8 ms·

College Notebook of Isaac Newton

283 points by Insanity 6y ago

dr_dshiv 6y ago
"On music" is on page 288.. A little bit of psychology precedes it.
growlist 6y ago
Pages 43 and 44! Although by some accounts Newton could be pretty nasty, a quick look at this almost makes me feel sorry for him given the advancement of his mind versus the state of knowledge at the time. Perhaps though he was in his element at that time, when so much was up for grabs.
- Aeolun 6y ago
  Looks like he was having fun to me.
- Jenz 6y ago
  http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/43 http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/43
screpy 6y ago
Why do they tell us about this process in schools only with an apple fall? Actually, there is a lot of effort behind it and we ignore it.
- loopz 6y ago
  Because success is either inherited or magical! That's the narrative, anyways. Of course, the people telling the narrative have success in telling the narrative, not the actual success!
- ponker 6y ago
  This has always been the dumbest Eureka myth because... Isaac Newton only noticed that shit falls downwards when an apple fell on his head?! If it was something that gave him some insight into the mechanism... like two differe tobjects falling at the same time and landing at the same time, causing him to think about force and mass etc... that would make much more sense.
  - stan_rogers 6y ago
    As it was relayed, the apple thing was the moment that he realised that the mysterious force holding the celestial objects in their orbits was exactly the same force as gravity. It's not that gravity was a new concept or anything. In fact, it goes back so far in our history that we still use the silly name "gravity" for the phenomenon; it was once though to be a property of an object or an element (in the "four elements" sense), and was opposed by another property called "levity". You will note that there is no current theory of levity. Galileo had already put numbers to gravity on Earth by that point, and the idea that the force holding things in their orbits acted according to an inverse square law was circulating before Newton got there. (There's no reason to believe he couldn't have come to that conclusion independently, but there's no reason to credit it to him either.) What was missing was the connection; the generalization. That's not obvious in any way. How do you get an inverse square law to work with Galilean gravity? It smacks of equants and deferents until you find a way to put the effective mass of a body, such as the Earth, at its centre. Imagine a world in which there's some inverse square force thingy holding the moon and planets in their orbits, and there's gravity and you know how that works, and nobody has even the slightest notion that they're in any way related. And then you have the OFFS moment.
    - emmelaich 6y ago
      Was there really a property proposed called levity? I thought that that was only mentioned in parodies of Newton. e.g. https://www.sciencephoto.com/media/363707/view/caricature-of-newton-s-laws-of-gravity- https://www.sciencephoto.com/media/363707/view/caricature-of...
      - stan_rogers 6y ago
        Yes, and it goes back at least as far as Aristotle (although he would have used a rather Greeker word). Levity would have been a property of fire and air in Aristotelian physics, where gravity was a property of earth and water.
  - JProthero 6y ago
    This is only partly a myth; there are contemporary accounts from Newton's acquaintances noting how he described being inspired by observing the fall of an apple from a tree. It was the fact that an apple falls from a tree specifically in the direction of the Earth's centre that was said to have piqued his curiosity. The apple falling on his head seems to have been a later embellishment.
- wenc 6y ago
  It's too bad the apple story is the only one the public imagination latched on to. Newton was so much more than that. Granted a lot of his discoveries were hard to explain without math, but he deserves a lot more credit for human history. I bet writers of children's stories had a hard time explaining Euler too. But somehow they managed to insert Einstein into the public imagination. And almost no one I know understands the photoeletric effect or the theory of relativity. I myself have the vaguest of understandings.
  - scollet 6y ago
    The end product is something successful I think. A series of children's books focused on the histories of physics, maths, philosophy, etc. while showing how each generation stands on the previous giants' shoulders would be stellar.
  - croissants 6y ago
    Unfounded conjecture: photos matter a lot. Especially when the photos of Einstein make him look like a kooky grandpa and the images of Newton make him look like a stiff, stern cartoon.
- deleted 6y ago
  [deleted]
abhayhegde 6y ago
