Prick hundreds of contemporary paintings and the air goes out of them. Prick a fine botanical and it bleeds.

Its lifeblood flows from an obligation to be both true and beautiful, a transcendent unit. This dual nature of botanical art — scientific in purpose, aesthetic in conception and execution — is on stunning display in the gallery of the LuEsther T. Mertz Library at the New York Botanical Garden.

“Paradise in Print” showcases 500 years of Caribbean history and culture through beautifully printed folio editions, rare books, and original watercolors from the library’s own archival treasury. The sheer wealth of information conveyed, together with the splendor of the roughly 65 individual plates, maps, and frontispieces, testifies to the crucial function of art in the history of medicine, agriculture, and exploration.

This exhibition clarifies, as succinctly as possible, the centrality of horticulture in the shared human project we call civilization. Man has been moving plants around since he first found a way to travel. Many of what are considered indigenous Caribbean crops were brought by the Europeans from Asia and the Pacific: bananas, lemons, mangoes, pomegranates, coconuts, coffee, sweet oranges, and sugarcane.

Others, such as chocolate, pineapple, avocado, and tobacco, were carried throughout the pre-Columbian Americas by seafaring native peoples. (In other words, man has been “erasing the ecological and cultural contexts” of plants long before Big Botany provided a target for anti-colonial academics.)

We know what Marlon Brando looked like as Fletcher Christian, a mutineer on board H.M.S. Bounty. But who recognizes a breadfruit, the plant at the heart of the 1786 mutiny? Who knows that Captain Bligh was not the tyrant Hollywood made of him?

The exhibition defends the “true character and brilliance” of the 32-year-old Captain Bligh, commissioned to bring food-producing breadfruit trees from Tahiti to counter hunger on West Indian plantations. On view is a 1792 edition of Bligh’s published account of the failed voyage, open to an engraved plan of the transport section of the Bounty, outfitted to carry and irrigate the 11,015 potted saplings lost in the mutiny.

Next to it is an elephant folio with a colored stipple engraving of the green breadfruit. Life-size, skin roughened by carpels, and still attached to a branch, the round fruit dominates the design. Two elongated, tawny seed pods provide chromatic balance and compositional movement, pulling the image up and across the page. One pod splits open, the drama of plant birth providing both narrative pleasure and botanical data.

Of all the lovely images on display, Étienne Denisse’s Caribbean fruits offer a benchmark for excellence in plant portraiture. Their robust exuberance commands the room, challenging all but the single Redouté. His chromolithograph of a flowering banana plant unfurls with baroque intensity, with color pushed to naturalism’s limits. The weight of the fruit, drawn in the field from life, is substantial. His passion flower, named for the wounds of Christ, has a tangible density. The faceted skin of a cherimoya, or custard apple, prickles the hand.

Denisse (active 1814–57) was the lithographer for the French royal court, working in the gardens of Paris’s natural history museum. He also lived in the Caribbean for 20 years, recording species and sending samples home to France. His work underscores the affinity of botanical art with figure drawing: The movement and stresses of the living plant, like those of the human body, are conveyed by drawing in inimitable ways. His renderings achieve not an ideal, but rather the palpable presence of an individual item of natural history.

Few New Yorkers know of their Botanical Garden’s long history in the Caribbean. Nathaniel and Elizabeth Britton, founders of the Garden, made their first trip to Puerto Rico in 1906. Over the next 27 years, they organized 16 expeditions to the island that yielded a total of 10, 139 specimens. They collaborated with naturalist Frances Worth Horne (1873–1967), a resident of Puerto Rico, who donated her collection of 750 watercolors of the island’s flowing plants to the Botanical Gardens four years before she died.

Twelve of Horne’e paintings comprise “Flora Borinquena,” the second of the exhibition’s nine sections. Cuba, with the region’s highest number of indigenous flowering plants — the majority of them not found anywhere else on earth — is represented by the fragile enchantments of American botanist Francisco Sauvalle (1807–79).

Throughout the 18th and into the 19th century, faith in art’s power to convey truths of the natural world was at its highest. The longer you look at these botanicals, the more enraptured you become by the generosity with which botanists and artists sought to understand and inhabit their subjects.

That phrase “botanical illustration” slights the expressive vitality at the heart of a tradition that dates from late antiquity and continues still. The quality of botanical art is judged on classical norms: on structural clarity and veracity of form, on an articulate treatment of space, on the harmonizing of larger and smaller elements into a larger rhythm. Precise scientific observation is raised to living art by the artist’s innate sense of design and original response to what is typical about each individual plant.

John Ruskin once lamented the waste of “exquisite original drawings and sketches of great botanists, now lying in inaccessible cupboards.” Not so with the Botanical Garden, 20 minutes out of Grand Central Terminal on Metro North Railroad.

Until August 19 (Bronx River Parkway and Fordham Road in the Bronx, 718-817-8700).