Folio Archives 335: Principia Mathematica by Isaac Newton 2008
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1wcarter
Principia Mathematica: Mathematical Principles of Natural Philosophy by Sir Isaac Newton - 2008
If you have any interest in science or mathematics, then this book is for you. If not, it is probably a pass.
The Principia, Newton’s grand opus, was written in Latin and first published in 1687. That a book on science and mathematics is still relevant almost 350 years later is extraordinary. It is one of the most important scientific books ever published and covers everything from gravitation theory and laws of planetary motion to geometry and an early form of calculus. It resulted in a great revolution in scientific study and set the foundation for future scientific advances. The fact that Stephen Hawking wrote the introduction to the Guide shows just how important this book is to science.
Published as two volumes.
Principia Mathematica
A translation of the Principia from the Latin by Bernard Cohen, Anne Whitman and Julia Buzenz. There are 16 colour plates and numerous integrated diagrams in its xxx + 494 pages.
A Guide To The Principia Mathematica
Written by Bernard Cohen, this explanatory volume is introduced by Stephen Hawking and there are contributions by Michael Nauenberg and George E. Smith. There are a few integrated diagrams in its xxvii + 385 pages.
Both volumes are bound in black cloth with silver and colour solar system decorations to the covers. They have black endleaves and a black two volume slipcase that measures 26.2x18.4x8.9cm.
An index of the other illustrated reviews in the "Folio Archives" series can be viewed here.
If you have any interest in science or mathematics, then this book is for you. If not, it is probably a pass.
The Principia, Newton’s grand opus, was written in Latin and first published in 1687. That a book on science and mathematics is still relevant almost 350 years later is extraordinary. It is one of the most important scientific books ever published and covers everything from gravitation theory and laws of planetary motion to geometry and an early form of calculus. It resulted in a great revolution in scientific study and set the foundation for future scientific advances. The fact that Stephen Hawking wrote the introduction to the Guide shows just how important this book is to science.
Published as two volumes.
Principia Mathematica
A translation of the Principia from the Latin by Bernard Cohen, Anne Whitman and Julia Buzenz. There are 16 colour plates and numerous integrated diagrams in its xxx + 494 pages.
A Guide To The Principia Mathematica
Written by Bernard Cohen, this explanatory volume is introduced by Stephen Hawking and there are contributions by Michael Nauenberg and George E. Smith. There are a few integrated diagrams in its xxvii + 385 pages.
Both volumes are bound in black cloth with silver and colour solar system decorations to the covers. They have black endleaves and a black two volume slipcase that measures 26.2x18.4x8.9cm.
An index of the other illustrated reviews in the "Folio Archives" series can be viewed here.
3DMulvee
I found the Guide to Principia Mathematica to be very dull. If you were looking to translate the main work from Latin to English then this would be useful, but I really struggled to read it. A two volume set looks more attractive than a one volume set, but this wasn’t well done. I think a second volume by a mathematician going through every proposition and stating which proofs are accurate and which are wrong (and explaining why), would be far more useful. I think this is ripe for another company to do a much better version
4astropi
>3 DMulvee: Well, if you ever want to trade let me know! I'd like to find a copy especially to read the secondary volume. By the way, you might find this interesting -
https://www.jstor.org/stable/301652
https://www.jstor.org/stable/301652
5DMulvee
>4 astropi: Well I need another company to do a better version first! From memory it took me 10 months to read the Guide. I was motivated and am a quick reader but I really struggled for the majority of the work as it isn’t relevant to a layman who is a fan of science history, but would be more appropriate for someone who was considering translating their own version. The final 100-150 pages were good, and it stated that there were errors in some of Newton’s proofs - but this would have been the more interesting part, a book that talked about the impact, success and failures of Newton’s work rather than focus on details that failed to inspire.
The other thing I took away is how much reliance there was in geometry and Euclid. I bought a copy of Euclid’s Elements (Kronecker Wallis) and thought I should read this before embarking on the main work itself
The other thing I took away is how much reliance there was in geometry and Euclid. I bought a copy of Euclid’s Elements (Kronecker Wallis) and thought I should read this before embarking on the main work itself
6jroger1
>1 wcarter: “If you have any interest in science or mathematics, then this book is for you. If not, it is probably a pass.”
