Final answer:
Karl Bötticher believed that both Greek and Gothic architecture successfully aimed to transcend human limitations and symbolize a connection to the divine through their impressive and towering structures.
Step-by-step explanation:
Karl Bötticher appreciated the efforts to exceed the limits of humanity and achieve a connection with the divine present in both Greek and Gothic architecture. The quest for reaching the heavens is mirrored in the towering structures of Gothic cathedrals as well as in the temples of ancient civilizations. Despite differing styles, Greek and Gothic architecture shared the ambition to create impressive structures that could represent the pinnacles of their respective civilizations and serve as bastions of learning, religion, and power. Both styles marked significant shifts in architectural design, emphasizing height, the use of light, and the creation of vast interior spaces devoid of obstructive columns.