Meantime, I should record that I finished this book as long ago as Thursday; it is a history of the reign of the Byzantine emperor Alexius I by his daughter Anna. Gibbon is (as so often) unfairly scathing about this book, saying that "an elaborate affectation of rhetoric and science betrays on every page the vanity of a female author". It's not that bad, but it's not that great either; if you're not especially interested in the events of the late eleventh century and early twelfth century at that end of the Mediterranean, you can skip it in good conscience.
I did take several things away from it. First off, the importance of the Norman invasion of Sicily and Calabria: Anna is completely obsessed with Robert Guiscard and especially his son Bohemond, who starts off as a thorn in the side of the Byzantine empire, conquering chunks of Albania, Macedonia and northern Greece, and ends up ruling Antioch after the success of the First Crusade. Bohemond is an rather impressive figure (see especially Anna's description in 13.10) who seems to be somewhat forgotten by posterity.
Second, as a lapsed historian of science, I was interested in Anna's account of these things. She has quite a long rant (6.7) about how wrong astrology is, but also writes on the one hand of her father tricking the Scythians into submission because he knew that an eclipse was about to take place, and on the other hand (twice) of important strategic decisions being made by writing the alternatives on two pieces of paper, praying over them all night, and then implementing whichever option is selected by the priest (one at 10.2, can't find the other). So she actually favours both astronomical knowledge and superstitious grounds for decision-making, and it's a bit surprising to me that she doesn't buy the combination.
Third, towards the end she starts reflecting on the fact that she is writing the history because she is effectively locked away from the rest of the world in a convent and has nothing else to do, and also on how she reconstructed the sequence of events from first-person accounts of her own relatives and of former soldiers who had become monks. It's a rather welcome glimpse of how the history book was actually written, and also makes one feel sorry for this talented woman who fell out with her younger brother and so was banished from public life.