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Article ID: CBB673858384

The chords theorem recalled to life at the turn of the eighteenth century (2021)

Del Centina, Andrea (Author)
Fiocca, Alessandra (Author)

Historia Mathematica
Volume: 56
Pages: 6-39

DOI: 10.1016/j.hm.2021.03.002

URI: https://www.sciencedirect.com/science/article/pii/S0315086021000203

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This paper is a historical account of the chords theorem, for conic sections from Apollonius to Boscovich. We comment the most significant proofs and applications, focusing on Newton's solution of the Pappus four lines problem. Newton's geometrical achievements drew L'Hospital's attention to the chords theorem as a fundamental one, and led him to search for a simple and direct proof, that he finally obtained by the method of projection. Stirling gave a very elegant algebraic proof; then Boscovich succeeded in finding an almost immediate geometrical proof, and showed how to develop the elements of conic sections starting from this theorem. Sommario Questo articolo è un resoconto storico sul teorema delle corde per le sezioni coniche, da Apollonio a Boscovich. Si commentano le più significative dimostrazioni ed applicazioni, focalizzando sulla soluzione di Newton del problema delle quattro rette di Pappo. I risultati geometrici di Newton attrassero l'attenzione di L'Hospital sul teorema delle corde come fondamentale, e lo condussero alla ricerca di una dimostrazione semplice e diretta, ottenuta col metodo di proiezione. Stirling diede una elegante dimostrazione algebrica; successivamente Boscovich riuscì a trovare una dimostrazione geometrica quasi immediata, e mostrò come sviluppare gli elementi delle sezioni coniche partendo da questo teorema.

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