What are Cauchy’s first and second limit theorems?

Question

precal · Answer

http://www.saintjoe.edu/~karend/m441/Cauchy.html

kinggeorge · Answer

This paper seems to talk about them. It might take some time to read through, but it mentions the first and second theorems due to Cauchy, and provides analogues. http://plms.oxfordjournals.org/content/s2-5/1/206.full.pdf

precal · Answer

@KingGeorge   I saw that one but it looked to technical, I posted a more historical explanation......   Oh Cauchy... the nightmares of my graduate program

2bornot2b · Answer

@precal  Can you please specify the theorems, I just can't find it in that long document of yours. And @KingGeorge you page is not opening for me, if you could post the theorems here, it would help a lot.

precal · Answer

do you have a calculus book around?

kinggeorge · Answer

I'll just attach the file. It's a real pain to write out.

2bornot2b · Answer

Yes, I have but they are not specifying either. I mean there are several theorems, but which one is called the ................ I don't understand

precal · Answer

I found one reference but it is known as the mean value theorem

kinggeorge · Answer

It is a very technical paper, but it does mention "two well-known theorems" that were made by Cauchy.

2bornot2b · Answer

Mean value theorem is not the same as cauchy's theorems are they?

precal · Answer

According to my calculus book, it states that the Genealized (or Cauchy's) Mean Value Theorem......  yes, it looks like it

precal · Answer

Cauchy did a lot of work in calculus.........like I said, "Nightmares of my graduate program"

kinggeorge · Answer

The mean value theorem doesn't really have to do with limits very much though... It doesn't seem like a "limit theorem" at least.

2bornot2b · Answer

Anyway thanks

kinggeorge · Answer

If you look through the thing I posted, Thm. 1 is on the second page, Thm. 2 is on the 8th page.

precal · Answer

what derivatives don't have anything to do with limits???????  
Let's see we teach limits first because they lead to derivatives, then we go to integration .  Sorry to tell you, they are all related.  A big spider web.

kinggeorge · Answer

They're definitely related, but I would hardly call it a limit theorem.

precal · Answer

ok I agree.  You are right, they are listed there.  I hope the asker can understand all of that  :)

kinggeorge · Answer

It certainly doesn't help that the paper is 106 years old :/

precal · Answer

oh boy!!!