The law of continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite". Kepler used the law of continuity to calculate the area of the circle by representing it as an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely many triangles with infinitesimal bases. Leibniz used the principle to extend concepts such as arithmetic operations from ordinary numbers to infinitesimals, laying the groundwork for infinitesimal calculus. The transfer principle provides a mathematical implementation of the law of continuity in the context of the hyperreal numbers.
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| - Law of continuity (en)
- Принцип непрерывности (ru)
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| - The law of continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite". Kepler used the law of continuity to calculate the area of the circle by representing it as an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely many triangles with infinitesimal bases. Leibniz used the principle to extend concepts such as arithmetic operations from ordinary numbers to infinitesimals, laying the groundwork for infinitesimal calculus. The transfer principle provides a mathematical implementation of the law of continuity in the context of the hyperreal numbers. (en)
- Принцип непрерывности (или закон непрерывности) — эвристический научно-философский принцип, используемый в естествознании — в математике, физике, биологии и других науках. Вкратце этот принцип можно свести к двум правилам: 1.
* Все изменения в природе происходят непрерывно, без скачков («»). 2.
* Всякое изменение требует ненулевого периода времени. Первым эти принципы ясно выразил Лейбниц (1676 год и далее), который добавил к ним несколько других, которые также связывал с принципом непрерывности: (ru)
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| - The law of continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite". Kepler used the law of continuity to calculate the area of the circle by representing it as an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely many triangles with infinitesimal bases. Leibniz used the principle to extend concepts such as arithmetic operations from ordinary numbers to infinitesimals, laying the groundwork for infinitesimal calculus. The transfer principle provides a mathematical implementation of the law of continuity in the context of the hyperreal numbers. A related law of continuity concerning intersection numbers in geometry was promoted by Jean-Victor Poncelet in his "Traité des propriétés projectives des figures". (en)
- Принцип непрерывности (или закон непрерывности) — эвристический научно-философский принцип, используемый в естествознании — в математике, физике, биологии и других науках. Вкратце этот принцип можно свести к двум правилам: 1.
* Все изменения в природе происходят непрерывно, без скачков («»). 2.
* Всякое изменение требует ненулевого периода времени. Первым эти принципы ясно выразил Лейбниц (1676 год и далее), который добавил к ним несколько других, которые также связывал с принципом непрерывности: 1.
* бесконечную делимость физических величин; 2.
* принцип неразличимости — в природе нет двух совершенно тождественных вещей. (ru)
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