# Download An elementary Treatise on Plane and Solid Geometry by Benjamin Peirce PDF

By Benjamin Peirce

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The empty set and a set containing one point are convex by convention. convex body A convex set that is closed, bounded, nonempty, and has at least one interior point. convex combination A sum of scalar multiples of one or more vectors where the scalars are non-negative and their sum is 1. A convex combination of two or more vectors lies in their convex hull. Convex polygon convex cover See convex hull. convex function A real-valued function f with the property that λ for f (1 − λλx1 ) + λλx2 ≤ (1 − λλx1 ) + λx 2 any two points x1 and x2 in the domain of the function and any λ in the interval [0, 1].

Central vanishing point The point on the horizon line in a perspective picture where the images of lines perpendicular to the picture plane meet. It is not necessarily in the center of the picture. glossary 26 center of a parallelogram – central vanishing point centrode – chord glossary centrode The instantaneous center of rotation of a rigid moving body. The centrode of two curves is the locus of the instantaneous center of rotation of a rigid body that has a point fixed on each curve. centroid The center of gravity of a geometric shape.

The other three points are the vertices of the circumcevian triangle. circumcircle A circle that intersects every vertex of a polygon. The center of the circumcircle of a triangle is the intersection of the three perpendicular bisectors of the sides of the triangle. circumconic A conic section that passes through the vertices of a given triangle. circumference The points of a circle. Also, the measure of the total arc length of a circle; it is 2π times the radius of the circle. circumnormal triangle The circumnormal triangle is obtained by rotating the circumtangential triangle by 60°.