Translating Newton’s Principia
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Translating Newton’s Principia
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Re: Translating Newton’s Principia
#2The problem mentioned in the article (a mathematical apparatus that is completely alien to us moderns) is the opposite of that of contemporary translators. Around 1750, Émilie, marquise du Châtelet, made the first translation into French (which her lover Voltaire called "the everyday language of Europe")
As a woman, she didn't have any university education, but that wouldn't have included calculus anyway. Her problem was the modern concepts, not the old "geometric" way of reasoning about quantities. So she had to write a bulky Commentaire that really was her magnum opus
As a woman, she was completely accepted as an equal by scientists of her time, but treated rather dismissively by later historians of science. Clearly, history doesn't obey Newtons's first law: it doesn't progress in a straight line.
Re: Translating Newton’s Principia
#3The problem mentioned in the article (a mathematical apparatus that is completely alien to us moderns) is the opposite of that of contemporary translators. Around 1750, Émilie, marquise du Châtelet, made the first translation into French (which her lover Voltaire called "the everyday language of Europe") As a woman, she didn't have any university education, but that wouldn't have included calculus anyway. Her problem…
BBC Radio 4 had a wonderful episode about Emilie du Châtelet just recently. [0]
Re: Translating Newton’s Principia
#4The author's take on V.18 is interesting. Clarke has the proposition here: https://mathcs.clarku.edu/~djoyce/java/elements/bookV/propV1...
It's not three pages long in Clarke (nor in Heath), and either way, the argument is only 10 statements long.
> But the reader who takes the trouble to decode the proposition will see that it is trivial primary school arithmetic.
This is also not super obvious from Clarke or Heath. I'd love to know how the author would render this proposition trivial to a fourth grader.
To be sure, the mathematics of Euclid is a very foreign country from what's commonly taught in schools today. But Newton's thought is firmly rooted in that foreign country.
Re: Translating Newton’s Principia
#5The author's take on V.18 is interesting. Clarke has the proposition here: https://mathcs.clarku.edu/~djoyce/java/elements/bookV/propV1... It's not three pages long in Clarke (nor in Heath), and either way, the argument is only 10 statements long. > But the reader who takes the trouble to decode the proposition will see that it is trivial primary school arithmetic. This is also not super obvious from Clarke or Heath.…
> I'd love to know how the author would render this proposition trivial to a fourth grader.
Looking at the diagram in your link, and labelling AE x, EB y, CF a and FD b, "Let AE, EB, CF, and FD be magnitudes proportional taken separately, so that AE is to EB as CF is to FD. I say that they are also proportional taken jointly, that is, AB is to BE as CD is to FD.", means :
If x/y = a/b, then also (x+y) / y = (a+b) / b.
To prove this is true, operate on the second equation to make it the same as the first:
1. Expand: x/y + y/y = a/b + b/b
2. Subtract 1 from both sides: x/y = a/b. QED.
Notation really makes all the difference!
Re: Translating Newton’s Principia
#6The author's take on V.18 is interesting. Clarke has the proposition here: https://mathcs.clarku.edu/~djoyce/java/elements/bookV/propV1... It's not three pages long in Clarke (nor in Heath), and either way, the argument is only 10 statements long. > But the reader who takes the trouble to decode the proposition will see that it is trivial primary school arithmetic. This is also not super obvious from Clarke or Heath.…
> I'd love to know how the author would render this proposition trivial to a fourth grader. Looking at the diagram in your link, and labelling AE x , EB y , CF a and FD b , "Let AE, EB, CF, and FD be magnitudes proportional taken separately, so that AE is to EB as CF is to FD. I say that they are also proportional taken jointly, that is, AB is to BE as CD is to FD.", means : If x/y = a/b, then also (x+y) / y = (a+b)…
I came to the comments to say this, and you beat me to it. Its a better proof than the ones in that link, IMHO. I'm not sure why the author felt the need for all those inequalities!
Re: Translating Newton’s Principia
#7[deleted]
Re: Translating Newton’s Principia
#8Chandrashekhar's Principa For the Common Reader, is a good version for modern audiences, including insightful commentary from a modern physicist looking at it.
Re: Translating Newton’s Principia
#9Chandrashekhar's Principa For the Common Reader, is a good version for modern audiences, including insightful commentary from a modern physicist looking at it.
I can second this recommendation - it took me a while to figure out the proofs, but it was wonderful to be exposed to a whole new style of reasoning that I had only seen filtered in a very indirect way in uni physics classes. His whole approach is regarded ultimately as a too-hard-to-imitate dead-end [ people regard it as having held back physics/maths research in Oxford/Cambridge for as many decades as his style was taught, as opposed to Leibniz's calculus ], but it's still very flashy and cool.
Re: Translating Newton’s Principia
#10I found the Green Lion Press version on Newton super helpful for distilling his argument so that a modern reader could understand it.