Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 8
... CONE . THE SPHERE . SPHERICAL TRIANGLES . SPHERICAL POLY- PAGE 195 220 224 254 GONS EXERCISES ON BOOK VIII . 257 287 BOOK IX . MEASUREMENT OF THE THREE ROUND BODIES 290 EXERCISES ON BOOK IX .. • · 308 MISCELLANEOUS EXERCISES ON SOLID ...
... CONE . THE SPHERE . SPHERICAL TRIANGLES . SPHERICAL POLY- PAGE 195 220 224 254 GONS EXERCISES ON BOOK VIII . 257 287 BOOK IX . MEASUREMENT OF THE THREE ROUND BODIES 290 EXERCISES ON BOOK IX .. • · 308 MISCELLANEOUS EXERCISES ON SOLID ...
Page 262
William Chauvenet. PROPOSITION III . - THEOREM . 15. Every section of a cone made by a plane passing through its vertex is a triangle . Let the cone S - ABCD be cut by a plane SBC , which passes through the vertex S and cuts the base in ...
William Chauvenet. PROPOSITION III . - THEOREM . 15. Every section of a cone made by a plane passing through its vertex is a triangle . Let the cone S - ABCD be cut by a plane SBC , which passes through the vertex S and cuts the base in ...
Page 294
... CONE . 9 area of the convex , or lateral , surface ts lateral area . 15. Definition . A pyramid is inscribed in a cone 294 ELEMENTS OF GEOMETRY .
... CONE . 9 area of the convex , or lateral , surface ts lateral area . 15. Definition . A pyramid is inscribed in a cone 294 ELEMENTS OF GEOMETRY .
Page 295
... cone and its vertex coincides with the vertex of the cone . It follows that the lateral edges of the pyramid are elements of the cone . An inscribed pyramid is wholly con- tained within the cone . 16. Definition . A pyramid is circum- B ...
... cone and its vertex coincides with the vertex of the cone . It follows that the lateral edges of the pyramid are elements of the cone . An inscribed pyramid is wholly con- tained within the cone . 16. Definition . A pyramid is circum- B ...
Page 297
... cone of revolution is equal to the product of the circumference of its base by half its slant height . Suggestion . Circumscribe a regular pyramid about the cone , and then sup- pose the number of its faces to be indefinitely increased ...
... cone of revolution is equal to the product of the circumference of its base by half its slant height . Suggestion . Circumscribe a regular pyramid about the cone , and then sup- pose the number of its faces to be indefinitely increased ...
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Common terms and phrases
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Popular passages
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 131 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 245 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.