“Art Deco” was not coined until 1968, when the art historian Bevis Hillier used the term in his book “Art Deco of the 20s and 30s.” In those times, you might have heard such terms as “le style moderne,” or “la mode 1925.” The latter refers to the Exposition Internationale des Arts Décoratifs et Industriels Modernes that took place in Paris in 1925. (It was also from the name of this exposition that Hillier derived “Art Deco.”) Le style moderne was not entirely new in 1925. It had begun to emerge just after World War I, when the French luxury-goods industries sought for novel ways to shake off the wartime torpor. In this, they were abetted by their government, which did not want to see the French lose their prestige in the decorative arts.

“Art Deco Design: Rhythm and Verve” is a small but stimulating exhibition at the New York Public Library’s Humanities and Social Sciences Library. The show mainly comprises works on paper drawn from the library’s collections.

Before 1914, the French were a leading force in Art Nouveau. Hector Guimard, René Lalique, and Emile Gallé defined a certain Gallic glamour. After the war, designers felt that Art Nouveau, and the Belle Époque to which the style gave expression, was played out. And yet Art Deco did not reject earlier styles. A wall text in the show says that Art Deco designers sometimes took Art Nouveau floral forms and filtered them through Cubism.

In addition to the organic relationship of Art Nouveau and Art Deco, ideas the show stresses are Art Deco’s attempt not to fall into the expensive-handicraft trap that doomed Art Nouveau as a mass style, Art Deco’s emphasis upon rendering motion and speed, and how the movement went from being an expression of the Jazz Age to being an expression of the Machine Age.

The show features outstanding examples of pochoir. Pochoir, the French word for stencil, refers to an elaborate process of stencil-coloring prints. The French took up pochoir in a big way in the 19th century, but the art reached its height in the 1920s, when designers used gouache in place of the thinner watercolors used previously. Pochoir achieved dramatic effects of layering and vibrant color.

While works by many artists and designers are on display — including Sonia Delaunay and John Held Jr. — the hero of the show is Eugène Alain Séguy (1889-1985), who used pochoir to breathtaking effect in textile designs and entomological illustrations. In the latter, Séguy’s pochoir produces images of beetles and butterflies that are stunningly accurate, yet also possesses a stylized quality. Séguy’s beetles come from his 1928 book “Insectes,” the butterflies from that year’s “Papillons.” These aren’t exactly obscure images — Séguy was one of the great French graphic artists of the era. But something about the installation makes these entomological images jump out at the viewer — you nearly gasp. The beetles — tan and black, green and black, or orange, green, and black — are rendered with brilliant anatomical precision. Their power derives in part from Séguy’s choice to show five on a page — not lined up in taxonomic style, but all as though crawling off in different directions. They convey determined motion. At the same time, Séguy ingeniously intertwines their antennae to yoke them together in a unified image.

The show also presents beautiful floral pochoirs and textile designs by Séguy. Sonia Delaunay pochoirs prefigure Matisse’s later “Jazz” cutouts, while Matisse himself shows up with a “Danse” color lithograph — red dancers on a green and black background — from the January-March 1939 issue of Verve, the magazine from whence the show gets half its subtitle. I thought, based on that title, that the show would include more of Verve than it does. The French magazine began in 1937, and lasted until 1960, during that time publishing many of the major Modernist artists and writers. Verve began just as Art Deco ran into a war, as Art Nouveau had done. After the war, a different “style moderne,” based on the German Bauhaus and other sources, came to dominate in many areas of design. Art Deco became, for a time, as unfashionable as Victoriana.

The show includes a vase, wallpaper, prints, drawings, and more, including a superb “Binding for Illustrated Book” by Pierre-Émile Legrain (1889-1929), the outstanding French bookbinder of the 1920s. Here is his binding — brown crushed levant morocco with gilt and silver tooling in swirling lines — from 1925 for Paul Valéry’s “La jeune Parque.”

The show is in the lovely Wachenheim Gallery on the first floor, a small and beautifully ornamented room. Looking at its richly veined marble walls and at its bronze ornamentation — mainly floral forms, heavily stylized, often swirling, as if in motion — made me think that the show should have worked these into the story. Like Carrère & Hastings, who designed the library, the designers of Art Deco often were products of the Ecole des Beaux-Arts. The Classical generation that preceded the Art Deco generation had already assimilated some of the spirit that was to inform the later art, as this very room makes manifest.

Be that as it may, the lover of modern decorative arts won’t go wrong with “Art Deco Design.”

Until January 11 (Fifth Avenue at 42nd Street).