66 THE HISTORY OE THE ORDER OF [book i.

plebeians hovelled ; and if noble castles were cold,dark, and dreary everywhere, they were infinitelyworse in Italy, from the horrible modes of torture;characteristic cruelty, too frightful to dwell on.Few of the infamous structures, built at the timestreated of, stand at present. Yet their ruins dis-close rueful corners. As to cathedrals, the agefor them, though at hand, had scarcely come inthe tenth or eleventh century; and when it did,it was simultaneously in Italy, England, France,and Germany.

If algebra was known in Italy in the tenth cen-tury (which might easily be, from the Moors), itwas kept secret there for three hundred years ; notintentionally, it is said, but simply because theItalians were not aware of what an importantthing they had. The archives of all the towns ofItaly, before Barbarossa, having perished, leavesmany matters obscure, which probably (as is to bewished) little deserve being known. Even whenthe Italian cities, without being exactly indepen-dent, appeared so, was it not that the emperorswere too busy at home to march across the Alpsto prevent them? For though often independentin fact, they always acknowledged in theory that theemperor was their sovereign. It was only worse,before the Popes and popular party took the name