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According to Hans Samelson's historical note "Differential Forms, the Early Days", both notions were introduced in Les Méthodes nouvelles de la Mécanique Céleste by Poincaré (vol. 3, Gauthier-Villars, Paris, 1899, pp. 9-15). Samelson notes

Given a p-form $\omega$ whose integral over any closed manifold is 0, then there is a (p - 1)-form, let's say $\psi$, that stands to $\omega$ in the relation described by Stokes's theorem (so that $\omega=d\psi$; he calls such an $\omega$ exact). Thus we have here the non-trivial half of what today one calls the Poincare Lemma: $\omega$ is $d\psi$ for some $\psi$ ($\omega$ is "exact") if and only if $d\omega = 0$ ($\omega$ is "closed").

Apparently, it had taken some time for the terminology to stabilize as, for instance, Goursat used the term "exacte" in his book for a form that today one calls closed (E. Goursat, Leçons sur le problème de Pfaff, Hermann, Paris, 1922).

According to Hans Samelson's historical note "Differential Forms, the Early Days", both notions were introduced in Les Méthodes nouvelles de la Mécanique Céleste by Poincaré (vol. 3, Gauthier-Villars, Paris, 1899, pp. 9-15). Samelson notes

Given a p-form $\omega$ whose integral over any closed manifold is 0, then there is a (p - 1)-form, let's say $\psi$, that stands to $\omega$ in the relation described by Stokes's theorem (so that $\omega=d\psi$; he calls such an $\omega$ exact). Thus we have here the non-trivial half of what today one calls the Poincare Lemma: $\omega$ is $d\psi$ for some $\psi$ ($\omega$ is "exact") if and only if $d\omega = 0$ ($\omega$ is "closed").

Apparently, it had taken some time for the terminology to stabilize as, for instance, Goursat used the term "exacte" in his book for a form that today one calls closed (E. Goursat, Leçons sur le problème de Pfaff, Hermann, Paris, 1922).

According to Hans Samelson's historical note "Differential Forms, the Early Days", both notions were introduced in Les Méthodes nouvelles de la Mécanique Céleste by H. Poincaré:

Given a p-form $\omega$ whose integral over any closed manifold is 0, then there is a (p - 1)-form, let's say $\psi$, that stands to $\omega$ in the relation described by Stokes's theorem (so that $\omega=d\psi$; he calls such an $\omega$ exact). Thus we have here the non-trivial half of what today one calls the Poincare Lemma: $\omega$ is $d\psi$ for some $\psi$ ($\omega$ is "exact") if and only if $d\omega = 0$ ($\omega$ is "closed").

Apparently, the terminology had taken some time to stabilize as, for instance, Goursat used the term "exacte" in his book for a form that today one calls closed (E. Goursat, Leçons sur le problème de Pfaff, Hermann, Paris 1922, p. 105).

According to Hans Samelson's historical note "Differential Forms, the Early Days", both notions were introduced in Les Méthodes nouvelles de la Mécanique Céleste by Poincaré (vol. 3, Gauthier-Villars, Paris, 1899, pp. 9-15). Samelson notes

Given a p-form $\omega$ whose integral over any closed manifold is 0, then there is a (p - 1)-form, let's say $\psi$, that stands to $\omega$ in the relation described by Stokes's theorem (so that $\omega=d\psi$; he calls such an $\omega$ exact). Thus we have here the non-trivial half of what today one calls the Poincare Lemma: $\omega$ is $d\psi$ for some $\psi$ ($\omega$ is "exact") if and only if $d\omega = 0$ ($\omega$ is "closed").

Apparently, it had taken some time for the terminology to stabilize as, for instance, Goursat used the term "exacte" in his book for a form that today one calls closed (E. Goursat, Leçons sur le problème de Pfaff, Hermann, Paris, 1922).

According to Hans Samelson's "Differential Forms, the Early Days", both notions were introduced in Les Méthodes nouvelles de la Mécanique Céleste by H. Poincaré:

Given a p-form $\omega$ whose integral over any closed manifold is 0, then there is a (p - 1)-form, let's say $\psi$, that stands to $\omega$ in the relation described by Stokes's theorem (so that $\omega=d\psi$; he calls such an $\omega$ exact). Thus we have here the non-trivial half of what today one calls the Poincare Lemma: $\omega$ is $d\psi$ for some $\psi$ ($\omega$ is "exact") if and only if $d\omega = 0$ ($\omega$ is "closed").

According to Hans Samelson's historical note "Differential Forms, the Early Days", both notions were introduced in Les Méthodes nouvelles de la Mécanique Céleste by H. Poincaré:

Given a p-form $\omega$ whose integral over any closed manifold is 0, then there is a (p - 1)-form, let's say $\psi$, that stands to $\omega$ in the relation described by Stokes's theorem (so that $\omega=d\psi$; he calls such an $\omega$ exact). Thus we have here the non-trivial half of what today one calls the Poincare Lemma: $\omega$ is $d\psi$ for some $\psi$ ($\omega$ is "exact") if and only if $d\omega = 0$ ($\omega$ is "closed").

Apparently, the terminology had taken some time to stabilize as, for instance, Goursat used the term "exacte" in his book for a form that today one calls closed (E. Goursat, Leçons sur le problème de Pfaff, Hermann, Paris 1922, p. 105).