He was certainly having fun! A refreshing peek through his mind. Whenever I mention the likes of Newton and their works, I frequently get attacked by some people. Their argument is that Newton was a terrible human being and despite his contributions to Science, Mathematics, and the process of discoveries in general, he does not deserve praise since appraisal implies we would be condoning his behavior. To that I usually reply, we would never accept some of his behaviors now and that does not mean his contributions are worthless. They believe we can never separate the "works" from a "person", to which I always disagree. EDIT: Grammar.
- batsigner 6y ago
  What is the point of your comment?
  - max_ 6y ago
    That being a human being that adds value to society does not require everyone to like you.
    - watwut 6y ago
      "Not everyone liked him" is sort of understatement. We can accept and celebrate his contributions without pretending that the dislike for Newton was all about some mild unlikability.
      - bryanrasmussen 6y ago
        I guess I'm in the medium unlikability school. I mean, he seems as unlikable as a significant number of programmers who are not Isaac Newton despite pretensions to equivalent accomplishment. https://inversesquare.wordpress.com/2008/03/21/friday-isaac-newton-blogging-how-mean-was-he/ https://inversesquare.wordpress.com/2008/03/21/friday-isaac-... on edit: meaning some programmers are not quick to make friends, and are not convivial, perhaps due to some neuro-atypical qualities, which I expect was probably the case with Newton. Not that programmers condemn people to death as their jobs generally do not require it.
sbr464 6y ago
You can download higher resolution versions of the notebook pages by using a dezoooming tool[1] on the image tiles. This example[2] generates a 4898×7711 png compared to a 1270×2000 jpg from the download link[3]. [1]: https://github.com/lovasoa/dezoomify https://github.com/lovasoa/dezoomify [2]: https://ophir.alwaysdata.net/dezoomify/dezoomify.html#https://images.lib.cam.ac.uk/content/images/MS-ADD-03969-001-00001_files/13/0_0.jpg https://ophir.alwaysdata.net/dezoomify/dezoomify.html#https:... [3]: https://images.lib.cam.ac.uk/content/images/MS-ADD-03969-001-00001.jpg https://images.lib.cam.ac.uk/content/images/MS-ADD-03969-001...
max_ 6y ago
Is that a "Hand" doodle? http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/15 http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/15
- pvida 6y ago
  It certainly seems so. I love how simple-yet-not-too-simple it is.
  - jq-r 6y ago
    It is the exactly the same hand symbol Henry VIII used to mark down interesting passages in Bible which he hoped would help him to annul his marriage to Catherine of Aragon.
    - ian0 6y ago
      Apparently called an index or manicule with examples spotted from the 12th century.. https://en.wikipedia.org/wiki/Index_(typography) https://en.wikipedia.org/wiki/Index_(typography)
      - lioeters 6y ago
        Delightful! I'd say this manicule is a proto-emoji of sorts. > Thomas Pynchon parodies this punctuation mark in his novel Gravity's Rainbow by depicting a middle finger, rather than an index finger, pointing at a line of text.
- runawaybottle 6y ago
  Newton used emojis??
- katzgrau 6y ago
  Came here for this comment :) Saw the hand and that immediately became my favorite thing in the notebook.
max_ 6y ago
Any possibility to have this typed & formatted for easy reading?
hank_z 6y ago
Any modern text recognition technology is applicable to his handwriting?
bra-ket 6y ago
The funny thing about Newton is that he was treating pseudo-science like alchemy with the same level of seriousness as actual science he helped advance so much. https://en.m.wikipedia.org/wiki/Isaac_Newton%27s_occult_studies#Alchemical_research https://en.m.wikipedia.org/wiki/Isaac_Newton%27s_occult_stud...
- beenBoutIT 6y ago
  Alchemy wasn't scientifically disproven until the 19th century, so Newton had no choice but to explore it. If transforming base metals to gold was scientifically plausible and illegal(as it was in Newton's day) most of us on this board would be chasing after it at full speed right now.
  - ip26 6y ago
    Making matters worse, nuclear fusion practically is alchemy.
    - redwall_hp 6y ago
      I've always thought there was something poetic about that. The ancient Greeks gave us the name "atom," the indivisible unit. The alchemists chased the goal of breaking down base metals (splitting the atom) and transmuting the components into gold. Then in the 20th century, the physics were finally mapped out. The atom was split, unveiling the subatomic world, and we know full well that atoms can be fused. The term "transmutation" is even used. It's like an ancient quest finally reached a conclusion, albeit not in the convenient way they would have hoped.
      - lioeters 6y ago
