伽利略指出，「只要下落的介質產生的阻力微不足道，或者在限定的真空條件下落下，落體將以均勻加速度下落。」[168]他也推導出均勻加速度正確的運動學規律，也就是說與所經歷時間的平方成比例（d ∝ t2）。[169]在伽利略之前，尼科爾·奧雷姆[170]與14世紀推導出勻加速改變的時間平方規則，[171]多明戈·德索托（Domingo de Soto）於16世紀提出，「落體在均勻介質中將勻加速下落。」[172]通過幾何結構和精確的數學語言，伽利略依據他所處時代的標準表達了時間平方規則。（這就為其他人也使用代數術語重新表達了這一規則留下餘地）。伽利略還總結道「除非對物體施加一個力，常常是摩擦力，否則物體將一直保持等速運動。這駁斥了當時為人們所普遍公認的亞里士多德假說---除非對物體施加外力，否則運動的物體將「自然」減速並停下來。正如讓·布里丹[173]所說的那樣，早在亞里斯多德提出這一假設幾個世紀之前，約翰·菲洛波努斯[174]就已提出了有關慣性的哲學思想。據喬瑟芬·李約瑟[175]所述，「在他們之前，墨子早在幾個世紀之前已經提出這一觀點。但是，這是首次使用數學表達這一觀點，並經過實驗驗證，並引入摩擦力的概念，這是驗證慣性中所取得的一次突破。」伽利略的慣性原理提到，「除非受到外力的作用，否則運動在水平面上的物體就會按照其原來的方向，保持等速運動。後來，這一原理納入了牛頓運動定律（牛頓第一運動定律）。
O'Connor, J. J.; Robertson, E. F. Galileo Galilei. The MacTutor History of Mathematics archive. 蘇格蘭聖安德魯大學. [2007-07-24]. （原始內容存檔於2009-10-06）. 引文使用過時參數coauthors (幫助)
O'Connor, J. J.; Robertson, E. F. "Galileo Galilei". The MacTutor History of Mathematics archive. University of St Andrews, Scotland. Retrieved 2007-07-24.
Sobel（2000, p. 5）Chapter 1. Retrieved on 26 August 2007. "But because he never married Virginia's mother, he deemed the girl herself unmarriageable. Soon after her 13th birthday, he placed her at the Convent of San Matteo in Arcetri."
Pedersen, O.（24–27 May 1984）. "Galileo's Religion". Proceedings of the Cracow Conference, The Galileo affair: A meeting of faith and science. Cracow: Dordrecht, D. Reidel Publishing Co.. pp. 75–102. Bibcode 1985gamf.conf...75P.
Panofsky, Erwin (1956). "Galileo as a Critic of the Arts: Aesthetic Attitude and Scientific Thought". Isis 47 (1): 3–15. doi:10.1086/348450. JSTOR 227542.
Rutkin, H. Darrel. "Galileo, Astrology, and the Scientific Revolution: Another Look". Program in History & Philosophy of Science & Technology, Stanford University. Retrieved 2007-04-15.
Einstein（1954, p.271）. "Propositions arrived at by purely logical means are completely empty as regards reality. Because Galileo realised this, and particularly because he drummed it into the scientific world, he is the father of modern physics—indeed, of modern science altogether."
United Nations Educational, Scientific and Cultural Organization (11 August 2005). "Proclamation of 2009 as International year of Astronomy"（PDF）. UNESCO. Retrieved 2008-06-10.
Kusukawa, Sachiko. "Starry Messenger: The Telescope". Department of History and Philosophy of Science of the University of Cambridge. Retrieved 2007-03-10.
Drake（1978, p. 494）, Favaro（1896, 6:111）. The pseudonym was a slightly imperfect anagram of Oratio Grasio Savonensis, a latinised version of his name and home town.
Brodrick（1965, c1964, p. 95）quoting Cardinal Bellarmine's letter to Foscarini, dated 12 April 1615. Translated from Favaro（1902, 12:171–172） (Italian).
