Origin of calculus

[pka]

How do I apply integration to find the area of the graphs? I don't understand what integration or differentiation is...

You don't need either integration or differentiation; just the ability to count and estimate.
How many square units are shaded in? This is a standard exercise in beginning calculus. The whole idea is to get students to realize what the course is all about. Many who have taught calculus do not realize that Newton worked out the integral before ever thinking about a derivative. Most do not know that Newton had two passions: astronomy & the Book of Revelation. He had to know the AREA swept out by the motions of the planets.

 

[Deleted member 4993]

You don't need either integration or differentiation; just the ability to count and estimate.
How many square units are shaded in? This is a standard exercise in beginning calculus. The whole idea is to get students to realize what the course is all about. Many who have taught calculus do not realize that Newton worked out the integral before ever thinking about a derivative. Most do not know that Newton had two passions: astronomy & the Book of Revelation. He had to know the AREA swept out by the motions of the planets.

Wasn't it Kepler who had proposed that concept of swept area of planatory locus (from which idea of elliptic motion and inverse square law come about)?

I read somewhere that it was Hooke who had proposed the idea of elliptic motions from Kepler's (and Tyco Brahe's) observations.

 

[pka]

Wasn't it Kepler who had proposed that concept of swept area of planatory locus (from which idea of elliptic motion and inverse square law come about)?

I read somewhere that it was Hooke who had proposed the idea of elliptic motions from Kepler's (and Tyco Brahe's) observations.

Well of course Newton stood on the shoulders of those Giants. BUT it was Newton who gave us The Calculus.

 

[Otis]

BUT it was Newton who gave us The Calculus

According to history, Gottfried Wilhelm Leibniz and Isaac Newton co-developed differential and integral calculus, working simultaneously but mostly independently. (Newton tried to alter this history, by editing his texts to remove references to contributions by Leibniz, after Leibniz died.)

BUT, it was Newton who gave us the awkward dot-notation. (Fortunately, Leibniz created a better notation that is now the standard.)

 

[lookagain]

According to history, Gottfried Wilhelm Leibniz and Isaac Newton co-developed differential and integral calculus,

I already made the post (indicating the equivalent content of what is in the quote box) right under pka's.

And, it was in the forum for many days.

All one need do is to keep my post there and not remove it.

You're welcome for my answer, everyone.

 

[greg1313]

I already made the post (indicating the equivalent content of what is in the quote box) right under pka's. .

You're welcome for my answer, everyone.

Thanks, lookagain.

I remember reading your contribution.

 

[Otis]

Gosh, I never saw your post Lookagain. (I have not been on these boards much, since the system began logging me off constantly over a year ago. That issue seems resolved, at least for now.)

It's disappointing when posts go missing. I know that when threads have been split in the past, sometimes posts get dropped secondary to system flaws. Maybe that's what happened.

Thank you for also pointing out pka's inadvertent distortion.