If I might be permitted to put on my professorial hat for a moment — Many people seem to believe that we should all be literate in history so we won’t repeat it; and in literature and the arts for our cultural awareness; and in psychology and sociology so we can learn about ourselves and others. But I would argue that no one can lay claim to a well-rounded education without a familiarity with science and mathematics. As President Kennedy said: “We choose to go to the moon not because it is easy but because it is hard.”
If I might be permitted to put on my professorial hat for a moment — Many people seem to believe that we should all be literate in history so we won’t repeat it; and in literature and the arts for our cultural awareness; and in psychology and sociology so we can learn about ourselves and others. But I would argue that no one can lay claim to a well-rounded education without a familiarity with science and mathematics. As President Kennedy said: “We choose to go to the moon not because it is easy but because it is hard.”
7DMulvee
>6 jroger1: This implies that you have read the work. I haven’t met anyone previously who has gotten through it. Could you give a review for those of us who have it at the bottom of their TBR pile, in case we need a prod to move it further up our lists?
8jroger1
>7 DMulvee:
I wish I could say I have read all of Newton or all of Euclid or all of Fourier or Apollonius, but it is enough for most people to dip their toes into these works. I haven’t read all of Shakespeare either, but I feel I’ve read enough to have an understanding of his talent and importance.
There is something in Western culture that says it’s okay to be illiterate in mathematics, and we pass this belief on to our kids with statements like “it’s okay, I wasn’t good in math either” or “you don’t need to study calculus to be a lawyer” when most supposedly well-educated people would never say those things about Dickens or Plato.
I wish I could say I have read all of Newton or all of Euclid or all of Fourier or Apollonius, but it is enough for most people to dip their toes into these works. I haven’t read all of Shakespeare either, but I feel I’ve read enough to have an understanding of his talent and importance.
There is something in Western culture that says it’s okay to be illiterate in mathematics, and we pass this belief on to our kids with statements like “it’s okay, I wasn’t good in math either” or “you don’t need to study calculus to be a lawyer” when most supposedly well-educated people would never say those things about Dickens or Plato.
9English-bookseller
>8 jroger1: I assume that we humans once past early childhood can usually communicate well with others if there is a common language.
I suspect that mathematical ability is not so commonly inherited or learned.
It is not OK to be innumerate as it rules out many well paid jobs and makes dealing with life a bit more challenging.
I suspect that mathematical ability is not so commonly inherited or learned.
It is not OK to be innumerate as it rules out many well paid jobs and makes dealing with life a bit more challenging.
10cpg
>1 wcarter: "If you have any interest in science or mathematics, then this book is for you."
Not necessarily. Many STEM professionals get along just fine without reading it, relying instead on those who stood on Newton's shoulders.
Not necessarily. Many STEM professionals get along just fine without reading it, relying instead on those who stood on Newton's shoulders.
11coynedj
>8 jroger1: >9 English-bookseller: I actually studied calculus at a later age. I have said many times that if I had known how useful it is, even just in concept if not in doing the calculations, I would have paid more attention in my college class. Unfortunately, the professor presented it as an intellectual exercise without mentioning how widepread it's uses are.
12jroger1
>10 cpg:
Admittedly, engineers can build bridges and design aircraft after studying the “cliff notes” of their profession (i.e., textbooks). But if they have any curiosity about where it all came from, they need to read some of the original work.
Admittedly, engineers can build bridges and design aircraft after studying the “cliff notes” of their profession (i.e., textbooks). But if they have any curiosity about where it all came from, they need to read some of the original work.
13jroger1
>11 coynedj:
Unfortunately, a dichotomy has developed in the math departments of our universities between those who teach “pure mathematics” without regard to its usefulness and those who teach “applied mathematics.” Sometimes it seems that these two camps of professors don’t have much respect for the work of the other camp.
Unfortunately, a dichotomy has developed in the math departments of our universities between those who teach “pure mathematics” without regard to its usefulness and those who teach “applied mathematics.” Sometimes it seems that these two camps of professors don’t have much respect for the work of the other camp.
