Bernoulli's book on integral calculus

[Vinay080]

The name of lectures of integral calculus written by Johann or Jeans Bernoulli (he is called by both names as far as I know) might be " lecciones mathematicæ de calculo integral". I searched for one day for the english translation, I couldn't even find the english title of his book on integral calculus. I found his books called Operae, in latin, which contains these lectures, but onceagain, I couldn't even find a single english edition. I am really in need of his book, as he was the first to study lebnizian calculus; ofcourse Jackob Bernoulli also studied with Johann Bernoulli; anyway please help me in finding Bernoulli's books on integral calculus, either in google books or anywhere. Atlast if nothing can be found, please say the title of english edition of his calculus lectures and the name of the translator of it.

I already have L'Hopital book on differential calculus (claimed to be the first textbook on differential calculus) which contains Johann Bernoulli's lectures on differential calculus, but it doesn't contain lectures on integral calculus. If possible can anyone also point out some of the oldest books on integral calculus.

 

[verty]

Here is an interesting article about Johann Bernoulli after l'Hopital's book was published. It talks about exponential functions and how Leibniz's calculus couldn't differentiate exponential functions.

Johann Bernoulli worked on that and communicated his result to Leibniz. Leibniz claimed to have thought about it as well but not to have gone as far. Leibniz then published the result in brief, giving Johann the credit. Johann certainly seemed to like this arrangement, have other people publish his results.

What this suggests is that he was interested in the differentiation side of things and any lectures on integration would likely follow Leibniz quite closely. This may be wrong but if he wanted to call this addition his own, it suggests he didn't add anything to the integration side. That may be why nothing was translated into English, because it wasn't an actual addition to what was there. And also, in the Newton-Leibniz dispute after 1711, Johann took Leibniz's side, attacking Newton's character. He certainly wasn't attacking Leibniz's character which should have been easy to do. If he had published material of his own beyond Leibniz on the integration side, he certainly might have been interested in denigrating Leibniz's reputation because he had exceeded him on the differentiation side (exponential curves) and on the integration side.

So I project that he didn't add anything and that is why it is hard to find his lectures.

 

[Vinay080]

@verty: Thank you very much. I found L'Hopital book to be really concentrated with the primary ideas of differential calculus. I am searching for a similar kind of integral calculus textbook, which is highly concentrated, in the sense of being really old; and the one which would be the first text to deal with it, with particularly "Leibnizian" views.

Can you please suggest any of those type of textbooks?

 

[verty]

I've found this interesting google book, look at the end of page 45 and page 46 here.

It lists all the books that were current at the time. For example, Cheyne published "the inverse method of fluxions" in 1711 and Stone published "the method of fluxions both direct and inverse" in 1730. Carré published "methode pour la mesure des surfaces" in 1700, etc.

The major popularisation of calculus as a whole seems to have come from Agnesi in 1748, the "analytical institutions".

 

[SteamKing]

The name of lectures of integral calculus written by Johann or Jeans Bernoulli (he is called by both names as far as I know) might be " lecciones mathematicæ de calculo integral". I searched for one day for the english translation, I couldn't even find the english title of his book on integral calculus. I found his books called Operae, in latin, which contains these lectures, but onceagain, I couldn't even find a single english edition. I am really in need of his book, as he was the first to study lebnizian calculus; ofcourse Jackob Bernoulli also studied with Johann Bernoulli; anyway please help me in finding Bernoulli's books on integral calculus, either in google books or anywhere. Atlast if nothing can be found, please say the title of english edition of his calculus lectures and the name of the translator of it.

I already have L'Hopital book on differential calculus (claimed to be the first textbook on differential calculus) which contains Johann Bernoulli's lectures on differential calculus, but it doesn't contain lectures on integral calculus. If possible can anyone also point out some of the oldest books on integral calculus.

I'm afraid you might be out of luck, as far as finding English translations of these works.

According to the start of this article, much of the Bernoulli brothers' work remained uncollected as of 1958, let alone published in any language.

http://www.jstor.org/stable/226604?seq=1#page_scan_tab_contents

What has been published was originally written in Latin, still the scientific lingua franca of the day.

