Algebraic Methods in Statistical Mechanics and Quantum Field by Gerard G. Emch

By Gerard G. Emch

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Extra info for Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Physics & Astronomical Monograph)

Example text

But here the distances D1 and D2 are those covered by the forces in different times: given two moving forces travelling at the same speed, one of which is equal to the weight, the force equal to the weight will lift it much more quickly than a force much smaller than the weight. Though this is superficially similar to R it is in fact quite different, and does not imply a recognition of a general principle (work in equals work out) such as is implicit in R . , add another slave or an ox) rather than to employ a machine with greater mechanical advantage.

Trans. Drachmann, The Mechanical Technology, p. 76, slightly modified). 20 (Opera, vol. II, p. 24–33). Engl. trans. Drachmann, The Mechanical Technology, p. 81, slightly modified. 43 Pace De Gandt, “Force et science des machines”, p. 114. 32 MARK J. SCHIEFSKY the ability of a small force to overcome a large weight is precisely the feature of the concentric circles that Heron himself explains by reference to the balance. In making the balance rather than the circle fundamental to his explanation of machines, Heron reverses the explanatory relationship between the circle and the balance from the Mechanica; there, as noted above (p.

57 44 MARK J. SCHIEFSKY FIGURE 13. 9). Drachmann’s reconstruction (The Mechanical Technology, p. 65), made from the figure in Ms L. 8, the moving force applied at the end of the lever corresponds to the force on the larger circle and the load to the weight on the smaller circle. But because the load rests partly on the ground, it requires less force to move it than in the other case. We imagine a vertical line HZ drawn through the corner of the load that remains on the ground. Z) is in equilibrium with the portion HZH.

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