Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 8
... CYLINDER . THE 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 ...
... CYLINDER . THE 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 ...
Page 259
... cylinder made by a plane perpendicular to its base is a rectangle . PROPOSITION II . - THEOREM . 8. The bases of a cylinder are equal . Let BD be the straight line joining two points of the perimeter of the lower base , and let a plane ...
... cylinder made by a plane perpendicular to its base is a rectangle . PROPOSITION II . - THEOREM . 8. The bases of a cylinder are equal . Let BD be the straight line joining two points of the perimeter of the lower base , and let a plane ...
Page 291
... cylinder . The cylinder is obviously wholly contained in the prism . 4. Definition . A right section of a cylinder is a section made by a plane perpendicular to its elements ; as abcdef . The intersection of the same plane with an ...
... cylinder . The cylinder is obviously wholly contained in the prism . 4. Definition . A right section of a cylinder is a section made by a plane perpendicular to its elements ; as abcdef . The intersection of the same plane with an ...
Page 293
... cylinder of revolution is equal to the product of the circumference of its base by its altitude . This may be ... cylinders of revo- lution are to each other as the squares of their altitudes , or as the squares of the radii of their ...
... cylinder of revolution is equal to the product of the circumference of its base by its altitude . This may be ... cylinders of revo- lution are to each other as the squares of their altitudes , or as the squares of the radii of their ...
Page 294
... cylinder of revolution this proposition may be formulated , VR . H. ( V. , Proposition IX . , Corol- lary . ) 13. COROLLARY II . The volumes of similar cylinders of revo- tion are to each other as the cubes of their altitudes , or as ...
... cylinder of revolution this proposition may be formulated , VR . H. ( V. , Proposition IX . , Corol- lary . ) 13. COROLLARY II . The volumes of similar cylinders of revo- tion are to each other as the cubes of their altitudes , or as ...
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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.