And indeed, just as promised, the book turned out to be a game of two very distinct halves. The first half was a kind of wide-roaming literature review of the classical, medieval and early modern texts that promised some kind of proto-telescopes or burning mirrors to their readers: that this was built on broadly the same foundations as Albert van Helden's 1977 monograph "The Invention of the Telescope" is made completely clear in the acknowledgements at the end. Let's be clear: the primary sources for this form a fragmentary, piecemeal soup, whose components interlock and separate eternally - despite all Reeves' hard work, there is no emergent narrative, no thread, no causal proof to be had here. Yet she gives the impression of needing to draw out a story based on the 16th century reception of travellers accounts of the Pharos, in order to give a structural punchline to this section: but unfortunately this never quite hits the spot.
The second half is very much more focused, and reads quite differently: it focuses on the minutiae of correspondence of Galileo and his circle circa 1608-9, as they received (possibly unreliable) reports of mirrors and telescopes coming from France and Holland (often embedded in pro- or anti-Jesuit propaganda), and tried to make up their minds what to make of them - was the new Dutch telescope truly something amazing, or based on the mirror, or was it yet another tall tale?
In the end, Reeves' central point (which hinges on whether Galileo thought the new telescope was built with a mirror or purely with lenses) is well argued, but extremely marginal: and it fails to mesh comfortably with the first half of her text. I came away feeling like I had read two 90-page monographs in quick succession: I desperately wanted her to find a way to knit the two together, to redeem her choice of structure - but this never really happened.
Look: "Galileo's Glassworks" is a lovely, compact, readable book, and pleasantly affordable too (a snip at £14.20 for the hardback). But Reeves can't really reconcile the broad generalities of the pre-history of the telescope with her ultra-close reading of Galileo's "Starry Messenger" and his letters. Ultimately, what's going on is some kind of mismatch in epistemological tone: the first half raises many open-ended issues, while the second half answers a single (quite different) question.
I suspect that somewhere along the way, Reeves lost track of whom she was talking to, and about what: the book ended up being just as much about Sarpi (or even about the ghost of della Porta!) as about Galileo himself, which is surely a sign that her aim drifted off true. Perhaps in the end she simply didn't have enough to say about Galileo in the second half that hadn't been amply said before: which would be a shame, as I would say the first half of her book is really very good, well worth the cover price on its own.