| Lecture I. | Areas of surfaces: Conversion of rectilineal figures to triangles of equal area, similar figures which have an area of a given proportion. |
| II. | Problems relating to areas. |
| III. | Figures in relation to figures (geometrical tracery). |
| IV. | Construction of helical and spiral curves (applied to screws, staircases, handrailing &c.) |
| V. | The ellipse and parabola, their perpendiculars and tangents (applied to arches, and their voussoirs). |
| VI. | Construction of curves from tabular data, as varying pressure, temperature, and resistance, involving the use of abscissa and ordinate; curves traced by a point in motion; cycloid, epicyloid, and trochoid curves applied to gearing; the conchoid and cissoid curves. |
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