Article ID: CBB000410829

Passage to the Limit in Proposition I, Book I of Newton's Principia (2003)

unapi

The purpose of this paper is to analyze the way in which Newton uses his polygon model and passes to the limit in Proposition I, Book I of his Principia. It will be evident from his method that the limit of the polygon is indeed the orbital arc of the body and that his approximation of the actual continuous force situation by a series of impulses passes correctly in the limit into the continuous centripetal force situation. The analysis of the polygon model is done in two ways: (1) using the modern concepts of force, linear momentum, linear impulse, and velocity, and (2) using Newton's concepts of motive force and quantity of motion. It should be clearly understood that the term force without the adjective motive, is used in the modern sense, which is that force is a vector which is the time rate of change of the linear momentum. Newton did not use the word force in this modern sense. The symbol F denotes modern force. For Newton force was motive force, which is measured by the change in the quantity of motion of a body. Newton's quantity of motion is proportional to the magnitude of the modern vector momentum. Motive force is a scalar and the symbol Fm is used for motive force. (the abstract)

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Authors & Contributors
Nauenberg, Michael
Ferraro, Giovanni
D'Andria, Antonio
Giovanni Capobianco
Enea, Maria Rosaria
Giannini, Giulia
Concepts
Mathematics
Calculus
Physics
Geometry
Celestial mechanics
Astronomy
Time Periods
18th century
17th century
19th century
Enlightenment
21st century
20th century, early
Places
France
England
Italy
Europe
Naples (Italy)
Russia
Institutions
St. Petersburg Academy of Sciences
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