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191.
Bruce Pourciau 《Archive for History of Exact Sciences》2003,57(4):267-311
The first proposition of the Principia records two fundamental properties of an orbital motion: the Fixed Plane Property (that the orbit lies in a fixed plane)
and the Area Property (that the radius sweeps out equal areas in equal times). Taking at the start the traditional view, that
by an orbital motion Newton means a centripetal motion – this is a motion ``continually deflected from the tangent toward
a fixed center' – we describe two serious flaws in the Principia's argument for Proposition 1, an argument based on a polygonal impulse approximation. First, the persuasiveness of the argument
depends crucially on the validity of the Impulse Assumption: that every centripetal motion can be represented as a limit of polygonal impulse motions. Yet Newton tacitly takes the Impulse Assumption for granted. The resulting gap in the argument for Proposition 1 is serious,
for only a nontrivial analysis, involving the careful estimation of accumulating local errors, verifies the Impulse Assumption.
Second, Newton's polygonal approximation scheme has an inherent and ultimately fatal disability: it does not establish nor
can it be adapted to establish the Fixed Plane Property. Taking then a different view of what Newton means by an orbital motion
– namely that an orbital motion is by definition a limit of polygonal impulse motions – we show in this case that polygonal approximation can be used to establish both the fixed plane and area properties without too much trouble, but that Newton's own argument still
has flaws. Moreover, a crucial question, haunted by error accumulation and planarity problems, now arises: How plentiful are
these differently defined orbital motions? Returning to the traditional view, that Newton's orbital motions are by definition
centripetal motions, we go on to give three proofs of the Area Property which Newton ``could have given' – two using polygonal
approximation and a third using curvature – as well as a proof of the Fixed Plane Property which he ``almost could have given.'
(Received August 14, 2002)
Published online March 26, 2003
Communicated by G. Smith 相似文献
192.
In this study, we test the security of a crucial plank in the Principia’s mathematical foundation, namely Newton’s path leading to his solution of the famous Inverse Kepler Problem: a body attracted toward an immovable center by a centripetal force inversely proportional to the square of the distance from the center must move on a conic having a focus in that center. This path begins with his definitions of centripetal and motive force, moves through the second law of motion, then traverses Propositions I, II, and VI, before coming to an end with Propositions XI, XII, XIII and this trio’s first corollary. To test the security of this path, we answer the following questions. How far is Newton’s path from being truly rigorous? What would it take to clarify his ambiguous definitions and laws, supply missing details, and close logical gaps? In short, what would it take to make Newton’s route to the Inverse Kepler Problem completely convincing? The answer is very surprising: it takes far less than one might have expected, given that Newton carved this path in 1687. 相似文献
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Bruce Pourciau 《Archive for History of Exact Sciences》1992,44(4):331-363
Communicated by C. Wilson 相似文献
196.
Zusammenfassung Nachweis, dass der DNS-Gehalt der Dottergranula in Hühnerembryonalzellen in der frühesten Entwicklungsperiode (0–18 h) temporär ansteigt.
The scanning electron microscope was made available by Analytica, Sollentuna and the scanning micrograph was taken by Mr.G. Alsterborg.
This work has been supported by the Swedish Natural Science Research Council (H.E.) and Kungliga Fysiografiska Sällskapet, Lund. 相似文献
The scanning electron microscope was made available by Analytica, Sollentuna and the scanning micrograph was taken by Mr.G. Alsterborg.
This work has been supported by the Swedish Natural Science Research Council (H.E.) and Kungliga Fysiografiska Sällskapet, Lund. 相似文献
197.
Pounds JA Bustamante MR Coloma LA Consuegra JA Fogden MP Foster PN La Marca E Masters KL Merino-Viteri A Puschendorf R Ron SR Sánchez-Azofeifa GA Still CJ Young BE 《Nature》2006,439(7073):161-167
As the Earth warms, many species are likely to disappear, often because of changing disease dynamics. Here we show that a recent mass extinction associated with pathogen outbreaks is tied to global warming. Seventeen years ago, in the mountains of Costa Rica, the Monteverde harlequin frog (Atelopus sp.) vanished along with the golden toad (Bufo periglenes). An estimated 67% of the 110 or so species of Atelopus, which are endemic to the American tropics, have met the same fate, and a pathogenic chytrid fungus (Batrachochytrium dendrobatidis) is implicated. Analysing the timing of losses in relation to changes in sea surface and air temperatures, we conclude with 'very high confidence' (> 99%, following the Intergovernmental Panel on Climate Change, IPCC) that large-scale warming is a key factor in the disappearances. We propose that temperatures at many highland localities are shifting towards the growth optimum of Batrachochytrium, thus encouraging outbreaks. With climate change promoting infectious disease and eroding biodiversity, the urgency of reducing greenhouse-gas concentrations is now undeniable. 相似文献
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