Table of contents of William Emerson's The Doctrine of Fluxions (1743) (2nd edn., 1757)

Preface

The Doctrine of Fluxions

Postulatum

Definitions

Notation

Axioms

Section I The Fundamental Principles and Operations of Fluxions

Prop.I. The fluxion of any fluent or generated quantity is equal to the sum of the fluxions of all the roots or sides, each multiply'd continually by the index of its power, and by the given fluent when divided by the said root or side

Prop.II If two fluents or variable quantities be equal to each other, or in a given ratio; their fluxions will be equal, or in the same given ratio. And if two flowing quantities be equal or in a given ratio, their contemporary fluents will be equal, or in the same given ratio

Prop.III To find the fluxions of quantities Prop. IV–VIII several theorems for finding the fluents of quantities from other given fluents

Prop.IX To transform fluxional quantities into others equal to them

Prop.X To find the fluents of quantities by infinite series

Prop.XI To find fluents by the table

Prop.XII To correct the fluent of a given fluxions

Prop.XIII To investigate a problem by the method of fluxion

Section II The investigation and solution of some of the most general and useful problems in the mathematics

Prob.I To find the maxima and minima of quantities

Prob.II To find the logarithms of numbers