        Some of the scientists working on the Manhattan Project were certainly aware of associations with mythological themes. > Oppenheimer later recalled that, while witnessing the explosion, he thought of a verse from the Hindu holy book, the Bhagavad Gita: > "If the radiance of a thousand suns were to burst at once into the sky, that would be like the splendor of the mighty one." I'm fond of mythopoetic perspectives on technology, to find parallels in texts from the antiquities or the Renaissance. From their point of view, we in the modern world must seem to live like magicians, communicating over vast distances, peering into our "looking glass".
noisy_boy 6y ago
Idle thought: imagine if Newton examined modern programming and said "let me show you a new approach I've been thinking about for a while ..."
rutherblood 6y ago
that handwriting is surprisingly legible
alister 6y ago
Page 32: > At which time I found that method of Infinite series. And in summer 1665 being forced from Cambridge by the Plague I computed the area of the Hyperbola of Boothby in Lincolnshire to two & fifty figures by the same method. [signed] Is. Newton He made a signed statement of his discovery just as in a 20th century engineer's/inventor's notebook. The mention of being forced from Cambridge because of the plague makes me wonder if some great discoveries are being made right now because many bright minds have been forced home by coronavirus.
- josh_fyi 6y ago
  What looks like y^2 (or superscript 2) is an abbreviation for "the".
  - alister 6y ago
    Thank you, I've corrected it. It raises the question of why anyone bothered with a 2 symbol abbreviation for just 3 letters.
    - MLR 6y ago
      Old English had a letter called thorn that would eventually be replaced with the modern th or a y (ye olde is just said the old). The y^e form was apparently used for the King James Bible in 1611 so it's plausible it might still have been a normal way of writing "the" as late as 1650, rather than as an affectation or abbreviation. Edit: He also uses y^t for that which I hadn't noticed at first glance.
    - jabirali 6y ago
      You could raise the same question about many historic ligatures, like abbreviating "et" to "&" in Latin?
  - LadyCailin 6y ago
    It's such a long word, makes sense to abbreviate it.
- 6y ago
vansul 6y ago
I love this book. They currently have his 1659-61 notebook on display at the Fitzwilliam Museum in Cambridge (scan available at [0]) Its opened on a page titled ‘Otiose et frustra expensa’ (Idle and vain expenses) where he lists his snack binges (including ‘cheries’, ‘Tarte’, ‘Marmolet’, ‘Custardes’, and ‘Cake bred). [0] https://mss-cat.trin.cam.ac.uk/manuscripts/uv/view.php?n=R.4.48c&n=R.4.48c#?c=0&m=0&s=0&cv=51&xywh=-1483%2C-2%2C5173%2C2778 https://mss-cat.trin.cam.ac.uk/manuscripts/uv/view.php?n=R.4...
dr_dshiv 6y ago
Newton credited the discovery of the inverse square law of gravity to Pythagoras (5th century BC), just as Coperinicus had credited heliocentrism to him. Here is Newton's argument: "For Pythagoras, as Macrobius avows, stretched the intestines of sheep or the sinews of oxen by attaching various weights, and from this learned the ratio of the celestial harmony. Therefore, by means of such experiments he ascertained that the weights by which all tones on equal strings .. were reciprocally as the squares of the lengths of the string by which the musical instrument emits the same tones. But the proportion discovered by these experiments, on the evidence of Macrobius, he applied to the heavens and consequently by comparing those weights with the weights of the Planets and the lengths of the strings with the distances of the Planets, he understood by means of the harmony of the heavens that the weights of the Planets towards the Sun were reciprocally as the squares of their distances from the Sun." This article has more: https://royalsocietypublishing.org/doi/10.1098 https://royalsocietypublishing.org/doi/10.1098
- philzook 6y ago
  That's an interesting suggestion I've never heard before, but your link appears to be down. I'm getting a 404. Is it possible this passage is referring to the reciprocal Pythagorean theorem? https://en.wikipedia.org/wiki/Pythagorean_theorem#Reciprocal_Pythagorean_theorem https://en.wikipedia.org/wiki/Pythagorean_theorem#Reciprocal...
  - anticsapp 6y ago
    I believe this is the article: https://muse.jhu.edu/article/495241 https://muse.jhu.edu/article/495241 I can't get a sci-hub for it though.
  - dr_dshiv 6y ago
    https://royalsocietypublishing.org/doi/10.1098/rsnr.1966.0014 https://royalsocietypublishing.org/doi/10.1098/rsnr.1966.001... My apologies, here is the article and citation. And no, not the reciprocal Pythagorean theorem -- learning about Pythagoreanism is a real rabbit hole, highly recommended :) McGuire, J. E., & Rattansi, P. M. (1966). Newton and the ‘Pipes of Pan’. Notes and records of the Royal Society of London, 21(2), 108-143.
deleted 6y ago
[deleted]
yitchelle 6y ago
It is remarkable that there are not alot corrections among the written text. The text is extremely readable and understanble, even for a non-mathematician like me.

