“Incommensurability is not to be feared:” On the general method for the centres of gravity in The Letters of A. Dettonville
Cortese, João
“Incommensurability is not to be feared:” On the general method for the centres of gravity in The Letters of A. Dettonville - 2023.
27
In the Lettres de A. Dettonville, Pascal expounds a “general method for the centers of gravity.” It is a method of indivisibles which is based on Archimedean statics and also exploits “arithmetic” resources (triangular sums). Fundamental to this method is the requirement of equal divisions of the magnitudes at play (generating the “regular portions” which will be manipulated in the sums). From the point of view of modern mathematical analysis, such a requirement seems too strong, and some statements made by Pascal in the Lettres de A. Dettonville could lead one to believe, as claimed by Pierre Costabel, that this constraint is not necessary, even for the author himself. In this article we intend to show that if we go back to the detail of Pascal’s procedure and if we consider certain neglected aspects of Archimedes’ method, as Pascal might have inherited it, it is possible to defend a more charitable reading, where the constraint of equal divisions ensures that this is an authentically “general method.”
“Incommensurability is not to be feared:” On the general method for the centres of gravity in The Letters of A. Dettonville - 2023.
27
In the Lettres de A. Dettonville, Pascal expounds a “general method for the centers of gravity.” It is a method of indivisibles which is based on Archimedean statics and also exploits “arithmetic” resources (triangular sums). Fundamental to this method is the requirement of equal divisions of the magnitudes at play (generating the “regular portions” which will be manipulated in the sums). From the point of view of modern mathematical analysis, such a requirement seems too strong, and some statements made by Pascal in the Lettres de A. Dettonville could lead one to believe, as claimed by Pierre Costabel, that this constraint is not necessary, even for the author himself. In this article we intend to show that if we go back to the detail of Pascal’s procedure and if we consider certain neglected aspects of Archimedes’ method, as Pascal might have inherited it, it is possible to defend a more charitable reading, where the constraint of equal divisions ensures that this is an authentically “general method.”
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