Book:Blaise Pascal/Traité des Sinus du Quart de Cercle

From ProofWiki
Jump to navigation Jump to search

Blaise Pascal: Traité des Sinus du Quart de Cercle

Published $1658$.
In English:

Treatise on the Sines of a Quadrant of a Circle


Subject Matter


Contents

Critical View

A great light burst upon me.
-- Gottfried Wilhelm von Leibniz


Historical Note

Gottfried Wilhelm von Leibniz reported that on reading Blaise Pascal's $1658$ work Traité des Sinus du Quart de Cercle, it was as though a great light burst upon him.

He realised that the tangent to a curve can be found by dividing the differences between the ordinates by the abscissas of two neighbouring points as these differences become arbitrarily small.

At the same time, he noticed that the area under the curve is the sum of the infinitely thin rectangles that make up this area.

And, most importantly, he noticed that the two processes, that is, differentiation and integration, were inverses of each other, linked together by the infinitesimal triangle.

Hence the Fundamental Theorem of Calculus was conceived.


Sources