14kermaier
Speaking of this edition itself, rather than of the content or context, I would say that the color plates badly miss the mark. They are unattractive, irrelevant, uninspiring and generally detract from the elegant clarity of edition overall. I find them so disagreeable, that I've actually contemplated using a razor to excise them from the book -- which wouldn't even leave a gap in the page numbers, as FS didn't bother to include them in the numbering.
15gmacaree
Even if you have an advanced education in maths (I do!), reading Newton or Euclid is very challenging. The notation and process is extremely different to what's taught today, which is what makes their work so interesting — they're key milestones in the evolution of mathematical language which we tend to take as immutable. Going through Principia in particular reminded me of reading Chaucer in Middle English.
>14 kermaier: Agreed.
>14 kermaier: Agreed.
16jroger1
>14 kermaier:
Actually, I don’t find the illustrations objectionable. In fact, some are rather clever in the way they illustrate the text. For example, when he writes about rays of light, the illustration is of a rainbow. A passage about fluids under pressure gets a photo of a geyser. His proposition about the velocity of waves is illustrated by an ocean wave, and a quotation about the orbits of Jupiter’s satellites is illustrated by a photo of Jupiter with its satellites.
They might not be the most beautiful illustrations FS has published, but they are appropriate to the text.
Actually, I don’t find the illustrations objectionable. In fact, some are rather clever in the way they illustrate the text. For example, when he writes about rays of light, the illustration is of a rainbow. A passage about fluids under pressure gets a photo of a geyser. His proposition about the velocity of waves is illustrated by an ocean wave, and a quotation about the orbits of Jupiter’s satellites is illustrated by a photo of Jupiter with its satellites.
They might not be the most beautiful illustrations FS has published, but they are appropriate to the text.
17cpg
>13 jroger1:
Advanced mathematical textbooks and modern research monographs are not the equivalent of Cliff notes. The former tend to be written to a higher standard of completeness, clarity, and logicality than math texts written before the modern era.
The dividing line between scholars who think we should spend time reading Principia and those who don't is not one that separates pure mathematicians from applied mathematicians. At best, it separates some historians of mathematics from the vast majority of research mathematicians, pure or applied.
I may be able to elaborate further on that last point after reviewing my notes from the semester that I taught our History of Math class. For now, I will just pick and choose some comments from Niccolo Guicciardini's article on the Principia published in Landmark Writings in Western Mathematics, 1640-1940. (A gorgeous book with a lovely sewn binding!)
Guicciardini is obviously a big fan of the Principia, but he makes some comments that help explain why not everyone is:
"To evaluate the impact of the Principia is a momentous task. From one point of view, one could say that its influence has not expired yet, since Newtonian mechanics is still adopted in many fields of science and since many problems faced by Newton--such as the three-body problem--are still open questions. However, such a statement is possible only by underevaluating the changes in the conceptions of mechanical principles, and the sophistication of mathematical techniques, that occurred after Newton's death."
"Basic concepts, such as the conservation of the angular momentum (of a system of particles) and the conservation of energy, were lacking from the Principia. Indeed, several mistakes that Newton did in studying rigid and fluid body dynamics . . . were due to his lack of understanding of these fundamental principles."
"The mathematical language in which Newton wrote his work became soon obsolete."
"In dealing with advanced topics, Newton had employed obscure, even flawed, mathematical methods."
After the work of Euler, d'Alembert and Lagrange, "the Principia's mathematical methods ceased to be of interest for practising mathematicians."
Advanced mathematical textbooks and modern research monographs are not the equivalent of Cliff notes. The former tend to be written to a higher standard of completeness, clarity, and logicality than math texts written before the modern era.
The dividing line between scholars who think we should spend time reading Principia and those who don't is not one that separates pure mathematicians from applied mathematicians. At best, it separates some historians of mathematics from the vast majority of research mathematicians, pure or applied.
I may be able to elaborate further on that last point after reviewing my notes from the semester that I taught our History of Math class. For now, I will just pick and choose some comments from Niccolo Guicciardini's article on the Principia published in Landmark Writings in Western Mathematics, 1640-1940. (A gorgeous book with a lovely sewn binding!)
