Ⅰ．Introductory Remarks on the Nature and Objects of Mathematics 1
Ⅱ．On Arithmetical Notation 7
Ⅲ．Elementary Rules of Arithmetic 13
Ⅳ．Arithmetical Fractions 19
Ⅴ．Decimal Fractions 25
Ⅵ．Algebraical Notation and Principles 33
Ⅶ．Elementary Rules of Algebra 41
Ⅷ．Equations of the First Degree 55
Ⅸ．On the Negative Sign,etc 63
Ⅹ．Equations of the Second Degree 77
Ⅺ．On Roots in General,and Logarithms 95
ⅩⅡ．On the Study of Algebra 105
ⅩⅢ．On the Definitions of Geometry 115
ⅩⅣ．On Geometrical Reasoning 121
ⅩⅤ．On Axioms 137
ⅩⅥ．On Proportion 143
ⅩⅦ．Application of Algebra to the Measurement of Lines, Angles,Proportion of Figures,and Surfaces 159
INDEX 171