I. Introduction. Algebraic Results;
II. Coordinates. Lengths of straight lines and areas of triangles;
III. Locus. Equation to locus;
IV. The straight line;
V. The straight line. polar equations and oblique coordinates;
VI. Equations representing two or more straight lines;
VII. Transformation of coordinates;
VIII. The circle;
IX. Systems of circles;
X. Conic sections. The parabola;
XI. The parabola (continued);
XII. The ellipse;
XIII. The hyperbola;
XIV. Polar Equation to conic;
XV. General equation. Tracing of curves;
XVI. General equation;
XVII. Miscellaneous propositions;