I. Introductory Remarks on the Nature and Objects of Mathematics
II. On Arithmetical Notation
III. Elementary Rules of Arithmetic
IV. Arithmetical Fractions
V. Decimal Fractions
VI. Algebraical Notation and Principles
VII. Elementary Rules of Algebra
VIII. Equations of the First Degree
IX. On the Negative Sign, etc
X. Equations of the Second Degree
XI. On Roots in General, and Logarithms
XII. On the Study of Algebra
XIII. On the Definitions of Geometry
XIV. On Geometrical Reasoning
XV. On Axioms
XVI. On Proportion
XVII. Application of Algebra to the Measurement of Lines, Angles, Proportion of Figures, and Surfaces