That’s reasonable, but most likely the Greeks didn’t know the orbits were ellipses, but just knew them as solutions to Newton’s laws and used calculus to approximate them as deviations from circles.
Obviously I disagree. How can you boldly state that they didn’t have things? Maybe there’s no written record, but someone writing about the Antikythera Mechanism should know the limits of that! Indeed, the Method of Mechanical Theorems was discovered after even the Mechanism. But there is a written record. There’s a lot more calculus in Archimedes than the method of exhaustion. That’s barely calculus and it’s interesting more because it’s rigorous than because it’s a forerunner to calculus. But the Method is a pretty big chunk of integral calculus.
The missing part is differential calculus; Newton’s laws do not appear in the written record. But Vitruvius appears to discuss how the planetary orbits are the result of inertia and centripetal force, so it is really not a big stretch to posit further elaboration.
That’s reasonable, but most likely the Greeks didn’t know the orbits were ellipses, but just knew them as solutions to Newton’s laws and used calculus to approximate them as deviations from circles.
The Greeks didn’t have Newton’s laws, or calculus except for the method of exhaustion for calculating certain areas.
Obviously I disagree. How can you boldly state that they didn’t have things? Maybe there’s no written record, but someone writing about the Antikythera Mechanism should know the limits of that! Indeed, the Method of Mechanical Theorems was discovered after even the Mechanism. But there is a written record. There’s a lot more calculus in Archimedes than the method of exhaustion. That’s barely calculus and it’s interesting more because it’s rigorous than because it’s a forerunner to calculus. But the Method is a pretty big chunk of integral calculus.
The missing part is differential calculus; Newton’s laws do not appear in the written record. But Vitruvius appears to discuss how the planetary orbits are the result of inertia and centripetal force, so it is really not a big stretch to posit further elaboration.