# 1656 Infinite and infinitesimal

## The book of science

Tom Sharp

Tom Sharp

John Wallis mathematics |

- In 1635, Bonaventura Cavalieri
- introduced infinitesimals,
- which he called indivisibles,
- as a means of calculating areas and volumes.
- John Wallis’s treatise on conic sections
- clarified Decartes’ work on analytic geometry
- and introduced the symbol ∞ for infinity
- and the symbol 1/∞ for the infinitesimal.
- Wallis’s work
*Arithmetica Infinitorum* - finds the area under a curve by integration
- and established the principle of interpolation
- to derive the value of π.
- Thus Wallis, James Gregory, and Isaac Barrow
- contributed to the development of integral calculus
- put to use by Isaac Newton and given
- modern notation by Gottfried Wilhelm Leibniz.

- The infinity symbol, ∞,
- the digit 8 on its side,
- traces a closed path
- without an end.
- More could be said
- approaching the symbol
- but not what it symbolizes
- unless turning into itself.

- John Wallis introduced the number line
- and interpreted negative numbers
- as values greater than infinity
- rather than as less than nothing.
- Me, I think of negative numbers
- as mere arithmetic conveniences
- and I’ve learned there are
- positive infinities greater than infinity.

James Gregory stated and proved the fundamental theorem of calculus for a special class of curves; Isaac Barrow proved the fundamental theorem in general, showing that differentiation and integration are inverses of each other. Isaac Newton was a student of Isaac Barrow.

See also in

The book of science:Zero—BrahmaguptaNumber system—Leonardo Pisano Bigollo (Fibonacci)Fundamental theorem of calculus—James Gregory, Isaac BarrowCalculus—Isaac Newton, Gottfried Wilhelm LeibnizPrincipia Mathematica—Isaac NewtonPi—Johann Heinrich Lambert, Ferdinand von LindemannReadings on wikipedia: