Abstract
In this chapter Latin and Arabic Middle Ages mechanics are compared, both based on virtual displacements VWLs. In the first part Arabs are considered who, with Thabit ibn Qurra, use as a principle of equilibrium a VWL for which the effectiveness of a weight on a scale is proportional to its virtual displacement measured along the arc of the circle described by the arm from which the weight is suspended. In the second part Latin scholars are considered who, with Jordanus de Nemore, assume as principles two distinct VWLs. A VWL is associated with the concept of gravity of position for which the efficacy of a weight on a scale is the greater the more its virtual displacement is next to the vertical. Another VWL is associated with the resistance of a weight to be lifted, which depends on the lifting entities in a given time. In formulas: What can raise a weight p of a height h can raise p/n of nh.
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Notes
- 1.
p. 12.
- 2.
The Arabic translation of Physica has a long and complicated history. The first translation is attributed to Ibn-an-Nadima (786–803). The best, and only extant today, is by Isahaq-ibn-Hunayn, at the end of the nineth century [334].
- 3.
De caelo was translated by al-Kindi circle during the 9th century.
- 4.
The attribution of this text to Euclid is controversial. It is known only recently in an Arabic version by Franz Woepcke [399].
- 5.
The expression Scientia de ponderibus comes from the translation from Arabic into Latin of al-Farabi’s work (Science of devices was instead translated as Scientia de ingenii) by Dominicus Gundissalinus [248], p. 17.
- 6.
pp. 3–4.
- 7.
p. 93.
- 8.
p. 5.
- 9.
pp. 77–118.
- 10.
pp. 84–85.
- 11.
pp. 2–3.
- 12.
p. 47.
- 13.
p. 31.
- 14.
Mohammed Abattouy registers a recent hitherto unknown copy in Florence [247], p. 17.
- 15.
A similar statement is found also in the Liber Euclidi de ponderosi et levi: “bodies are equal in strength whose motions through equal places, in the same air or the same water, are equal in times” and in some following propositions [171], p. 27.
- 16.
p. 90.
- 17.
pp. 33–35.
- 18.
p. 120.
- 19.
pp. 146–147.
- 20.
pp. 50–63.
- 21.
pp. 92, 94. Translation in [171].
- 22.
pp. 37–38.
- 23.
p. 90. Translation in [171].
- 24.
p. 92. English translation, my accommodation.
- 25.
p. 44.
- 26.
p. 164.
- 27.
p. 94. Translation in [171].
- 28.
p. 149.
- 29.
p. 38.
- 30.
p. 44.
- 31.
p. 15.
- 32.
- 33.
vol. 2, p. 122.
- 34.
p. 75.
- 35.
p. 26.
- 36.
p. 82r.
- 37.
p. 3.
- 38.
p. 150. Translation in [171].
- 39.
pp. 174, 176. English translation adapted.
- 40.
p. 208.
- 41.
This proposition states that given four quantities, A, B, H, K, if (A + B)∕A > (H + K)∕H, then (A + B)∕B < (H + K)∕K [221], p. 104, 105. So assumed A = a, B = b, H = p(a;)K = p(b), c = a from (a + b)∕c < p(a + b)∕p(c) i.e. (a + b)∕a < [p(a) + p(b)]∕p(a) it follows (a + b)∕b > [p(a) + p(b)]∕p(b) = p(a + b)∕ p(b).
- 42.
p. 176. Translation in [171].
- 43.
pp. 176, 178. Translation in [171].
- 44.
pp. 182, 184. Translation in [171].
- 45.
pp. 184, 186. Translation in [171].
- 46.
p. 186. Translation in [171].
- 47.
Proposition R 3.01, p. 204
- 48.
p. 190. Translation in [171].
- 49.
p. 190. Translation in [171].
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Capecchi, D. (2012). Arabic and Latin science of weights. In: History of Virtual Work Laws. Science Networks. Historical Studies, vol 42. Springer, Milano. https://doi.org/10.1007/978-88-470-2056-6_4
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