Guicciardini is obviously a big fan of the Principia, but he makes some comments that help explain why not everyone is:
"To evaluate the impact of the Principia is a momentous task. From one point of view, one could say that its influence has not expired yet, since Newtonian mechanics is still adopted in many fields of science and since many problems faced by Newton--such as the three-body problem--are still open questions. However, such a statement is possible only by underevaluating the changes in the conceptions of mechanical principles, and the sophistication of mathematical techniques, that occurred after Newton's death."
"Basic concepts, such as the conservation of the angular momentum (of a system of particles) and the conservation of energy, were lacking from the Principia. Indeed, several mistakes that Newton did in studying rigid and fluid body dynamics . . . were due to his lack of understanding of these fundamental principles."
"The mathematical language in which Newton wrote his work became soon obsolete."
"In dealing with advanced topics, Newton had employed obscure, even flawed, mathematical methods."
After the work of Euler, d'Alembert and Lagrange, "the Principia's mathematical methods ceased to be of interest for practising mathematicians."
18jroger1
>17 cpg:
My remark about textbooks being the equivalent of Cliff Notes was tongue in cheek, or at least partially so. Math textbooks, especially advanced ones, are little more than a catalog of theorems and proofs followed by another theorem and proof, and so on and on, with little or no explanation of why we should care. Either that or they describe a problem and then show how to solve it without really explaining why the procedure works. Neither of these two kinds of textbooks is inspiring or even very enlightening.
Scientific American printed an article a few years ago asking how an airplane can fly. Engineers are very adept at following the formulas they learned from textbooks and then, lo and behold, the aircraft flies. But that process misses the nub of the issue — how can those formulas make such a heavy thing get off the ground?
Maybe I’m being too philosophical and should blindly follow the rules, but I’m not made that way. Newton showed us how to build a physics and a calculus from the ground up, something today’s textbooks don’t even attempt to do, and students are missing out on a fundamental understanding of their profession.
I taught mathematics from middle school through graduate school, but I don’t claim to be a mathematician because I didn’t do any original work in the field. My specialty was the history of mathematics.
My remark about textbooks being the equivalent of Cliff Notes was tongue in cheek, or at least partially so. Math textbooks, especially advanced ones, are little more than a catalog of theorems and proofs followed by another theorem and proof, and so on and on, with little or no explanation of why we should care. Either that or they describe a problem and then show how to solve it without really explaining why the procedure works. Neither of these two kinds of textbooks is inspiring or even very enlightening.
Scientific American printed an article a few years ago asking how an airplane can fly. Engineers are very adept at following the formulas they learned from textbooks and then, lo and behold, the aircraft flies. But that process misses the nub of the issue — how can those formulas make such a heavy thing get off the ground?
Maybe I’m being too philosophical and should blindly follow the rules, but I’m not made that way. Newton showed us how to build a physics and a calculus from the ground up, something today’s textbooks don’t even attempt to do, and students are missing out on a fundamental understanding of their profession.
I taught mathematics from middle school through graduate school, but I don’t claim to be a mathematician because I didn’t do any original work in the field. My specialty was the history of mathematics.
19cpg
>18 jroger1:
1) After posting my #17 above, I did a little Googling which left me with the impression that I have unfairly understated the number of mathematicians who find value in reading the premodern authors.
2) I still don't agree that Newton did a better job of building calculus from the ground up than modern authors do. (Or even than I'll do when the semester starts in a few weeks. Ghosts of Departed Quantities will be exorcised from my classroom!)
3) I think there's a sort of "Ontogeny Recapitulates Philogeny" question in the teaching of mathematics. Roughly: Should mathematical concepts be taught to an individual student in the chronological order that mankind discovered those concepts? In the course I referred to in (2), I do intend to present not just the real numbers but other number systems that have been used to mathematically model the line. And in an introductory functional analysis class I'll be teaching in an upcoming semester, I won't be able to resist sharing historical vignettes from the phenomenal (Smyth Sewn!) History of Banach Spaces and Linear Operators. But for the most part, I want to present the simplest known rigorous approaches in my classes, and (in my opinion) those tend to be modern.
