Torricelli’s principle

Capecchi, Danilo

doi:10.1007/978-88-470-2056-6_6

Torricelli’s principle

Danilo Capecchi²

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Part of the book series: Science Networks. Historical Studies ((SNHS,volume 42))

Abstract

This chapter is devoted entirely to Evangelista Torricelli who formulated a principle of equilibrium without referring explicitly to dynamic aspects. In the first part some elements of centrobarica are introduced. In the central part Torricelli’s principle is introduced: The centre of gravity of an aggregate of heavy bodies cannot lift by itself. Following this law, which in a first reading does not seem to be a VWL, Torricelli and his successors derived the VWL based on virtual displacements for which any force that can lift a weight p to a height h can raise p/n of nh. In the final part generalization and simplification of Torricelli’s principle are presented.

In the common interpretation, Torricelli’s principle is a criterion of statics which claims that it is impossible for the centre of gravity of a system of bodies in equilibrium to sink from any virtual movement of the bodies. This criterion had a vital role in the history of mechanics. It represents a generalisation of the ancient principle that a single body is in equilibrium if its centre of gravity cannot sink. The generalisation devised by Torricelli states that if the centre of gravity of an aggregate of rigid bodies, considering the aggregate as a whole, is evaluated according to Archimedean rules, then this point has effectively the physical meaning of a centre of gravity.

The first part of this chapter is taken from [275] which is summarized and largely revised.

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Notes

1.
II B 14, 297 b.
2.
vol. 2, p. 20.
3.
vol. 2, p. 25, in note 6.
4.
p. 10.
5.
p. 1.
6.
p. 1.
7.
p. 1.
8.
In addition, Descartes will show that in the sphere, according to the theory of gravity force in his day, although there is a centre of gravity, it does not coincide with its centre but is lower [96], vol. 2, p. 245.
9.
vol. II, pp. 156–186.
10.
pp. 74–75.
11.
pp. 187–208. It seems that the Appendix was prior to Le mecaniche. The composition of the work according to some historians dates from the period between 1585 and 1588 [123], vol. 1, pp. 181–182.
12.
This paper is considered as authentic of Galileo for sure by Favaro [123], vol. 8, p. 439 and with some doubt by Caverni [284] vol. 4, pp. 164–166.
13.
p. 215.
14.
It is now known with certainty that Rome was the birthplace of Torricelli. On Torricelli’s birth one can see the recent works by Bretoni [258, 263].
15.
pp. 84–95.
16.
pp. 31–33.
17.
p. 11.
18.
pp. 13–14.
19.
vol. 2, pp. 24–26.
20.
p. 10.
21.
vol. 4, pp. 156–212.
22.
pp. 9–10.
23.
pp. 9–10.
24.
p. 15.
25.
E. Torricelli, Galilean collection, manuscript n. 150, c. 112.
26.
E. Torricelli, Galileian collection, manuscript n. 150, c. 112.
27.
p. 100.
28.
p. 16.
29.
It will appear in the second edition of the Discorsi e dimostrazioni matematiche [120]. It is worth noting that the proof of the law of the inclined plane shown in the Dialogo [116], pp. 215–218, is different from that reported in the Le mecaniche [119], p. 181. The first is based on the principle of virtual work, the second on the law of the lever.
30.
p. 98.
31.
p. 18.
32.
It is interesting to note that Torricelli in De motu gravium refers also a demonstration of the law of the inclined plane, alternative to that developed with his principle, very similar to that of Galileo in the Le mecaniche. This, if not to commit the sin of plagiarism to Torricelli, could prove that he actually did not know Le mecaniche.
33.
p. 99.
34.
p. 99.
35.
p. 99.
36.
p. 100.
37.
p. 100.
38.
pp. 14–15
39.
It seems strange that Torricelli could have made a such trivial error; there is the possibility that his text is simply imprecise. Indeed it is a mystery why Torricelli uses the body BFF with a side parallel to the beam AC, as if it were fixed to it. If this were actually fixed the centre of gravity of the whole could rise.
40.
vol. 3, pp. 243–245.
41.
vol. 4, pp. 65–67.
42.
vol. 4, pp. 65–67.
43.
vol. 3, pp. 91–92; pp. 96–99; pp. 99–100.
44.
vol. 3, p. 100. In [284], vol. 4, p. 64, there is the reference to a Torricelli’s manuscript which faces the same argument with the law of static moments, while maintaining a tone that suggests some doubt on the solution found.
45.
vol. 3, pp. 243–244.
46.
vol. 3, pp. 243–244.
47.
p. 234.
48.
vol. 1, p. 233.
49.
vol. 5, pp. 21–22.
50.
vol. 5, p. 22.
51.
pp. 311–312.
52.
vol. 2, p. 119; p. 133.
53.
p. 176.
54.
p. 2.

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Università La Sapienza, Rome, Italy
Danilo Capecchi

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Capecchi, D. (2012). Torricelli’s principle. In: History of Virtual Work Laws. Science Networks. Historical Studies, vol 42. Springer, Milano. https://doi.org/10.1007/978-88-470-2056-6_6

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DOI: https://doi.org/10.1007/978-88-470-2056-6_6
Publisher Name: Springer, Milano
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