Piero della Francesca, The Senigallia Madonna and Child with Two Angels.

Narrow windows sometimes afford expansive views. Consider, for example, “Piero della Francesca: Personal Encounters” at the Metropolitan Museum of Art, an exhibition of four small paintings made for private devotion by one of the foundational artists of the Italian Renaissance.

Borrowed from three European museums and one American collection, the four works aren’t among Piero’s most celebrated. But they are all the devotional paintings he is known to have made (not counting “The Flagellation,” which is intimately scaled but has a formal and conceptual complexity that puts it into a separate category). Organized by Keith Christiansen, chairman of the Met’s European paintings department, this exhibition is the first to bring them together. Two picture St. Jerome in his wilderness retreat and two portray the Madonna and Child, one thought to be Piero’s earliest known painting and the other among his last. Of the four, only the later Madonna and Child is instantly recognizable as a Piero, and it’s a beauty. The other three have suffered from the fading of fugitive pigments and abuse by cleanings and restorations.

The mother and child pictures bring to mind something I’ve often wondered: Why was the image of a naked baby — usually with prominently exposed genitals — so popular back then? In “The Sexuality of Christ in Renaissance Art and in Modern Oblivion,” Leo Steinberg proposed that it had to do with theological debates about whether Jesus was a human being or a transcendent divinity.

Without doubting Steinberg’s thesis, I think of the baby as a metaphor of newness. It seems to me not just coincidental that this image would become ubiquitous in a time when the European minds were crossing over from the medieval age of faith to a new age of reason, science and individualism.

On the face of it, Piero’s “Madonna and Child” (circa 1439-40) appears to belong to the earlier era of dogmatic belief. Seen from the waist up and framed by an open window, Mary cradles her oversize baby so that his naked body faces the viewer. Another window behind her affords a glimpse of tree-dotted hills in the distance.

As a painting, it’s fairly unremarkable. But there’s something striking on the panel’s back side: an image of a bowl — a renfrescatoio, or wine bucket — incised and painted in shades of brown to resemble a piece of intarsia. Pinpricks in exactly measured spots prove that the bowl image was essentially a study in perspective, a subject that Piero and many other Renaissance intellectuals were famously fond of.

Perspective is a way of constructing how the world appears to a single person. Its appearance in art coincided with the rising philosophical idea that all we can know about the world must come through the senses of our uniquely located bodies. Neither divine revelation nor divinely sanctioned earthly authority would trump the claims of the individual’s perceptually informed reason.

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