poetry and Leonardo da Vinci’s prolix notebooks scribbled in reverse script. He never married and had no children, leading Mr. Luzzi to surmise it “likely” that he was a “closeted gay man.” His posthumous reputation fluctuated vertiginously. 

Only one of Botticcelli’s Dante illustrations was illustrated, the “Map of Hell,” an exercise in satanic cartography. “Secrets” is a map, too, not of the netherworld but of the drawings’ fate. En route we meet the likes of John Ruskin and Walter Pater, who did much to make the case for both Dante and Botticelli in 19th century England. Jacob Burkhardt’s “The Civilization of the Renaissance in Italy” gets its due. Botticelli enjoyed talented advocates.

Turning to the 20th century, Mr. Luzzi focuses on the efforts of Bernard Berenson, a Jewish immigrant of Lithuanian extraction who studied at Harvard and went on to build a career as an impresario of Renaissance art, authenticating works — not always with perfect precision — and then selling them to Boston Brahmins. Botticelli’s “Story of Lucretia” hangs in the Isabella Stewart Gardner Museum on his account. Sometimes, there is accounting for taste.