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Well, I have yet to take a philosophy class in college, but I'll take a stab. Forgive me if its less than completely fleshed out, as I must admit that I only recognize perhaps half of the names discussed in your class, Schwan...
Anyway, I assume your class began Soc/Plato/Aristotle. I lump them together because with my basic knowledge of philosophy and ancient world history, they really studied and taught much the same things.
Aristotle especially believed that there were basic tenets that ordered the universe. He once stood on a beach to watch a ship disappear, and noted that the prow and sails disappeared before the poopdeck and stern. This set him to meditiating on the shape of the earth, questioning the validity of the "cubic earth" theory, etc. Long story short, he questioned the structure of the universe.
Same basic time frame (I believe), Euclid propose the first basic parameters of geometry. BAM - physics is born.
Fast forward to Descartes. Descartes is a lazy, arrogant bitch. Decides mathematics is much too difficult and time consuming, theorizes that by assigning numbers graphical points, mathematics becomes more efficient and capable of handling theoretical problems. Modern geometry born. Students around the world riot.
In essence, this quick answer is leaning toward the gothic arch as being a more rational product of the human mind.
Aristotle's theory of the earth's curvature was not an epiphany; it was a conclusion arrived at after observation and hypothesizing.
Likewise, though much of Descartes philosophy was determined by (imo) his lethargy, it was arrived at through rational determination.
Both have to do with geometry and physics, and as has been mentioned, the gothic arch was designed to handle heavier loads.
Short and sweet, with a notable lack of elaboration and support, but I'm at work.
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I'll be the one to protect you from your enemies and all your demons.
I'll be the one to protect you from a will to survive and voice of reason.
I'll be the one to protect you from your enemies and your choices, son.
They're one and the same I must isolate you, isolate and save you from yourself."
- A Perfect Circle
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