The subsequent Crusades against the Mohammedans had the effect, among others, of extending the knowledge of mathematics and geometry among the Crusaders, sciences in which the Saracens excelled; and in coming home again to the West, they applied their geometrical knowledge to the development of Gothic architecture to such an extent that, towards the end of the fourteenth century, this architecture could show examples of the most lofty and daring constructions in stone that were marvels in the science of building. Some Gothic buildings present with their fretted pinnacles, spires, flying buttresses, intersecting and pierced work, in flamboyant tracery, daring vaulting, and inter-penetrating mouldings, a worked-out solution of some intricate mathematical problem. In its complicated phases Gothic construction is more scientific than artistic, however much one may admire the grouping or design of the Gothic pile as a picturesque conception. Returning to the Romanesque style, we find that in the sixth century Theodoric the Ostrogoth had, in the erections of churches, palaces, and of his tomb in Ravenna—his capital—sown the first seeds of the future developments of the German Romanesque, and in some degree of the later German Gothic style. In producing these works his ambition was to emulate the grandeur of Imperial Rome. The Longobards, the successors of the Ostrogoths, continued this building activity through the Middle Ages, and have left to us monuments of their genius in the early and rude Duomo Vecchio of Brescia, and amongst many others of their noblest works were Sant’ Ambrogio at Milan, and San Zeno at Verona. Prior to the Carlovingian era, the Germanic people began to cultivate the fine arts in a tentative manner. This was brought about by the contact of German chiefs and warriors with Italian pomp and splendour, which also bred in them a love for personal adornment, that strongly marked the nobles and warriors of this period. Charlemagne was crowned Emperor of Germany at Rome, on Christmas Day in the year A.D. 800. The dream and ambition of this great German Prince was to establish a mighty Christian Empire in the West of Europe that should rival pagan Rome itself, not only in military power, but in a widespread culture of literature, science, and artistic excellence. These were the days of Chivalry, of the Crusaders; the days when men were rich in high and lofty ideals; when those knightly mystics, Wolfram von Eschenbach and Vogelweide, sang of the Parsival and the Quest of the Holy Graal, of songs of love and chivalry, of deliverance from wrongs, and of many stirring and tuneful themes.