Elements of Geometry and Trigonometry |
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Page 10
... convex set which is , nevertheless , not the convex hull of a finite ( or even denumerable ) set of points . Bearing this in mind , we make the following definition : Definition . The convex hull of a finite set of points is called a ...
... convex set which is , nevertheless , not the convex hull of a finite ( or even denumerable ) set of points . Bearing this in mind , we make the following definition : Definition . The convex hull of a finite set of points is called a ...
Page 287
... convex solid polyhedra is a convex solid polyhedron : P = 1P1 + λ2P2 . If Q is a " face " of P ( i.e. , a face , edge , or vertex ) then Q = A1Q1 + A2Q2 , where Q1 and Q2 are " faces " of P1 and P2 lying in support planes with parallel ...
... convex solid polyhedra is a convex solid polyhedron : P = 1P1 + λ2P2 . If Q is a " face " of P ( i.e. , a face , edge , or vertex ) then Q = A1Q1 + A2Q2 , where Q1 and Q2 are " faces " of P1 and P2 lying in support planes with parallel ...
Page 283
... convex function f : R " → R is outer semi - continuous at any x Є R " , i.e. Vε > 0 , 380 : ye B ( x , 8 ) ⇒ aƒ ( y ) ▽ aƒ ( x ) + B ( 0 , ɛ ) . ( 6.2.1 ) PROOF . Assume for contradiction that , at some x , there are ɛ > 0 and a ...
... convex function f : R " → R is outer semi - continuous at any x Є R " , i.e. Vε > 0 , 380 : ye B ( x , 8 ) ⇒ aƒ ( y ) ▽ aƒ ( x ) + B ( 0 , ɛ ) . ( 6.2.1 ) PROOF . Assume for contradiction that , at some x , there are ɛ > 0 and a ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
14 other sections not shown
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adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex