Fermat's treatise on quadrature: A new reading

The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, R x+m/n dx, or under a higher hyperbola, R x-m/n dx with the appropriate limits of integration in each case , has a second part which was not understood by Fermat s contemporaries. This second part of the Treatise is obscure and difficult to read and even the great Huygens described it as'published with many mistakes and it is so obscure (with proofs redolent of error) that I have been unable to make any sense of it'. Far from the confusion that Huygens attributes to it, in this paper we try to prove that Fermat, in writing the Treatise, had a very clear goal in mind and he managed to attain it by means of a simple and original method. Fermat reduced the quadrature of a great number of algebraic curves to the quadrature of known curves: the higher parabolas and hyperbolas of the first part of the paper. Others, he reduced to the quadrature of the circle. We shall see how the clever use of two procedures, quite novel at the time: the change of variables and a particular case of the formulaof integration by parts, provide Fermat with the necessary tools to square very easily curves as well-known as the folium of Descartes, the cissoid of Diocles or the witch of Agnesi.

Fortifications. Etat, en forme de mémoire, des souterrains et des battimens militaires qui sont à la citadelle de Saint-Jean-Pied-de-Port

Ancien possesseur : Argenson, Antoine-René de Voyer (1722-1787 ; marquis de Paulmy d')

Mémoire sur le chemin de St-Jean-Pied-de-Port à Roncevaux, au mois d'aoust 1753

Ancien possesseur : Argenson, Antoine-René de Voyer (1722-1787 ; marquis de Paulmy d')

Indications des différens chemins et défilés des frontières de France et d'Espagne, relatifs à la carte de Saint-Jean-Pied-de-Port

Ancien possesseur : Argenson, Antoine-René de Voyer (1722-1787 ; marquis de Paulmy d')

Mémoire sur les bandes béarnoises

Ancien possesseur : Argenson, Antoine-René de Voyer (1722-1787 ; marquis de Paulmy d')

State power and protected areas: Dynamics and contradictions of forest conservation in Madhya Pradesh, India

The traditionally coercive and state-controlled governance of protected areas for nature conservation in developing countries has in many cases undergone change in the context of widespread decentralization and liberalization. This article examines an emerging "mixed" (coercive, community- and market-oriented) conservation approach in managed-resource protected areas and its effects on state power through a case study on forest protection in the central Indian state of Madhya Pradesh. The findings suggest that imperfect decentralization and partial liberalization resulted in changed forms, rather than uniform loss, of state power. A forest co-management program paradoxically strengthened local capacity and influence of the Forest Department, which generally maintained its territorial and knowledge-based control over forests and timber management. Furthermore, deregulation and reregulation enabled the state to withdraw from uneconomic activities but also implied reduced place-based control of non-timber forest products. Generally, the new policies and programs contributed to the separation of livelihoods and forests in Madhya Pradesh. The article concludes that regulatory, community- and market-based initiatives would need to be better coordinated to lead to more effective nature conservation and positive livelihood outcomes.