Clairaut's "most important and profound discovery"
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From: James Dow Allen on 11 Feb 2010 05:42 One reads in http://www-history.mcs.st-andrews.ac.uk/Biographies/Clairaut.html about Alexis Clairaut's 1752 paper "Theorie de la Lune" on the three-body problem and that Euler called this "the most important and profound discovery that has ever been made in mathematics." Even allowing for a bit of hyperbole, this sounds like strong praise from Euler! Can anyone summarize Clairaut's "profound" discovery for the layman? (I tried Googling but with little luck. I did find pages like http://adsabs.harvard.edu/full/1970JHA.....1..144F By the way, what's with the format on that page? Is it supposed to be more user-friendly than pdf? Or does it have another purpose?) James Dow Allen
From: David Bernier on 11 Feb 2010 07:36 James Dow Allen wrote: > One reads in > http://www-history.mcs.st-andrews.ac.uk/Biographies/Clairaut.html > about Alexis Clairaut's 1752 paper "Theorie de la Lune" on the > three-body problem and that Euler called this > "the most important and profound discovery that has > ever been made in mathematics." > > Even allowing for a bit of hyperbole, this sounds like strong praise > from Euler! Can anyone summarize Clairaut's "profound" discovery > for the layman? From the MacTutor biography of Clairaut: "However, by the spring of 1748, Clairaut realized that the difference [...]" By spring 1748, Clairaut had revised his previous assertion that Newton's law of gravity was incorrect. The "proof" that Newton's law was incorrect had been based on an analysis of theory and observations for the motion of the moon. The moon's motion pretty much has to be treated as a three-body problem. So Clairaut figured out what had been overlooked by those (including Clairaut and Euler as approver) saying Newton's law was incorrect. Euler read about Clairaut's "short" explanation, but wasn't fully satisfied. An Academy prize problem was set on the moon's motion, and Clairaut got the prize around 1752. Then, one can suppose that Euler thought Clairaut's paper brought great progress (at least) in understanding the motion of the moon: "Euler [...] showing how frustrated he had been not solving the problem himself, wrote to Clairaut [...]" (from MacTutor). Google Books has a scan of the second edition of Clairaut's "Theorie de la lune" (1765): < http://books.google.com/books?id=U1EVAAAAQAAJ > David Bernier > (I tried Googling but with little luck. I did find pages like > http://adsabs.harvard.edu/full/1970JHA.....1..144F > By the way, what's with the format on that page? Is it > supposed to be more user-friendly than pdf? Or does it > have another purpose?) > > James Dow Allen
From: James Dow Allen on 11 Feb 2010 11:10 On Feb 11, 7:36 pm, David Bernier <david...(a)videotron.ca> wrote: > James Dow Allen wrote: > > One reads in > > http://www-history.mcs.st-andrews.ac.uk/Biographies/Clairaut.html > > about Alexis Clairaut's 1752 paper "Theorie de la Lune" on the > > three-body problem and that Euler called this > > "the most important and profound discovery that has > > ever been made in mathematics." > > > Even allowing for a bit of hyperbole, this sounds like strong praise > > from Euler! Can anyone summarize Clairaut's "profound" discovery > > for the layman? > > From the MacTutor biography of Clairaut: > [snip] > Google Books has a scan of the second edition of Clairaut's > "Theorie de la lune" (1765): > <http://books.google.com/books?id=U1EVAAAAQAAJ> You quote a slightly longer excerpt from the webpage I'd already cited. Then post a link to a 161-page pay-per-view book. I wonder if you thought you were being helpful. :-) James
From: Chip Eastham on 11 Feb 2010 11:30 On Feb 11, 11:10 am, James Dow Allen <jdallen2...(a)yahoo.com> wrote: > On Feb 11, 7:36 pm, David Bernier <david...(a)videotron.ca> wrote: > > > > > James Dow Allen wrote: > > > One reads in > > > http://www-history.mcs.st-andrews.ac.uk/Biographies/Clairaut.html > > > about Alexis Clairaut's 1752 paper "Theorie de la Lune" on the > > > three-body problem and that Euler called this > > > "the most important and profound discovery that has > > > ever been made in mathematics." > > > > Even allowing for a bit of hyperbole, this sounds like strong praise > > > from Euler! Can anyone summarize Clairaut's "profound" discovery > > > for the layman? > > > From the MacTutor biography of Clairaut: > > [snip] > > Google Books has a scan of the second edition of Clairaut's > > "Theorie de la lune" (1765): > > <http://books.google.com/books?id=U1EVAAAAQAAJ> > > You quote a slightly longer excerpt from the webpage I'd already > cited. Then post a link to a 161-page pay-per-view book. > > I wonder if you thought you were being helpful. :-) > > James I thought he was! It clarified the controversy to the point where I felt grateful sci.math is not inundated by cranks complaining about Newton's theory of gravity. Clairaut's book is in French, but it cost me nothing to download. regards, chip
From: José Carlos Santos on 11 Feb 2010 11:36
James Dow Allen escreveu: >>> One reads in >>> http://www-history.mcs.st-andrews.ac.uk/Biographies/Clairaut.html >>> about Alexis Clairaut's 1752 paper "Theorie de la Lune" on the >>> three-body problem and that Euler called this >>> "the most important and profound discovery that has >>> ever been made in mathematics." >>> Even allowing for a bit of hyperbole, this sounds like strong praise >>> from Euler! Can anyone summarize Clairaut's "profound" discovery >>> for the layman? >> From the MacTutor biography of Clairaut: >> [snip] >> Google Books has a scan of the second edition of Clairaut's >> "Theorie de la lune" (1765): >> <http://books.google.com/books?id=U1EVAAAAQAAJ> > > You quote a slightly longer excerpt from the webpage I'd already > cited. Then post a link to a 161-page pay-per-view book. > > I wonder if you thought you were being helpful. :-) I certainly understand why you don't think David Bernier was being helpful, but I don't see why you say that he posted "a link to a 161-page pay-per-view book". It is not pay-per-view. AFAIK there are no pay-per-view books at Google Books. Besides, this book in particular can also be read here: http://gallica.bnf.fr/ark:/12148/bpt6k110454w.image.r=clairaut+lune.f1.langEN Best regards, Jose Carlos Santos |