Talk:De motu corporum in gyrum

Not That There's Anything Wrong With That

Newton told Halley that he had proved that the inverse-square force necessarily resulted in an elliptical orbit. (Can't find it right now. I'll send it to you later.) Instead of this proof, Newton sent De Motu to Halley. This treatise contained a demonstration of how an elliptical orbit can be related to the inverse-square force. This was the opposite of what was promised.Lestrade 14:36, 4 February 2006 (UTC)Lestrade

Orbital speed

How did Newton know that all of the planets move at the same speed and also know what that speed was? How did he know that a comet moves faster than a planet? Does today's science agree with Newton's pronouncements about the speeds of planets and comets?Lestrade (talk) 18:20, 11 April 2008 (UTC)Lestrade

According to Newton, the ellipticity of a planet's orbit depends on its speed. Wikipedia shows the orbital speeds of the planets are as follows, in kilometers per second: Mercury 48, Venus 35, Earth 30, Mars 24, Jupiter 13, Saturn 10, Uranus 7, Neptune 5, Pluto 4.6. If Newton was right, then the planets should all have differently shaped orbits. Pluto, the slowest, would be the most circular. Mercury, the fastest, would be the most elliptic, almost parabolic. Is this true?Lestrade (talk) 17:42, 29 April 2008 (UTC)Lestrade

Funny footer

It's only a few pages long. It was the basis of the most important scientific book ever written. Then why is it almost impossible to find De motu in print? Could it be that Newton's idiosyncratic geometry is so unreadable that it might as well have been written by Professor Irwin Corey?Lestrade (talk) 21:19, 11 April 2008 (UTC)Lestrade

Yeah, I'm doing a project on him and I can't find it. whatn is wi6th that. Please replyTailsfan2 (talk) 17:32, 21 October 2008 (UTC)

Missing Law

There's a law missing: Law 3 is actually what became Newton's 3rd law (equal and opposite reaction), and Laws 3-5 listed on this page should all be shifted down one. —Preceding unsigned comment added by 128.12.93.134 (talk) 11:12, 9 June 2009 (UTC)

Ellipse theorem

(The following discussion, copied here in relevant part, took place on Wikipedia:Reference desk/Mathematics starting 29 Sept 2009. It's copied here (in part) because it may indicate the content of a suitable explanatory comment that may be used to improve the main article.Terry0051 (talk) 16:40, 1 October 2009 (UTC))

In Proposition XI, Problem VI of the Principia (the inverse square law for ellipse focus), Newton refers to the 'writers on Conics' for proof of this property of the ellipse : all 'tangentially circumscribing' parallelograms have the same area.

I've tried Appolonius and Archimedes for this theorem but cannot find it there. Geometric proof anyone?

Dunloskinbeg (talk) 06:48, 29 September 2009 (UTC)

That doesn't sound right at all to me, are you sure you're quoting him right? A circle is an ellipse and you can get as large an area as you like with a rhombus round it. Dmcq (talk) 09:55, 29 September 2009 (UTC)

[ Comment agreeing that it doesn't sound right ][ ... ] Think of a unit circle $x^{2}+y^{2}=1$ and a rhombus with vertices $(\pm 1/\sin \alpha ,0)$ and $(0,\pm 1/\cos \alpha )$ for some small alpha. --CiaPan (talk) 11:45, 29 September 2009 (UTC)

Hah! The explanation is in De motu corporum in gyrum article, first section 'Contents of "De Motu"', part 2 Lemmas:

All parallelograms touching a given ellipse (to be understood: at the end-points of conjugate diameters) are equal in area.

Conjugate diameters do not have their own article on Wikipedia nor in http://mathworld.wolfram.com/ but they are two such chords of an ellipse that each of them halves all chords parallel to the other. --CiaPan (talk) 12:41, 29 September 2009 (UTC)

Now they have, thanks to Jim.belk — see conjugate diameters --CiaPan (talk) 06:31, 1 October 2009 (UTC)

Now the proof is quite simple: an ellipse is an image of a circle in some affine transformation; a pair of conjugate diams is an image of a pair of perpendicular diams of the circle, and the parallelogram is an image of a square tangent to the circle. All such squares have equal area, and area ratios are preserved by affine transformation (as long as it's not degenerate, i.e. detA≠0), so all parallelograms considered have equal areas, too. --CiaPan (talk) 12:52, 29 September 2009 (UTC)

I've seen the phrase "Writers on X say..." or "Books on X say..." before, I think always in books written before 1900. Nowadays of course we use the much more self explanatory "It is well known that...".--RDBury (talk) 14:43, 29 September 2009 (UTC)

[ End of copied discussion ]

Newton and Galileo

A question has been raised about whether Newton gave mathematical demonstration of Galileo's laws. It looks as if Newton used and built on Galileo's results rather than as if he proved them (for the restricted conditions in which they are valid).

There is no mention of Galileo (as far as I can see) in the first version of Newton's 'De motu' (links to cited sources are already in the main article text). On the other hand, Newton did later acknowledge Galileo in connection with the first two laws of motion when he expanded the 1684 'De motu' and produced the 'Principia' of 1687 (Scholium to Corollary 6, at page 31 in the 1729 translation. At that point Newton credited Galileo with the discovery that the descent of bodies (under practically constant force) was proportional to the square of the time, and Newton also credited Galileo with making that discovery by using the relationships that Newton had just set out in the first two laws of motion and their first two corollaries (for which, see pages 19 to 24 in the 'Principia', 1729 translation).

In 'De motu', Newton applied the proportionality between distance and square of the time for infinitesimal use, and he stated application that as his fourth 'hypothesis' in the 1684 'De motu' (compare Lemma 10 in the 'Principia'). (btw, it looks as if Newton in 1684 was using the term 'hypothesis' to mean something like 'starting-point', according to its etymology, and not to mean something conjectural or uncertain. That seems to emerge especially because in the passage cited above from the Scholium to Corollary 6, Newton writes that he has been discussing things that "have been receiv'd by Mathematicians and are confirm'd by abundance of experiments". Clearly he was not talking about guesses or speculations.)

It doesn't look as if any source has been mentioned that points to a proof by Newton of Galileo's laws, as opposed to the sources that show Newton appearing to use the acknowledged prior results of Galileo rather than to prove them. Terry0051 (talk) 16:28, 16 December 2009 (UTC)

Date

This item appears on the Wiki "this day in history" page for 10 December, but that's a Gregorian calendar and this event took place on 20 December 1684, 10 December O.S. I presume that everyone involved in this page knew that, or knew that it needed to be calculated, but I see no reference to the calendar issue here so I don't want to change it.Vanhorn (talk) 08:22, 10 December 2011 (UTC)