Galileo's argument about falling bodies is logically sound.
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Historical and physics literature details Galileo's theoretical and experimental frameworks regarding falling bodies, establishing the validity and soundness of his propositions concerning uniform acceleration and vacuum conditions.
The most perplexing aspect of Galileo's work in physics is without doubt the sharp distinction one can draw between his essentially dynamic studies in such juvenilia as De Motu and the consciously kinematical approach of his later output—particularly the Two New Sciences . Whether one chooses to call this a shift from the “why” of motion to the “how”, or, as I should prefer, a shift from dynamics to kinematics, there can be no denying its existence. The Galileo who wrote that “The present does not seem to be the proper time to investigate the cause of the acceleration of natural motion …” is, on the face of it, a very different man from the one who had earlier written almost an entire treatise on precisely this topic.
Galileo, Falling Bodies and Inclined Planes: An Attempt at Reconstructing Galileo's Discovery of the Law of Squares* | The British Journal for the History of Science | Cambridge Core Search Institution Login Search Hostname: page-component-66d9dcfd78-nqrk7 Total loading time: 0 Render date: 2026-08-07T19:10:28.278Z Has data issue: false hasContentIssue false Home > Journals > The British Journal for the History of Science > Volume 3 Issue 3 > Galileo, Falling Bodies and Inclined Planes: An Attempt...
English Français The British Journal for the History of Science Article contents Extract References Galileo, Falling Bodies and Inclined Planes: An Attempt at Reconstructing Galileo's Discovery of the Law of Squares * Published online by Cambridge University Press: 05 January 2009 W. C. Humphreys Article Metrics Article contents Extract References Get access Share Cite Rights & Permissions [Opens in a new window] Extract The most perplexing aspect of Galileo's work in physics is without doubt the sharp distinction one can draw between his essentially dynamic studies in such juvenilia as De Motu and the consciously kinematical approach of his later output—particularly the Two New Sciences .
Google Scholar 3 3 This experiment consists in thinking of a body being cut into two unequal pieces as it falls freely, or of two pieces of the same material being joined while falling. In either case, there is no reason to believe that the velocities of fall will be changed. 4 4 On Motion and On Mechanics , 107 . Google Scholar 5 5 Ibid. , 107–109. See also Galileo's , Dialogue concerning the Two Chief World Systems , trans. Drake , Stillman ( Berkeley , 1953 ), 151 – 152 Google Scholar : Salviati asks Simplicio whether a cotton or lead pendulum will remain in motion longer and Simplicio chooses the latter. “Salv.
(15), 340 – 341 Google Scholar : “By extending the axiom of the proportionality between velocity and distance to the motion of bodies rolling down smooth inclined planes, so that the distance travelled is replaced by the vertical distance from the starting point, Galileo was able to deduce from his false premise the correct proposition that the final velocity of a body rolling down an inclined plane depends solely on the amount of the vertical descent of the moving body and not on the angle of inclination of the plane.
Google Scholar 27 27 This first portion of the proof is an abbreviated version of Galileo's argument in Theorem III, Proposition III of Two New Sciences. Loc. cit. , 185 – 186 [215–218]. Google Scholar 28 28 It is likely that Galileo never completely cleared up in his own mind the distinctions
180–185 [214–219] of the Crew-de Salvio translation.) This undoubtedly has some bearing on the fact noted by Professor Hall in his recent paper ( op. cit. (26), 192) that correspondence with Luca Valerio in May of 1609 seems to involve residual confusion on Galileo's part about the speeds of bodies on inclined planes. Although Galileo's own contribution to the correspondence is lost it would not be surprising to find that even at this late date he was still drawing incorrect inferences from his earlier dynamical studies. 29 29 Dialogue , 23 . Google Scholar 30 30 Ibid. , 23–24. 31 31 Ibid. , 24–25. 32 32 Ibid. , 26.
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Galileo, Falling Bodies and Inclined Planes: An Attempt at Reconstructing Galileo's Discovery of the Law of Squares * Volume 3, Issue 3 W. C. Humphreys DOI: https://doi.org/10.1017/S0007087400002673 Available formats PDF Please select a format to save. By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services Please confirm that you accept the terms of use. Cancel Save × Save article to Google Drive To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies.