283 points by Insanity 6y ago

"On music" is on page 288.. A little bit of psychology precedes it.

Pages 43 and 44! Although by some accounts Newton could be pretty nasty, a quick look at this almost makes me feel sorry for him given the advancement of his mind versus the state of knowledge at the time. Perhaps though he was in his element at that time, when so much was up for grabs.

Aeolun 6y ago
Looks like he was having fun to me.
Jenz 6y ago
http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/43 http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/43

screpy 6y ago

Why do they tell us about this process in schools only with an apple fall? Actually, there is a lot of effort behind it and we ignore it.

loopz 6y ago
Because success is either inherited or magical! That's the narrative, anyways. Of course, the people telling the narrative have success in telling the narrative, not the actual success!
ponker 6y ago
This has always been the dumbest Eureka myth because... Isaac Newton only noticed that shit falls downwards when an apple fell on his head?! If it was something that gave him some insight into the mechanism... like two differe tobjects falling at the same time and landing at the same time, causing him to think about force and mass etc... that would make much more sense.
- stan_rogers 6y ago
  As it was relayed, the apple thing was the moment that he realised that the mysterious force holding the celestial objects in their orbits was exactly the same force as gravity. It's not that gravity was a new concept or anything. In fact, it goes back so far in our history that we still use the silly name "gravity" for the phenomenon; it was once though to be a property of an object or an element (in the "four elements" sense), and was opposed by another property called "levity". You will note that there is no current theory of levity. Galileo had already put numbers to gravity on Earth by that point, and the idea that the force holding things in their orbits acted according to an inverse square law was circulating before Newton got there. (There's no reason to believe he couldn't have come to that conclusion independently, but there's no reason to credit it to him either.) What was missing was the connection; the generalization. That's not obvious in any way. How do you get an inverse square law to work with Galilean gravity? It smacks of equants and deferents until you find a way to put the effective mass of a body, such as the Earth, at its centre. Imagine a world in which there's some inverse square force thingy holding the moon and planets in their orbits, and there's gravity and you know how that works, and nobody has even the slightest notion that they're in any way related. And then you have the OFFS moment.
  - emmelaich 6y ago
    Was there really a property proposed called levity? I thought that that was only mentioned in parodies of Newton. e.g. https://www.sciencephoto.com/media/363707/view/caricature-of-newton-s-laws-of-gravity- https://www.sciencephoto.com/media/363707/view/caricature-of...
    - stan_rogers 6y ago
      Yes, and it goes back at least as far as Aristotle (although he would have used a rather Greeker word). Levity would have been a property of fire and air in Aristotelian physics, where gravity was a property of earth and water.
- JProthero 6y ago
  This is only partly a myth; there are contemporary accounts from Newton's acquaintances noting how he described being inspired by observing the fall of an apple from a tree. It was the fact that an apple falls from a tree specifically in the direction of the Earth's centre that was said to have piqued his curiosity. The apple falling on his head seems to have been a later embellishment.
wenc 6y ago
It's too bad the apple story is the only one the public imagination latched on to. Newton was so much more than that. Granted a lot of his discoveries were hard to explain without math, but he deserves a lot more credit for human history. I bet writers of children's stories had a hard time explaining Euler too. But somehow they managed to insert Einstein into the public imagination. And almost no one I know understands the photoeletric effect or the theory of relativity. I myself have the vaguest of understandings.
- scollet 6y ago
  The end product is something successful I think. A series of children's books focused on the histories of physics, maths, philosophy, etc. while showing how each generation stands on the previous giants' shoulders would be stellar.
- croissants 6y ago
  Unfounded conjecture: photos matter a lot. Especially when the photos of Einstein make him look like a kooky grandpa and the images of Newton make him look like a stiff, stern cartoon.
deleted 6y ago
[deleted]

abhayhegde 6y ago

He was certainly having fun! A refreshing peek through his mind. Whenever I mention the likes of Newton and their works, I frequently get attacked by some people. Their argument is that Newton was a terrible human being and despite his contributions to Science, Mathematics, and the process of discoveries in general, he does not deserve praise since appraisal implies we would be condoning his behavior. To that I usually reply, we would never accept some of his behaviors now and that does not mean his contributions are worthless. They believe we can never separate the "works" from a "person", to which I always disagree. EDIT: Grammar.