See Langford（1966, pp. 133–134）, and Seeger（1966, p. 30）, for example. Drake（1978, p. 355）asserts that Simplicio's character is modelled on the Aristotelian philosophers, Lodovico delle Colombe and Cesare Cremonini, rather than Urban. He also considers that the demand for Galileo to include the Pope's argument in the Dialogue left him with no option but to put it in the mouth of Simplicio（Drake, 1953, p. 491）. Even Arthur Koestler, who is generally quite harsh on Galileo in The Sleepwalkers (1959), after noting that Urban suspected Galileo of having intended Simplicio to be a caricature of him, says "this of course is untrue"（1959, p. 483）.
Fantoli（2005, p. 139）, Finocchiaro（1989, pp. 288–293）. Finocchiaro's translation of the Inquisition's judgement against Galileo is available on-line. "Vehemently suspect of heresy" was a technical term of canon law and did not necessarily imply that the Inquisition considered the opinions giving rise to the verdict to be heretical. The same verdict would have been possible even if the opinions had been subject only to the less serious censure of "erroneous in faith"（Fantoli, 2005, p. 140; Heilbron, 2005, pp. 282–284）.
Drake（1978, p. 356）. The phrase "Eppur si muove" does appear, however, in a painting of the 1640s by the Spanish painter Bartolomé Esteban Murillo or an artist of his school. The painting depicts an imprisoned Galileo apparently pointing to a copy of the phrase written on the wall of his dungeon（Drake, 1978, p. 357）.
William Shea, M. A. The Galileo Affair 2006. Available online William Shea (January 2006). "The Galileo Affair". Grupo de Investigación sobre Ciencia, Razón y Fe (CRYF). Unpublished work. Retrieved 12 September 2010.
In Sidereus Nuncius（Favaro,1892, 3:81（Latin）) Galileo stated that he had reached this conclusion on 11 January. Drake（1978, p. 152）, however, after studying unpublished manuscript records of Galileo's observations, concluded that he did not do so until 15 January.
In the Capellan model only Mercury and Venus orbit the Sun, whilst in its extended version such as expounded by Riccioli, Mars also orbits the Sun, but the orbits of Jupiter and Saturn are centred on the Earth
In Kepler's Thomist 'inertial' variant of Aristotelian dynamics as opposed to Galileo's impetus dynamics variant all bodies universally have an inherent resistance to all motion and tendency to rest, which he dubbed 'inertia'. This notion of inertia was originally introduced by Averroes in the 12th century just for the celestial spheres in order to explain why they do not rotate with infinite speed on Aristotelian dynamics, as they should if they had no resistance to their movers. And in his Astronomia Nova celestial mechanics the inertia of the planets is overcome in their solar orbital motion by their being pushed around by the sunspecks of the rotating sun acting like the spokes of a rotating cartwheel. And more generally it predicted all but only planets with orbiting satellites, such as Jupiter for example, also rotate to push them around, whereas the Moon, for example, does not rotate, thus always presenting the same face to the Earth, because it has no satellites to push around. These seem to have been the first successful novel predictions of Thomist 'inertial' Aristotelian dynamics as well as of post-spherist celestial physics. In his 1630 Epitome（See p514 on p896 of the Encyclopædia Britannica 1952 Great Books of the Western World edition）Kepler keenly stressed he had proved the Sun's axial rotation from planetary motions in his Commentaries on Mars Ch 34 long before it was telescopically established by sunspot motion.
Drake（1978, p. 209）. Sizzi reported the observations he and his companions had made over the course of a year to Orazio Morandi in a letter dated 10 April 1613（Favaro,1901, 11:491 （Italian）). Morandi subsequently forwarded a copy to Galileo.
In geostatic systems the apparent annual variation in the motion of sunspots could only be explained as the result of an implausibly complicated precession of the Sun's axis of rotation（Linton, 2004, p. 212; Sharratt, 1994, p. 166; Drake, 1970, pp. 191–196）. This did not apply, however, to the modified version of Tycho's system introduced by his protegé, Longomontanus, in which the Earth was assumed to rotate. Longomontanus's system could account for the apparent motions of sunspots just as well as the Copernican.
Drake（1978, pp. 19,20）. At the time when Viviani asserts that the experiment took place, Galileo had not yet formulated the final version of his law of free fall. He had, however, formulated an earlier version which predicted that bodies of the same material falling through the same medium would fall at the same speed（Drake, 1978, p. 20）.
