Jan Lievens. "Forest Interior with a Draftsman," 1660s, pen and brown ink and brown wash on paper. (Katya Kallsen/Maida and George Abrams, Collection)

There are fewer then 10 surviving sketchbooks from Dutch artists working in the 17th century, which might seem surprising, given how many artists were active during this golden age, how much of what they produced strikes us as naturalistic, and how essential sketching was to the artistic process.

A new exhibition at the National Gallery of Art, “Drawing for Paintings in the Age of Rembrandt,” includes two of those books — and a host of other drawings that relate directly to paintings — that have survived. In the process, it dismantles many of our assumptions about how drawings were used during one of the most brilliant epochs of image-making.

The standard view of drawings and paintings, influenced by pop culture and ideas borrowed from other historical eras, goes like this: The artist transcribes vivid impressions directly from the real world into his or her sketchbook, and then in the studio transforms these into something more polished, ambitious and inspired. But the evidence — scattered, incomplete and sometimes frustrating — gathered in this fascinating show suggests that artists used a lot of different methods, which were both more complex and workmanlike than the combination of photographic capture and inspired transfiguration suggested by romantic ideals of making art.

Michiel van Musscher. "An Artist in His Studio with His Drawings," mid-1660s, oil on panel. (Liechtenstein; The Princely Collections, Vaduz-Vienna)

The material contained in sketchbooks often amounted to a catalogue of possibilities that could be reproduced and inserted into larger, finished artworks. One work in the show is telling: Michiel van Musscher’s “An Artist in his Studio With his Drawings,” painted in the mid-1660s, shows a young man sitting before an easel mixing paints on his palette. On the floor around him are drawings of boats, which he seems to be using as templates ready-made for insertion into his unfinished painting.

Other drawings support the idea that this was an established way of building up a painting, like inserting pre-written bits of code into a larger program. Hendrick Avercamp, an artist who specialized in winter scenes, produced drawings of individual characters — a smiling young man ice skating in elegant clothing, a young woman defending her hands against the chill by nestling them in the folds of her apron — which were inserted into multiple paintings. Two relatively finished sketches by Dirck Hals not only show male figures that would be reproduced in different paintings, but one features a man smoking a pipe that would be changed to a violin in a different iteration of the figure. It also includes different options for the placement of his legs. One can imagine a recipe-like set of unwritten instructions that might go along with this kind of sketch: If pipe, then use legs No. 1; if violin, then legs No. 2.

This suggests a rather mechanical approach to painting, which is both true and misleading. Dutch artists were entrepreneurs who produced a lot of product to meet their clients’ needs, and the use of existing drawings helped systematize and streamline that process. But painting, no matter how realistic-seeming the results, was always a highly systematized process, with a distinct division of labors that suggests something of the assembly line. According to Dutch writers, the education of an artist began not with looking at the real world, but with looking at images of it, drawings made by master artists who had already mastered the process of speaking a three-dimensional world in the language of two-dimensional shapes and colors. The painting was assembled from this grammar of representation, with a lot of contrivance along the way.

The process wasn’t entirely mechanical, however, as the many small deviations between drawings and paintings (discerning them is one of the pleasures of this exhibition) make clear. Balthasar van der Ast specialized in painting flowers, and, like other flower painters he used existing drawings to inform his lush bouquets. An image of a red-and-cream-colored tulip against a white background not only captures one of the great commodities of the era — the tulip — but may well have been a page from a catalogue advertising this particular varietal, the Admiral Pottebacker. But the same tulip appears in a finished painting from about 1630, although in slightly different form. That small difference — the image is rotated slightly, and the petals of the flower are a bit more closed up — suggests a great deal of visual and spatial virtuosity on the part of the painter.

It also captures something about time that runs like a quiet but intriguing theme in the background of the show. The painter has not only represented the same tulip at slightly different moments, he was working within a form, the flower painting, which relied on drawings to create ensembles of flowers that bloomed at different times of the year.

Pieter Jansz Saenredam. "St. Bavo, Haarlem, View in the Choir," pen and gray wash on paper. (Noord-Hollands Archief, Kennemer Atlas, Haarlem)

Saenredam’s "The Choir of the St. Bavo in Haarlem," oil on panel. (Fondation Custodia, Collection Frits Lugt)

Finished artworks often seem to suggest time transfixed and arrested — the cliche is that art is “timeless,” which means that not only does it endure the fads and vicissitudes of changing tastes, but that great artworks seem to capture a single moment in perfect perpetuity. But these static moments are imaginary bouquets culled not from reality, but from the storehouse of representation. We may learn this lesson again and again over a lifetime of looking at painted images, and yet still cling to the fantasy that somewhere, behind the painting, or lurking in the aura of the thing, is some hint of an actual, real, fleeting moment, captured and preserved. That need to find the mythical fixed instant captured by the artist is likely ineradicable, given how closely related it is to our larger need to hold on to memory and deny the ephemeral nature of experience.

Often, we seem to get to the truth of life, despite its fluidity and fleeting nature, by some kind of triangulation. We know we must have been happy at some particular moment because we have a photograph proving it to be the case; and people tell us it was so; and our own memory recorded the fact, even if it can’t bring it back to any kind of deeply felt immediacy. Two sketches in this exhibition offer a similar sense of being able to work backward to a moment that has fled forever. Cornelis Bega and Gerrit Berckheyde apparently sketched the same model, a peasant woman in a headscarf and long dress, at the same time. The face, dress and even the pose — she raises her skirt with her left hand — are almost identical. But she is seen from slightly different angles, and in Berckheyde’s image, she holds a glass, but in Bega’s, she does not.

The two sketches show subtle but different routes from source to image, capturing different intimations of weariness and self-consciousness from the model. But, taken together, they imply an actual moment in time that is thrilling to encounter. It isn’t present in the images themselves, only in the act of imagination with which we link them in our mind.

Jacob van Ruisdael. "View over Amsterdam and the IJ," c. 1665, black chalk, gray wash on paper. (Rijksmuseum)

The exhibition encompasses the multiple uses of drawings. Often, they were used to work out the basic geometry of an image, whether it was the methodical perspective of an architectural painting of a church interior, or the basic way the bulk of a woman making lace will occupy the rectangular space of a painting. From some artists, including Vermeer, we have no drawings at all. In other cases, drawings were made after a painting was finished, often to record it for the artist’s own records, or in some cases to change or adapt aspects of the painting the artist may have rethought. Scientific analysis has revealed some common habits — drawings transferred to the panel before paint was applied — but by no means a single method for conjuring a finished work.

That is to be expected in a competitive business. The production of paintings in the Age of Rembrandt wasn’t just a matter of intellectual and artistic skill. It was a business, with proprietary trade secrets closely held. Which is what makes the bits and pieces of history gathered in this captivating exhibition all the more interesting. By all rights, most of this material, like all those lost sketchbooks from the 17th century, shouldn’t exist at all.

Paintings for Drawings in the Age of Rembrandt is on view at the National Gallery of Art West Building through Jan. 2. For more information, visit nga.gov.