and support troops to get close enough to exploit the breach, more zigzag trenches could be dug even closer to the walls, with more parallel trenches to protect and conceal the attacking troops. After each step in the process, the besiegers would ask the besieged to surrender. If the forlorn hope stormed the breach successfully, the defenders could expect no mercy. Emerging theories The castles that in earlier years had been formidable obstacles were easily breached by the new weapons. For example, in Spain, the newly equipped army of Ferdinand and Isabella was able to conquer Moorish strongholds in Granada in 1482–1492 that had held out for centuries before the invention of cannons. In the early 15th century, Italian architect Leon Battista Alberti wrote a treatise entitled De Re aedificatoria, which theorized methods of building fortifications capable of withstanding the new guns. He proposed that walls be "built in uneven lines, like the teeth of a saw". He proposed star-shaped fortresses with low, thick walls. However, few rulers paid any attention to his theories. A few towns in Italy began building in the new style late in the 1480s, but it was only with the French invasion of the Italian peninsula in 1494–1495 that the new fortifications were built on a large scale. Charles VIII invaded Italy with an army of 18,000 men and a horse-drawn siege-train. As a result, he could defeat virtually any city or state, no matter how well defended. In a panic, military strategy was completely rethought throughout the Italian states of the time, with a strong emphasis on the new fortifications that could withstand a modern siege. New fortresses The most effective way to protect walls against cannonfire proved to be depth (increasing the width of the defences) and angles (ensuring that attackers could only fire on walls at an oblique angle, not square on). Initially, walls were lowered and backed, in front and behind, with earth. Towers were reformed into triangular bastions. This design matured into the trace italienne. Star-shaped fortresses surrounding towns and even cities with outlying defences proved very difficult to capture, even for a well-equipped army. Fortresses built in this style throughout the 16th century did not become fully obsolete until the 19th century, and were still in use throughout World War I (though modified for 20th-century warfare). During World War II, trace italienne fortresses could still present a formidable challenge,