Abstract
Having been drawn into numerous digressions related to the science of falling bodies, Salviati and his friends finally planned, at the close of their first day of discussion, to return to the science of the strength of materials when they meet again. To this end, the Second Day of the Dialogues commences with a refresher course on the Law of the Lever, which had been known since ancient times. It is upon this law that Galileo bases his subsequent analysis of beam breaking.
Any two heavy bodies are in equilibrium at distances which are inversely proportional to their weights.
—Galileo Galilei
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Notes
- 1.
See Archimedes’ The Centers of Gravity of Planes, which can be found in Heath, T. (Ed.), The Works of Archimedes, Dover Publications, Mineola, NY, 2002.
- 2.
For definition of perturbata see Todhunter’s Euclid. Book V, Def. 20. [Trans.]
- 3.
The one fundamental error which is implicitly introduced into this proposition and which is carried through the entire discussion of the Second Day consists in a failure to see that, in such a beam, there must be equilibrium between the forces of tension and compression over any cross-section. The correct point of view seems first to have been found by E. Mariotte in 1680 and by A. Parent in 1713. Fortunately this error does not vitiate the conclusions of the subsequent propositions which deal only with proportions—not actual strength—of beams. Following K. Pearson (Todhunter’s History of Elasticity) one might say that Galileo’s mistake lay in supposing the fibres of the strained beam to be inextensible. Or, confessing the anachronism, one might say that the error consisted in taking the lowest fibre of the beam as the neutral axis. [Trans.]
- 4.
To emphasize this point, the resistance to fracture is just the bending force which must be applied in a transverse direction at the prism’s end so as to break it.—[K.K.]
- 5.
H is a third proportional, so \(H/DE = DE/AB\).—[K.K.]
- 6.
The preceding paragraph beginning with Proposition VI is of more than usual interest as illustrating the confusion of terminology current in the time of Galileo. The translation given is literal except in the case of those words for which the Italian is supplied. The facts which Galileo has in mind are so evident that it is difficult to see how one can here interpret “moment" to mean the force “opposing the resistance of its base,” unless “the force of the lever arm AB” be taken to mean “the mechanical advantage of the lever made up of AB and the radius of the base B”; and similarly for “the force of the lever arm CD.” [Trans.]
- 7.
For example, the Dual Range Force Sensor (Model DFS-BTA), Vernier, Beaverton, OR.
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Kuehn, K. (2015). The Law of the Lever. In: A Student's Guide Through the Great Physics Texts. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1366-4_6
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