A similar situation pertains to the works of Euler. He wrote volumes of mathematical papers, mostly in Latin, but because Euler wrote so voluminously, no one has gotten round to translating much of his work from Latin into other modern languages. It has been estimated that Euler's writing would fill 60-80 quarto volumes when collected:

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

Euler suffered from eyesight problems most of his life and went completely blind towards the end of it, yet that seemed not to have affected the volume of his work at all.

 

[Vinay080]

I've found this interesting google book, look at the end of page 45 and page 46 here.

It lists all the books that were current at the time. For example, Cheyne published "the inverse method of fluxions" in 1711 and Stone published "the method of fluxions both direct and inverse" in 1730. Carré published "methode pour la mesure des surfaces" in 1700, etc.

The major popularisation of calculus as a whole seems to have come from Agnesi in 1748, the "analytical institutions".

Thank you very much. I have Edmund Stone book, which contains integral calculus as the appendix for the L'Hopitals differential calculus. I look forward to see the other two textbooks.

I'm afraid you might be out of luck, as far as finding English translations of these works.

According to the start of this article, much of the Bernoulli brothers' work remained uncollected as of 1958, let alone published in any language.

http://www.jstor.org/stable/226604?seq=1#page_scan_tab_contents

What has been published was originally written in Latin, still the scientific lingua franca of the day.

A similar situation pertains to the works of Euler. He wrote volumes of mathematical papers, mostly in Latin, but because Euler wrote so voluminously, no one has gotten round to translating much of his work from Latin into other modern languages. It has been estimated that Euler's writing would fill 60-80 quarto volumes when collected:

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

Euler suffered from eyesight problems most of his life and went completely blind towards the end of it, yet that seemed not to have affected the volume of his work at all.

Thank you for the reply. I might require to learn Latin now, if all I need is in Latin. I will read the article...

 

[SteamKing]

Thank you for the reply. I might require to learn Latin now, if all I need is in Latin. I will read the article...

Well, good luck. Be forewarned though. The Latin used in writing European scientific works differs a little from the Latin used by Caesar and Cicero. Make sure you study these differences.

 

[verty]

Vinay080, I have to ask, why are you so interested in these old books? I have certainly enjoyed reading about these old mathematicians, for example I read that Klingenstierna who was a Swedish mathematician actually visited the Bernoulli's and lectured on calculus in Sweden. I was hoping he wrote a book because that would have been very early indeed but it seems he lectured but didn't ever write a book on it.

Is it just out of interest or are you part of a museum or something? I think it is a most interesting topic to be researching.

 

[Ankel]

@verty: Thank you very much. I found L'Hopital book to be really concentrated with the primary ideas of differential calculus. I am searching for a similar kind of integral calculus textbook, which is highly concentrated, in the sense of being really old; and the one which would be the first text to deal with it, with particularly "Leibnizian" views.

Can you please suggest any of those type of textbooks?

Vinay, please stop being such a pest. I already told you on Genofond that Bernoulli's calculus is available in English and Latin, but only the Latin version is digitized and I linked you to it on the forum. In short; there is no English version of it for you to read. Learning Latin will take a lot of time, specially the ancient Latin (which is quite difficult, you'll need to learn the abstract symbols) that the books are written in. I can point you to many many books on calculus that are very old and very classical, but I do not know whether they may be of your concern as they are highly obscure.

 

[Ankel]

Vinay, please stop being such a pest. I already told you on Genofond that Bernoulli's calculus is available in English and Latin, but only the Latin version is digitized and I linked you to it on the forum. In short; there is no English version of it for you to read. Learning Latin will take a lot of time, specially the ancient Latin (which is quite difficult, you'll need to learn the abstract symbols) that the books are written in. I can point you to many many books on calculus that are very old and very classical, but I do not know whether they may be of your concern as they are highly obscure.

But I must say, in your own language, that; Tumhari zabaan may bhot sari calculus ki kitabein hein joh bhot purani hei, agar tumhey sanskrit parni athi hai, to pher bolo.

 

[SteamKing]

Learning Latin will take a lot of time, specially the ancient Latin (which is quite difficult, you'll need to learn the abstract symbols) that the books are written in.

