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

## Blaise Pascal: *Traité des Sinus du Quart de Cercle*

Published $\text {1658}$

In English:

*Treatise on the Sines of a Quadrant of a Circle*

### Subject Matter

### Contents

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## Critical View

*A great light burst upon me.*

## 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 infinitesimally 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

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.19$: Leibniz ($\text {1646}$ – $\text {1716}$)