The area of a regular polygon is measured by half of the product of its perimeter by the radius of the inscribed circle.—The area of a circle is measured by half of the product of the circumference by the radius.—The areas of circles are to each other as the squares of the radii.
The area of a sector of a circle is measured by half of the product of the arc by the radius.—Measure of the area of a segment of a circle.
2. OF PLANES AND BODIES TERMINATED BY PLANE SURFACES.
Conditions required to render a right line and a plane respectively perpendicular.
Of all the lines which can be drawn from a given point to a given plane, the perpendicular is the shortest, and the oblique lines are longer in proportion to their divergence from the foot of the perpendicular.
Parallel right lines and planes.—Angles which have their sides parallel, and their openings turned in the same direction, are equal, although situated in different planes.
Dihedral angle.—How to measure the ratio of any dihedral angle to the right dihedral angle.
Planes perpendicular to each other.—The inter of two planes perpendicular to a third plane, is perpendicular to this third plane.
Parallel planes.—when two parallel planes are cut by a third plane the inters are parallel.—Two parallel planes have their perpendiculars common to both.
The shortest distance between two right lines, not intersecting and not parallel.