batsigner 6y ago
What is the point of your comment?
- max_ 6y ago
  That being a human being that adds value to society does not require everyone to like you.
  - watwut 6y ago
    "Not everyone liked him" is sort of understatement. We can accept and celebrate his contributions without pretending that the dislike for Newton was all about some mild unlikability.
    - bryanrasmussen 6y ago
      I guess I'm in the medium unlikability school. I mean, he seems as unlikable as a significant number of programmers who are not Isaac Newton despite pretensions to equivalent accomplishment. https://inversesquare.wordpress.com/2008/03/21/friday-isaac-newton-blogging-how-mean-was-he/ https://inversesquare.wordpress.com/2008/03/21/friday-isaac-... on edit: meaning some programmers are not quick to make friends, and are not convivial, perhaps due to some neuro-atypical qualities, which I expect was probably the case with Newton. Not that programmers condemn people to death as their jobs generally do not require it.

sbr464 6y ago

You can download higher resolution versions of the notebook pages by using a dezoooming tool[1] on the image tiles. This example[2] generates a 4898×7711 png compared to a 1270×2000 jpg from the download link[3]. [1]: https://github.com/lovasoa/dezoomify https://github.com/lovasoa/dezoomify [2]: https://ophir.alwaysdata.net/dezoomify/dezoomify.html#https://images.lib.cam.ac.uk/content/images/MS-ADD-03969-001-00001_files/13/0_0.jpg https://ophir.alwaysdata.net/dezoomify/dezoomify.html#https:... [3]: https://images.lib.cam.ac.uk/content/images/MS-ADD-03969-001-00001.jpg https://images.lib.cam.ac.uk/content/images/MS-ADD-03969-001...

max_ 6y ago

Is that a "Hand" doodle? http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/15 http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/15

pvida 6y ago
It certainly seems so. I love how simple-yet-not-too-simple it is.
- jq-r 6y ago
  It is the exactly the same hand symbol Henry VIII used to mark down interesting passages in Bible which he hoped would help him to annul his marriage to Catherine of Aragon.
  - ian0 6y ago
    Apparently called an index or manicule with examples spotted from the 12th century.. https://en.wikipedia.org/wiki/Index_(typography) https://en.wikipedia.org/wiki/Index_(typography)
    - lioeters 6y ago
      Delightful! I'd say this manicule is a proto-emoji of sorts. > Thomas Pynchon parodies this punctuation mark in his novel Gravity's Rainbow by depicting a middle finger, rather than an index finger, pointing at a line of text.
runawaybottle 6y ago
Newton used emojis??
katzgrau 6y ago
Came here for this comment :) Saw the hand and that immediately became my favorite thing in the notebook.

max_ 6y ago

Any possibility to have this typed & formatted for easy reading?

hank_z 6y ago

Any modern text recognition technology is applicable to his handwriting?

bra-ket 6y ago

The funny thing about Newton is that he was treating pseudo-science like alchemy with the same level of seriousness as actual science he helped advance so much. https://en.m.wikipedia.org/wiki/Isaac_Newton%27s_occult_studies#Alchemical_research https://en.m.wikipedia.org/wiki/Isaac_Newton%27s_occult_stud...

beenBoutIT 6y ago
Alchemy wasn't scientifically disproven until the 19th century, so Newton had no choice but to explore it. If transforming base metals to gold was scientifically plausible and illegal(as it was in Newton's day) most of us on this board would be chasing after it at full speed right now.
- ip26 6y ago
  Making matters worse, nuclear fusion practically is alchemy.
  - redwall_hp 6y ago
    I've always thought there was something poetic about that. The ancient Greeks gave us the name "atom," the indivisible unit. The alchemists chased the goal of breaking down base metals (splitting the atom) and transmuting the components into gold. Then in the 20th century, the physics were finally mapped out. The atom was split, unveiling the subatomic world, and we know full well that atoms can be fused. The term "transmutation" is even used. It's like an ancient quest finally reached a conclusion, albeit not in the convenient way they would have hoped.
    - lioeters 6y ago
      Some of the scientists working on the Manhattan Project were certainly aware of associations with mythological themes. > Oppenheimer later recalled that, while witnessing the explosion, he thought of a verse from the Hindu holy book, the Bhagavad Gita: > "If the radiance of a thousand suns were to burst at once into the sky, that would be like the splendor of the mighty one." I'm fond of mythopoetic perspectives on technology, to find parallels in texts from the antiquities or the Renaissance. From their point of view, we in the modern world must seem to live like magicians, communicating over vast distances, peering into our "looking glass".

