1. By the early eleventh century, however, the empire had regained almost half of its lost possessions, its new frontiers were secure, and its influence extended far beyond its borders. 然而，到11世纪早期，帝国已收复了几乎一半的失地，新的边境得到了保障，其影响力远远超出了国界。
2. Naked aggression and an attempt to change frontiers by force could not go unchallenged. 对公然侵略和企图用武力改变疆域，人们不会坐视不管。
3. The principal mark of genius is not perfection but originality, the opening of new frontiers. 天才的主要标志不是完美，而是独创性，即开拓新的领域。
4. Compared with the East, however, the West faced a greater number of external threats along more permeable frontiers. 然而，与东方相比，西方在更容易渗透的边界上面临着更多的外部威胁。
5. Mobility of this kind meant also mobility of ideas, their transference across frontiers, their simultaneous impact upon many groups of people. 这种流动也是思想的流动，思想转移跨越国界，与此同时还对许多群体产生着影响。