I'm not sure which "abstract symbols" you are talking about here. Most of the corpus of Latin literature is written in, "wait for it", the Latin alphabet. If you are reading this post, you are reading the Latin alphabet. Medieval and Renaissance Latin needs only a little training in the variations of the script used for handwriting. Printed Latin has a few tricky bits, but on the whole should be no problem to decipher.

It takes about two to three years of studying Latin in school to get familiar with the grammar and the syntax.

 

[Vinay080]

Vinay080, I have to ask, why are you so interested in these old books? ...Is it just out of interest or are you part of a museum or something? I think it is a most interesting topic to be researching.

<< Post edited by Mentors >>

How these old books are connected to my goal is completely different story; I have a map for doing that (my current age, 19), I want to study brain, to understand in depth, I need to understand Quantum Mechanics, for that I need to understand mathematics perfectly well, for that primarily I need to understand calculus well, for that I need to solve some of the philosophical questions (for example, definitions, axioms, infinitesimals, points, etc); Leibniz seems to have resisted all attacks on him against his infinitesimal concept, to undersand how he resisted, what gave him enthusiasm, to understand calculus well, I need to go into the minds of Leibniz and others of antiquity; the best way to do that is to read their own works rather than the diluted now-gen books.

 

[Vinay080]

I can point you to many many books on calculus that are very old and very classical, but I do not know whether they may be of your concern as they are highly obscure.

Thank you for the time of your short human life. I will be happy, if you can post the "first" few Leibnizian calculus books involving the expalnation of integral calculus. I am also studying Newton's book on quadrature of curves, but, I want to understand Leibnizian views...

 

[Vinay080]

@verty: Wow.. I really like the book "Analytical institutions" (which you named before), I am seeing the "Advertisment by the Editor" of it now, that itself seems impressive...

 

[verty]

<< Quoted Post edited by Mentors >>

How these old books are connected to my goal is completely different story; I have a map for doing that (my current age, 19), I want to study brain, to understand in depth, I need to understand Quantum Mechanics, for that I need to understand mathematics perfectly well, for that primarily I need to understand calculus well, for that I need to solve some of the philosophical questions (for example, definitions, axioms, infinitesimals, points, etc); Leibniz seems to have resisted all attacks on him against his infinitesimal concept, to undersand how he resisted, what gave him enthusiasm, to understand calculus well, I need to go into the minds of Leibniz and others of antiquity; the best way to do that is to read their own works rather than the diluted now-gen books.

I personally think it is wrong to ignore that each of us is different. We grew up with different experiences, faced different challenges, believe different things. We are now in the information age where the similar news is shown everywhere but I think it is wrong to think that you understand people from elsewhere because you see some news from where they are.

An example is Vietnam. You may think you know about Vietnam because you can read about Diem and the war and the Viet Cong and you can understand them. But I think you can't because their experience is so different. For example, they distrust market economies, they believe they cause people to become selfish. So if you were talking to a Vietnamese person, they would act strangely to you because they would want you to show that you aren't selfish. Now because of what I've written here, do you think you understand them? Surely not, right? Even living there, you couldn't really understand.

Or look at the apartheid struggle in South Africa, do you really think you can read "The Long Walk to Freedom" and know what it was like? Surely not, right? You can't know what it was like to live in a hut built out of corregated iron while the rich white folks have movie theatres and beaches and parks and golf courses. No one can know that. Or what it was like to refuse to give up your seat on the bus and start a whole series of riots, etc. Or for example, the march on Washington where they assembled at the Washington Monument, who can know what that felt like to those who were never seen as important but were now important? Or how it felt to Russians when Boris Nemtsov was shot on that bridge?

You can never get into the mind of another, you only have your own experiences and that makes you who you are. I definitely disagree that one can read and know. I feel pretty strongly on this as you can tell. I think it denigrates people's feelings to say "I know what you mean" because you have read some book, that is simply absurd.

Anyhow, I think you are from Pakistan or perhaps Kashmir and how can we know what living there was like? We can't. I think I've made my point.

