De Linearum Curvarum cum Lineis Rectis Comparatione

work by Fermat

Written by

The Information Architects of Encyclopaedia Britannica

Last updated

June 25, 2026

Quick Summary

"De Linearum Curvarum cum Lineis Rectis Comparatione" (Concerning the Comparison of Curved Lines with Straight Lines) was a paper by Pierre de Fermat published in 1660. In this work, Fermat demonstrated that certain algebraic curves, such as the semicubical parabola, could be precisely measured (rectified) and compared to straight lines. This was a significant achievement as it challenged the prevailing view that algebraic curves were generally impossible to rectify. Fermat's methods for determining tangents to curves and finding their maximum and minimum points also contributed to his recognition as a pioneer of differential calculus.12

Summary created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

2 Britannica Sources

Ask Britannica AI about this topic

Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.

Pierre de Fermat
Analyses of curves
In a paper entitled “De Linearum Curvarum cum Lineis Rectis Comparatione” (“Concerning the Comparison of Curved Lines with Straight Lines”), he showed that the semicubical parabola and certain other algebraic curves were strictly rectifiable. He also solved the related problem of finding the surface area of a segment of…
Read More
In a paper entitled “De Linearum Curvarum cum Lineis Rectis Comparatione” (“Concerning the Comparison of Curved Lines with Straight Lines”), he showed that the semicubical parabola and certain other algebraic curves were strictly rectifiable. He also solved the related problem of finding the surface area of a segment of…
Read More