noisy_boy 6y ago

Idle thought: imagine if Newton examined modern programming and said "let me show you a new approach I've been thinking about for a while ..."

rutherblood 6y ago

that handwriting is surprisingly legible

alister 6y ago

Page 32: > At which time I found that method of Infinite series. And in summer 1665 being forced from Cambridge by the Plague I computed the area of the Hyperbola of Boothby in Lincolnshire to two & fifty figures by the same method. [signed] Is. Newton He made a signed statement of his discovery just as in a 20th century engineer's/inventor's notebook. The mention of being forced from Cambridge because of the plague makes me wonder if some great discoveries are being made right now because many bright minds have been forced home by coronavirus.

josh_fyi 6y ago
What looks like y^2 (or superscript 2) is an abbreviation for "the".
- alister 6y ago
  Thank you, I've corrected it. It raises the question of why anyone bothered with a 2 symbol abbreviation for just 3 letters.
  - MLR 6y ago
    Old English had a letter called thorn that would eventually be replaced with the modern th or a y (ye olde is just said the old). The y^e form was apparently used for the King James Bible in 1611 so it's plausible it might still have been a normal way of writing "the" as late as 1650, rather than as an affectation or abbreviation. Edit: He also uses y^t for that which I hadn't noticed at first glance.
  - jabirali 6y ago
    You could raise the same question about many historic ligatures, like abbreviating "et" to "&" in Latin?
- LadyCailin 6y ago
  It's such a long word, makes sense to abbreviate it.
6y ago

vansul 6y ago

I love this book. They currently have his 1659-61 notebook on display at the Fitzwilliam Museum in Cambridge (scan available at [0]) Its opened on a page titled ‘Otiose et frustra expensa’ (Idle and vain expenses) where he lists his snack binges (including ‘cheries’, ‘Tarte’, ‘Marmolet’, ‘Custardes’, and ‘Cake bred). [0] https://mss-cat.trin.cam.ac.uk/manuscripts/uv/view.php?n=R.4.48c&n=R.4.48c#?c=0&m=0&s=0&cv=51&xywh=-1483%2C-2%2C5173%2C2778 https://mss-cat.trin.cam.ac.uk/manuscripts/uv/view.php?n=R.4...

dr_dshiv 6y ago

Newton credited the discovery of the inverse square law of gravity to Pythagoras (5th century BC), just as Coperinicus had credited heliocentrism to him. Here is Newton's argument: "For Pythagoras, as Macrobius avows, stretched the intestines of sheep or the sinews of oxen by attaching various weights, and from this learned the ratio of the celestial harmony. Therefore, by means of such experiments he ascertained that the weights by which all tones on equal strings .. were reciprocally as the squares of the lengths of the string by which the musical instrument emits the same tones. But the proportion discovered by these experiments, on the evidence of Macrobius, he applied to the heavens and consequently by comparing those weights with the weights of the Planets and the lengths of the strings with the distances of the Planets, he understood by means of the harmony of the heavens that the weights of the Planets towards the Sun were reciprocally as the squares of their distances from the Sun." This article has more: https://royalsocietypublishing.org/doi/10.1098 https://royalsocietypublishing.org/doi/10.1098

philzook 6y ago
That's an interesting suggestion I've never heard before, but your link appears to be down. I'm getting a 404. Is it possible this passage is referring to the reciprocal Pythagorean theorem? https://en.wikipedia.org/wiki/Pythagorean_theorem#Reciprocal_Pythagorean_theorem https://en.wikipedia.org/wiki/Pythagorean_theorem#Reciprocal...
- anticsapp 6y ago
  I believe this is the article: https://muse.jhu.edu/article/495241 https://muse.jhu.edu/article/495241 I can't get a sci-hub for it though.
- dr_dshiv 6y ago
  https://royalsocietypublishing.org/doi/10.1098/rsnr.1966.0014 https://royalsocietypublishing.org/doi/10.1098/rsnr.1966.001... My apologies, here is the article and citation. And no, not the reciprocal Pythagorean theorem -- learning about Pythagoreanism is a real rabbit hole, highly recommended :) McGuire, J. E., & Rattansi, P. M. (1966). Newton and the ‘Pipes of Pan’. Notes and records of the Royal Society of London, 21(2), 108-143.

deleted 6y ago

[deleted]

yitchelle 6y ago

It is remarkable that there are not alot corrections among the written text. The text is extremely readable and understanble, even for a non-mathematician like me.