 

[Ankel]

<< Quoted Post edited by Mentors >>

How these old books are connected to my goal is completely different story; I have a map for doing that (my current age, 19), I want to study brain, to understand in depth, I need to understand Quantum Mechanics, for that I need to understand mathematics perfectly well, for that primarily I need to understand calculus well, for that I need to solve some of the philosophical questions (for example, definitions, axioms, infinitesimals, points, etc); Leibniz seems to have resisted all attacks on him against his infinitesimal concept, to undersand how he resisted, what gave him enthusiasm, to understand calculus well, I need to go into the minds of Leibniz and others of antiquity; the best way to do that is to read their own works rather than the diluted now-gen books.

You may not be able to understand Quantum Mechanics, nobody can. It is perhaps impossible, if not ridiculously difficult, to understand it completely. The likes of Einstein, Feynman, Dirac, Schroedinger, Pauli, De Broglie and Planck were themselves perplexed by Quantum Mechanics, it also led Feynman to utter the famous quote, "I think I can say safely that nobody understands quantum mechanics."

However; you may proceed onto your journey if you wish. But remember, the greatest question of them all is "Why does the Universe exist?" - This question, although it may remain unanswerable for the rest of our lives and the lives of our descendants, it may be answered through a correct theory of quantum gravity (the candidates include String Theory and Loop Quantum Gravity). String Theory proposes that there is no beginning, and neither is there an end, that before the Big Bang, there existed another universe which steadily contracted into a point and imploded for reasons beyond our comprehension, leading to the creation of another Universe and that is the one we exist in.

I would suggest that you embark onto your journey into understanding String Theory/Loop Quantum Gravity instead. And for that, you need a lot of mathematics. And you need modern mathematics with modern notation; If you learn all of calculus from old books like Newton and Bernoulli, you will soon hit a wall. Trust me, something similar to this has happened to me before.

 

[Ankel]

I personally think it is wrong to ignore that each of us is different. We grew up with different experiences, faced different challenges, believe different things. We are now in the information age where the similar news is shown everywhere but I think it is wrong to think that you understand people from elsewhere because you see some news from where they are.

An example is Vietnam. You may think you know about Vietnam because you can read about Diem and the war and the Viet Cong and you can understand them. But I think you can't because their experience is so different. For example, they distrust market economies, they believe they cause people to become selfish. So if you were talking to a Vietnamese person, they would act strangely to you because they would want you to show that you aren't selfish. Now because of what I've written here, do you think you understand them? Surely not, right? Even living there, you couldn't really understand.

Or look at the apartheid struggle in South Africa, do you really think you can read "The Long Walk to Freedom" and know what it was like? Surely not, right? You can't know what it was like to live in a hut built out of corregated iron while the rich white folks have movie theatres and beaches and parks and golf courses. No one can know that. Or what it was like to refuse to give up your seat on the bus and start a whole series of riots, etc. Or for example, the march on Washington where they assembled at the Washington Monument, who can know what that felt like to those who were never seen as important but were now important? Or how it felt to Russians when Boris Nemtsov was shot on that bridge?

You can never get into the mind of another, you only have your own experiences and that makes you who you are. I definitely disagree that one can read and know. I feel pretty strongly on this as you can tell. I think it denigrates people's feelings to say "I know what you mean" because you have read some book, that is simply absurd.

Anyhow, I think you are from Pakistan or perhaps Kashmir and how can we know what living there was like? We can't. I think I've made my point.

Me and Vinay are Indian and India is perfectly fine with no such problems, it is infact turning into a very modern society. The situation is much worse in Pakistan. It used to be a very beautiful country, but that all changed when in the 70s, the president allowed Afghani refugees to live in Pakistan. And since they have a very "commanding" nature, they destructed the country into chaos. Pakistan, from the 40s to 70s, was prospering at a very rapid rate. Even religion was slowly dying out because the urge to understand science was growing throughout the nation and it was only beginning to produce geniuses like Abdus Salam, and then suddenly...the president permitted the Afghani refugees to invade the country, then... the rest is history. I can safely say that this was arguably the greatest mistake ever committed in the history of this unfortunate nation, and I am sure many Pakistani's will agree with me.

 

[berkeman]

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