in architecture, the draught of a building, fortification, &c. wherein are expressed the several heights, widths, and thicknesses, such as they would appear were the building cut down perpendicularly from the roof to the foundation. Whence the profile is also called the section, sometimes orthographical section, and by Vitruvius also scagiography.

this sense, amounts to the same with elevation; and stands opposed to a plan or ichnography.

Profile is also used for the contour or outline of a figure, building, member of architecture, or the like; as a base, a cornice, &c. Hence profiling is sometimes used for designing, or describing the member with rule, compass, &c.

Thus \( \{a, a+d, a+2d, a+3d, \ldots\} \) increasing by the difference \( d \).

In numbers \( \{1, 4, 7, 10, \ldots\} \) increasing by the difference 3.

Geometric Progression, or Continued Geometric Proportion, is when the terms do increase or decrease by equal ratios: thus,

\[ \frac{a}{r}, \frac{a}{r^2}, \frac{a}{r^3}, \ldots \] increasing from a continual multiplication by \( r \).

\[ \frac{a}{r}, \frac{a}{r^2}, \frac{a}{r^3}, \ldots \] decreasing from a continual division by \( r \).

See the articles Fluxions, Geometry, and Series.