Cool. I had wondered about that too. I wish young me had thought to consult the Principia. The local Catholic college might have had an edition in Latin.

Seems a distinction without much of a difference. But then, I am practical

I had exactly the same thought.

A more significant issue with Newton’s Laws of Motion is with the Second. It’s taught to us as stating F=m*a. That isn’t a “misreading,” it’s making a statement Newton himself never did in The Principia. He wrote, instead, that the change in the “quantity of motion” is proportional to the applied force and in the same direction.

Newton’s “quantity of motion” is what we know today as “momentum,” or the entity (mv). Though Newton had developed differential calculus long before writing The Principia, he didn’t use it in that publication – he used geometric arguments only, considering geometry to be far more rigorous, and more likely to gain acceptance for his ideas. There is thus no reference to a time rate of change of anything. F=m*a is a formulation introduced much later.

I’ve never seen so many lines and circles drawn as that in my copy of the Philosophiæ Naturalis Principia Mathematica, with every theorem and postulate explained in paragraphs of scholia that require more than a beginner’s acquaintance with geometry. And if you think that’s bad, try his Opticks. Thanks to having broken down and buying a copy of the The Great Works of the Western World, back in the 90s. I ought to read more of them someday, along with my four volume set of Churchill’s History of the English Speaking Peoples.

It’s hard to find straight lines in any practical part of outer space thanks to GR.

But what is straight?

The shortest distance between any two distinct points.

Cool. I had wondered about that too. I wish young me had thought to consult the Principia. The local Catholic college might have had an edition in Latin.

Seems a distinction without much of a difference. But then, I am practical

I had exactly the same thought.

A more significant issue with Newton’s Laws of Motion is with the Second. It’s taught to us as stating F=m*a. That isn’t a “misreading,” it’s making a statement Newton himself never did in

The Principia.He wrote, instead, that the change in the “quantity of motion” is proportional to the applied force and in the same direction.Newton’s “quantity of motion” is what we know today as “momentum,” or the entity (mv). Though Newton had developed differential calculus long before writing

The Principia,he didn’t use it in that publication – he used geometric arguments only, considering geometry to be far more rigorous, and more likely to gain acceptance for his ideas. There is thus no reference to a time rate of change of anything. F=m*a is a formulation introduced much later.I’ve never seen so many lines and circles drawn as that in my copy of the

Philosophiæ Naturalis Principia Mathematica, with every theorem and postulate explained in paragraphs of scholia that require more than a beginner’s acquaintance with geometry. And if you think that’s bad, try hisOpticks. Thanks to having broken down and buying a copy of theThe Great Works of the Western World, back in the 90s. I ought to read more of them someday, along with my four volume set of Churchill’sHistory of the English Speaking Peoples.It’s hard to find straight lines in any practical part of outer space thanks to GR.

But what is straight?

The shortest distance between any two distinct points.

And I thought I’d never need 7th grade geometry!

That’s why we talk of geodesic lines instead.