Most of us have, at some point, fallen under the spell of one of Johannes Vermeer's luminous paintings, works so real and intimate they make us feel we are intruders spying on a private moment from another time.

Therefore a book about the 17th-century Dutch artist is destined have a popular appeal. Laura J Snyder's The Eye Of The Beholder, however, is not only about Vermeer. It has another subject, a neighbour of the artist in Delft, born within days of him, who shared many friends, yet whose only documented interaction with him was after his death.

This is the story of Antoni van Leeuwenhoek, the pioneering lens-maker known as "the father of microbiology". At its heart is the jaw-dropping moment, when, looking through a microscope at murky lake-water, he was shocked to find it teeming with a "veritable aquarium" of tiny life. "The motion of these animalcules in the water," he wrote, "was so swift, and so various, downwards, and round about, that I confess that I could not but wonder at it."

As Snyder puts it, Leeuwenhoek had realised "that there exists a new world of living beings, a world never before seen, never before even imagined - a world in the water we drink, perhaps even in the food we eat - even, it will turn out inside our own bodies."

Snyder has written narrative non-fiction before, taking as her subject, in The Philosopher's Breakfast Club, the relationships between Charles Babbage, John Herschel, William Whewell and Richard Jones. But those were men who definitely met. Here, she has dared to write a book revolving around two ideas that are entirely speculative, two possibilities that have long tantalised historians: that the two men knew each other and that, controversially, Vermeer used, not only lenses, but a camera obscura to aid his work. As Snyder builds a picture of their times and the world in which the two men were working and raising families "within a three-minute walk from each other", she tries to catch the two in a "mathematical net".

As the title suggests, Snyder's real interest lies in the fact that, in their use of lenses, they were pioneers in a revolution in seeing. When I began reading this book, I developed the theory that Vermeer was the hook to draw us to Leeuwenhoek, to take us to the lens of his microscopes, so that we could marvel. Soon, though, it became clear that both men were hooks to lure us into a time in history, a way of observing what was at the heart of the scientific revolution taking place across Europe.

The tale of Leeuwenhoek, in particular, is so suffused with excitement it feels like a thriller: one that starts with the wonder of looking, for the first time, at the structure of a bee's eye then telescopes down to the tiniest forms. He gazed through his microscopes at his own semen and was astounded to observe wriggling spermatozoa, saw red blood cells for the first time, took plaque from his mouth and found there "more animals in the unclean matter on the teeth in one's mouth than there are men in a whole Kingdom". An eccentric character, not university educated, but driven by curiosity, frequently he experimented on himself, growing lice on the hairs of his legs or drinking "pounds" of French wine then examining his sweat.

The intrigue in Vermeer's tale, meanwhile, revolves mainly around whether he did or did not use a camera obscura - a notion that has long been controversial and has been postulated by, among others, the artist David Hockney. Snyder stresses that there is no documentation showing he did, though she makes a strong case that his paintings indicate he was aided by a small-scale device with a mirror. She does not believe, as architect Philip Steadman has suggested, that he traced his paintings from inside a room-type camera obscura. Rather, she suggests he "looked at nature through the camera obscura to learn about light, shadow, tone and colour". He was using lens-based devices, she claims, in much the same way "as the natural philosophers used it: to experiment with light, to investigate and discover its optical properties."

Snyder has her own way of looking at a subject, her own style of seeing into history. She looks back into its murky waters and makes lost connections visible. The philosophy of science, however, is where she has her greatest clarity. She uses her subjects as a springboard to explore how we learn to see and how, in the 17th century, pioneers were training themselves to see the world in a different way. This "learning to see" is as relevant to us now as ever, since, as Snyder points out, neuroscience has shown that seeing is not entirely innate, but learned through experience. "The most radical influence of the 17th century on our time," she writes, "is the realisation that seeing requires more than simply opening one's eyes... one needs to learn how to engage in attentive looking, often with instruments, to make sense of the world around us."

Eye Of The Beholder: Johannes Vermeer, Antoni van Leeuwenhoek And The Reinvention Of Seeing by Laura J Snyder is published by Head of Zeus, £25