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Early Calculus

Early Calculus

(OP)
My old Calculus text (Johnson and Kiokemeister) says that Calculus was "well known" before Newton and Liebnitz. Alright, known by whom? Any proof anyone?

RE: Early Calculus

My old Calculus text (Ford and Ford © 1963) didn't go into any sort of 'history' of it's origin.

But in checking Wikipedia, it states in a section titled 'History':

"Modern calculus was developed in 17th-century Europe by Isaac Newton and Gottfried Wilhelm Leibniz, but elements of it have appeared in ancient India, Greece, China, medieval Europe, and the Middle East."

It then goes on to provide more details about the 'Ancient' and 'Medieval', as well as 'Modern' origins of Calculus.

https://en.wikipedia.org/wiki/Calculus

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RE: Early Calculus

(OP)
Yes, I know others dabbled in it, but it seems that Newton solidified the ideas. Like many people tried to develop a flying machine, but it took the Wright Bros. to make it really happen.
If he had done it later, he would have received the Nobel Prize for Math. (+ for physics, astronomy, optics, etc.)

RE: Early Calculus

Much of the basis of Einstein's work on relativity was pulled from experiments done by other scientist but they hadn't pulled together the implications of their results.

RE: Early Calculus

Considering that Einstein was never really known as an 'experimental' physicist, this would only be expected. This was what he was best at, taking what others had observed but which they could not rationalize with what others had found, and making the connections and correlations that until then had alluded the broader community of physicist and other scientists.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA
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UG/NX Museum:

The secret of life is not finding someone to live with
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RE: Early Calculus

i always liked the story of its development for the purpose of calculating volume of wine barrels... prior to Liebnitz.
"This inspired Kepler to study how to calculate areas and volumes and to write a book about the subject, Nova stereometria doliorum vinariorum (New solid geometry of wine barrels), which was his main contribution to the development of the integral calculus."

RE: Early Calculus

I was ready up on this over the weekend and it is to me at least surprising that someone didn't generalize the concept sooner. Archimedes when he was trying to determine the area of a circle, put series of triangle pie slices inside of the circle. Even then he knew that the more pie slices ,the smaller they are, the better he would approximate the area of the circle. The was called the Method of Exhaustion, using geometric shapes to approximate areas. I would have thought that a generalized form of calculus would have been just around the corner due to the idea of getting a good approximation by using even smaller and smaller shapes was already there. 600 years later in China a method of calculating spherical volumes with indivisibles was discovered. 1200 years after that Cavalieri figured out the same in Europe and created Cavalieri's theorem, which would lead to infinitesimals. The part that I find interesting and maybe I am overly simplifying things. Maybe, algebra really needed to get to a certain point. But the idea of calculus had been floating around loosely for 1000 to 1800 years.



RE: Early Calculus

As with lots of inventions, there are many moving parts that have to exist to make something complex like calculus to work. The fundamental theorem of calculus requires not only algebra, but also limit theory, in addition to the general concepts of antiderivatives and infinitesimals. The issue that you see over that period of history is that the development of something like Cavalieri's theorem is that it's not at all obvious that the concept is applicable in general, without the actual mathematical background that was finally present in Newton's time. The first known proof of the fundamental theorem of calculus wasn't done until the 17th century; this would really be the first time that integrals can be shown to be generally applicable and calculable, and that integrals and derivatives are inverse mathematical operations.

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RE: Early Calculus

The 'Nobel Prize for Math(s)' (mentioned above) = The Fields Medal.

The Nobel Prize itself doesn't include the field of mathematics.

RE: Early Calculus

Archimedes was also hamstrung by the lack of a decent set of numerals. Symbology can make a significant difference.

RE: Early Calculus

Quote (DB)

Archimedes was also hamstrung by the lack of a decent set of numerals. Symbology can make a significant difference.

Modern mathematicians don't hesitate to create new symbology as they go along. smile

RE: Early Calculus

Euler, of a similar time period, dabbled in the same material and wrote volumes of material. 2000 years prior to Columbus 'discovering' the world was round, the Greeks measured the diameter and circumference...

Dik

RE: Early Calculus

I think it's a bit inaccurate to say that Columbus "discovered" that the world was round. I suspect that it had already been 'discovered' by the astronomers and others, just that until Columbus had reached what he thought were the 'Indies', no one had successfully demonstrated that it was. And even then, his claim that he had made it to the 'Indies' missed the mark by quite a distance, better than half the circumference of the globe.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

RE: Early Calculus

Anyone educated in 1492 knew the world was round and had a general understanding of the size.
This is the root of the myth that no one would fund Columbus because the world was flat.
If the unknown continent had not been in the way, there was no chance that the technology at the same could sustain such a long voyage at sea.

RE: Early Calculus

jgailla... aye, and there be monsters...

RE: Early Calculus

back to Newton and Leibniz, Newton was interested in function of time (hence xdot and xdoubledot) but Leibniz used dy/dx the more general expression.

I heard that Columbus pushed (tweeted?) the idea that the world was smaller than people had calc'd, since the ships of the day couldn't manage the full voyage (they could barely manage to get to the US), though I think they knew enough about the tradewinds to use them efficiently.

another day in paradise, or is paradise one day closer ?

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