Groleau, Rick. "Galileo's Battle for the Heavens. July 2002". Ball, Phil (2005-06-30). "Science history: setting the record straight. 30 June 2005". The Hindu（Chennai, India）.
Lucretius, De rerum natura II, 225–229; Relevant passage appears in: Lane Cooper, Aristotle, Galileo, and the Tower of Pisa（Ithaca, N.Y.: Cornell University Press, 1935）, p. 49.
Simon Stevin, De Beghinselen des Waterwichts, Anvang der Waterwichtdaet, en de Anhang komen na de Beghinselen der Weeghconst en de Weeghdaet [The Elements of Hydrostatics, Preamble to the Practice of Hydrostatics, and Appendix to The Elements of the Statics and The Practice of Weighing]（Leiden, Netherlands: Christoffel Plantijn, 1586）reports an experiment by Stevin and Jan Cornets de Groot in which they dropped lead balls from a church tower in Delft; relevant passage is translated in: E. J. Dijksterhuis, ed., The Principal Works of Simon Stevin Amsterdam, Netherlands: C. V. Swets & Zeitlinger, 1955 vol. 1, pp. 509, 511.
Clagett（1968, p. 561）. Oresme, however, regarded this discovery as a purely intellectual exercise having no relevance to the description of any natural phenomena, and consequently failed to recognise any connection with the motion of falling bodies（Grant, 1996, p.103）.
Sharratt（1994, p. 198）, Wallace（2004, pp.II 384, II 400, III 272）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 only fall with a strictly uniform acceleration in a vacuum, and that it would otherwise eventually reach a uniform terminal velocity.
Two of his non-scientific works, the letters to Castelli and the Grand Duchess Christina, were explicitly not allowed to be included（Coyne 2005, p. 347）.
Heilbron（2005, p. 307）; Coyne（2005, p. 347）The practical effect of the ban in its later years seems to have been that clergy could publish discussions of heliocentric physics with a formal disclaimer assuring its hypothetical character and their obedience to the church decrees against motion of the earth: see for example the commented edition (1742) of Newton's 'Principia' by Fathers Le Seur and Jacquier, which contains such a disclaimer（'Declaratio'）before the third book (Propositions 25 onwards) dealing with the lunar theory.
Discourse of His Holiness Pope Pius XII given on 3 December 1939 at the Solemn Audience granted to the Plenary Session of the Academy, Discourses of the Popes from Pius XI to John Paul II to the Pontifical Academy of the Sciences 1939–1986, Vatican City, p. 34
An earlier version had been delivered on 16 December 1989, in Rieti, and a later version in Madrid on 24 February 1990（Ratzinger, 1994, p. 81）. According to Feyerabend himself, Ratzinger had also mentioned him "in support of" his own views in a speech in Parma around the same time（Feyerabend, 1995, p. 178）.
Robert Henry Herman, Vincenzo Galilei. Dialogo della musica antica et della moderna of Vincenzo Galilei: translation and commentary, Part 1. North Texas State University, 1973. p. 17
Clagett, Marshall（editor & translator）. Nicole Oresme and the Medieval Geometry of Qualities and Motions; a treatise on the uniformity and difformity of intensities known as Tractatus de configurationibus qualitatum et motuum. Madison, WI: University of Wisconsin Press. 1968. ISBN 0-299-04880-2.
Finocchiaro, Maurice A. Book Review—The Person of the Millennium: The Unique Impact of Galileo on World History. The Historian. Fall 2007, 69 (3): 601–602. doi:10.1111/j.1540-6563.2007.00189_68.x.
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Galilei, Galileo Galileo: Two New Sciences（Translation by Stillman Drake of Galileo's 1638 Discourses and mathematical demonstrations concerning two new sciences）University of Wisconsin Press 1974 ISBN 978-0-299-06400-6
Galilei, Galileo, and Guiducci, Mario. Discourse on the Comets. Translated by Stillman Drake. In Drake & O'Malley（1960, pp. 21–65）. 1960 [1619].
Galilei, Galileo; Scheiner, Christoph. On Sunspots. Translated and with and introduction by Eileen Reeves and Albert Van Helden. Chicago: University of Chicago Press. 2010. ISBN 978-0-226-70715-0.
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