4) Probably the last Smyth Sewn book I'll refer to in this thread is Physics for Mathematicians. I am embarrassed about how little of this book I've read. Previous to today, the main thing I could say about it is that it is a rip-off that Spivak passed away before he was able to publish further volumes. But my Googling today reminded me that Spivak starts out this book by spending 50-odd pages interpreting the Principia!
1) After posting my #17 above, I did a little Googling which left me with the impression that I have unfairly understated the number of mathematicians who find value in reading the premodern authors.
2) I still don't agree that Newton did a better job of building calculus from the ground up than modern authors do. (Or even than I'll do when the semester starts in a few weeks. Ghosts of Departed Quantities will be exorcised from my classroom!)
3) I think there's a sort of "Ontogeny Recapitulates Philogeny" question in the teaching of mathematics. Roughly: Should mathematical concepts be taught to an individual student in the chronological order that mankind discovered those concepts? In the course I referred to in (2), I do intend to present not just the real numbers but other number systems that have been used to mathematically model the line. And in an introductory functional analysis class I'll be teaching in an upcoming semester, I won't be able to resist sharing historical vignettes from the phenomenal (Smyth Sewn!) History of Banach Spaces and Linear Operators. But for the most part, I want to present the simplest known rigorous approaches in my classes, and (in my opinion) those tend to be modern.
4) Probably the last Smyth Sewn book I'll refer to in this thread is Physics for Mathematicians. I am embarrassed about how little of this book I've read. Previous to today, the main thing I could say about it is that it is a rip-off that Spivak passed away before he was able to publish further volumes. But my Googling today reminded me that Spivak starts out this book by spending 50-odd pages interpreting the Principia!
20jroger1
>19 cpg:
I’m not against all textbooks. Indeed, the best ones organize concepts in a more logical manner than the originators did. My biggest wish is that they provide more explanatory text. I spoke with an author of a text once who claimed to agree with me, but he says the fault lies with the publishers. In an attempt to keep the page count to a minimum, thereby increasing the profit, they eliminate most of the explanatory material written by the authors because they think it unnecessary.
I’m not against all textbooks. Indeed, the best ones organize concepts in a more logical manner than the originators did. My biggest wish is that they provide more explanatory text. I spoke with an author of a text once who claimed to agree with me, but he says the fault lies with the publishers. In an attempt to keep the page count to a minimum, thereby increasing the profit, they eliminate most of the explanatory material written by the authors because they think it unnecessary.
21kermaier
>16 jroger1: Oh, I get the intended correspondences between the illustrations and the text, but I find them to be obvious and painfully literal, in a vein I'd expect from an elementary school textbook. And, given the awkward compositions and poor reproduction quality of most of the photos, I think the book would've been noticeably improved had they been simply omitted.
22treereader
The divide between pure and applied math has the same roots as the divide between physics and math, theory and application, etc. It’s been around for a long, long time because it is a natural divide. Few can truly master the breadth and depth of the tools and ideas required on both sides when evaluating a given problem. There’s just not enough time to study or practice everything so we specialize. The two sides are expected to collaborate and work as a team.
23billburden
>5 DMulvee: Can you opine on the construction of Kronecker Wallis books? How are the bindings? Are they sewn?
24DMulvee
>23 billburden: The only Kronecker Wallis I own is Euclid’s Elements. The construction is a little basic. I would guess it is glued rather than sewn. The paper quality isn’t the highest (you can see an outline of what is on the other side). However I didn’t see a better version of Euclid on the market and the continuation of Byrne’s work for all chapters meant that I am pleased with this (even given the basic construction)
25pythagoras
>24 DMulvee: My copy of the Kronecker Wallis Euclid is definitely sewn. I can see the threads.
26DMulvee
>25 pythagoras: Sorry you are right this is definitely sewn. I should have checked
27billburden
Thanks for the info! Kronecker Wallis's continuation of Byrne's work is an incredible accomplishment and a big reason to purchase the book. However, I have come across some really shoddy publishing where you go through the book once and the papers begin to fallout. So, for 200 euros, I wanted to be sure that it would at least meet basic standards.
