Division of polygons into triangles.—Sum of their interior angles.—Equality and construction of polygons.
Similar polygons.—Their decomposition into similar triangles.—The right lines similarly situated in the two polygons are proportional to the homologous sides of the polygons.—To construct, on a given line, a polygon similar to a given polygon.—The perimeters of two similar polygons are to each other as the homologous sides of these polygons.
Of the right line and the circumference of the circle.
Simultaneous equality of arcs and chords in the same circle.—The greatest arc has the greatest chord, and reciprocally.—Two arcs being given in the same circle or in equal-circles, to find the ratio of their lengths.
Every right line drawn perpendicular to a chord at its middle, passes through the centre of the circle and through the middle of the arc subtended by the chord.—Division of an arc into two equal parts.—To pass the circumference of a circle through three points not in the same right line.
The tangent at any point of a circumference is perpendicular to the radius passing through that point.
The arcs intercepted in the same circle between two parallel chords, or between a tangent and a parallel chord, are equal.
Measure of angles.
If from the summits of two angles two arcs of circles be described with the same radius, the ratio of the arcs included between the sides of each angle will be the same as that of these angles.—Division of the circumference into degrees, minutes, and seconds.—Use of the protractor.
An angle having its summit placed, 1o at the centre of a circle; 2o on the circumference of that circle; 3o within the circle between the centre and the circumference; 4o without the circle, but so that its sides cut the circumference; to determine the ratio of that angle to the right angle, by the consideration of the arc included between its sides.