The Essentials of Geometry, Plane and Solid, As Taught in French and German Schools

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1871 edition. Excerpt: ...of these polygons. Proportion of the circumference to the diameter. Rectification of the circumference. 96. The name of circle is given to the surface comprised by the circumference. (Fig. 78.) A circular sector is the part of the circle terminated by two radii, and the corresponding arc s. A circular segment is the portion of the circle comprised between two chords, or between a chord and a corresponding arc9. AOB is a circular sector; CMND and MXN are two circular segments, the first of two bases, and the second of one base. Circles that have the same radii are equal if the respective radii are equal. All circles are similar. 97. A polygon is inscribed in a circumference, or a circumference is circumscribed about a polygon, when all the sides of a polygon are chords to the circumference. A polygon is circumscribed about a circumference, or a circumference is inscribed in a polygon, when all the sides of the polygon are tangents to the circumference. Figure 79 represents a hexagon inscribed in a circumference, and a quadrilateral circumscribed about the same. s "Un secteur est la portion d'un cercle comprise entre deux rayons." Amiot, Elements, op. cit., 15ieme Leijon, p. 56. 9 "Un segment de cercle est la portion d'un cercle comprise entre un arc et sa corde." Ibid. 98. If a circumference is divided into equal parts, and through the points of division chords or tangents be traced, the inscribed or circumscribed polygon will be regular. In the first case, all its sides are equal, because they are chords of equal arcs, and the angles are also equal, because they are inscribed angles embraced by the same arc. (Fig. 80.) The same thing is verified in the case when the straight lines are tangents drawn through the points...