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Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei or mononymously as Galileo, was an Italian astronomer, physicist, engineer and polymath. He was born in Pisa, then part of the Duchy of Florence. Galileo has been called the father of observational astronomy, classical physics, the scientific method, and modern science.
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That unequal weights would fall with the same speed may have been proposed as early as 60BC by the Roman philosopher Lucretius. Observations that similarly sized objects of different weights fall at the same speed are documented in sixth-century works by John Philoponus, of which Galileo was aware. In the 14th century, Nicole Oresme had derived the time-squared law for uniformly accelerated change, and in the 16th century, Domingo de Soto had suggested that bodies falling through a homogeneous medium would be uniformly accelerated. De Soto, however, did not anticipate many of the qualifications and refinements contained in Galileo's theory of falling bodies. He did not, for instance, recognise, as Galileo did, that a body would fall with a strictly uniform acceleration only in a vacuum, and that it would otherwise eventually reach a uniform terminal velocity.
A biography by Galileo's pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass. This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. While this story has been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is generally accepted by historians that it was at most a thought experiment which did not actually take place. An exception is Stillman Drake, who argues that the experiment did take place, more or less as Viviani described it. Howev
However, Galileo's values were much smaller than previous estimates of the apparent sizes of the brightest stars, such as those made by Brahe, and enabled Galileo to counter anti-Copernican arguments such as those made by Tycho that these stars would have to be absurdly large for their annual parallaxes to be undetectable. Other astronomers such as Simon Marius, Giovanni Battista Riccioli, and Martinus Hortensius made similar measurements of stars, and Marius and Riccioli concluded the smaller sizes were not small enough to answer Tycho's argument.
Grassi's arguments and conclusions were criticised in a subsequent article, Discourse on Comets, published under the name of one of Galileo's disciples, a Florentine lawyer named Mario Guiducci, although it had been largely written by Galileo himself. Galileo and Guiducci offered no definitive theory of their own on the nature of comets, although they did present some tentative conjectures that are now known to be mistaken.
Ingoli may have been commissioned by the Inquisition to write an expert opinion on the controversy, with the essay providing the basis for the Inquisition's actions. The essay focused on eighteen physical and mathematical arguments against heliocentrism. It borrowed primarily from Tycho Brahe's arguments, notably that heliocentrism would require the stars as they appeared to be much larger than the Sun. The essay also included four theological arguments, but Ingoli suggested Galileo focus on the physical and mathematical arguments, and he did not mention Galileo's biblical ideas.
Galileo's resulting book, Dialogue Concerning the Two Chief World Systems, was published in 1632, with formal authorization from the Inquisition and papal permission. Earlier, Pope Urban VIII had personally asked Galileo to give arguments for and against heliocentrism in the book and to be careful not to advocate heliocentrism. Whether unknowingly or deliberately, Simplicio, the defender of the Aristotelian geocentric view in Dialogue Concerning the Two Chief World Systems, was often caught in his own errors and sometimes came across as a fool.
Observations that similarly sized objects of different weights fall at the same speed are documented in sixth-century works by John Philoponus, of which Galileo was aware. In the 14th century, Nicole Oresme had derived the time-squared law for uniformly accelerated change, and in the 16th century, Domingo de Soto had suggested that bodies falling through a homogeneous medium would be uniformly accelerated. De Soto, however, did not anticipate many of the qualifications and refinements contained in Galileo's theory of falling bodies.
This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. While this story has been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is generally accepted by historians that it was at most a thought experiment which did not actually take place. An exception is Stillman Drake, who argues that the experiment did take place, more or less as Viviani described it. However, most of Galileo's experiments with falling bodies were carried out using inclined planes where both the issues of timing and air resistance were much reduced.
In Galileo’s Two New Sciences (1638), the character Salviati, widely regarded as Galileo's spokesman, held that "In a medium totally devoid of all resistance all bodies would fall with the same speed." Salviati also held that this could be experimentally demonstrated by the comparison of pendulum motions in air with bobs of lead and of cork which had different weights but which were otherwise similar. ===== Time-squared law ===== Galileo proposed that a falling body would fall with a uniform acceleration, as long as the resistance of the medium through which it was falling remained negligible, or in the limiting case of its falling through a vacuum.
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