## Schultze and Sevenoak's Plane and Solid Geometry |

### From inside the book

Results 1-5 of 22

Page 342

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**lateral edges**. TRUNCATED PRISM RECTANGULAR PARALLELOPIPED RIGHT SECTION 567. DEF . A right section of a prism is a ... edge of a prism , it is perpen- dicular to every**lateral edge**( 504 ) . 568. DEF . A parallelopiped is a prism ... Page 343

... edges ? of vertices ? PROPOSITION I. THEOREM 572. The sections of a prism made by parallel planes cutting all the

... edges ? of vertices ? PROPOSITION I. THEOREM 572. The sections of a prism made by parallel planes cutting all the

**lateral edges**are congruent polygons . M D K Given KM , a prism intersected by parallel planes AD and A'D ' , cutting all ... Page 344

... lateral area , E a

... lateral area , E a

**lateral edge**, and P the perimeter of right section GK . To prove Proof . = L PXE . BB ' GH . .. area AB ' : = GHX BB ' GH X E. Similarly area BC ' HI X E , etc. But ( 497 ) ( 350 ) L = area AB ' + area BC ' + ... Page 346

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**lateral edge**of the oblique prism . M ' K B GİL Di M K C A B Given GM , a right section of oblique prism AD ' , and GM ' , a right prism whose altitude is equal to a**lateral edge**of AD ' . To prove AD ' GM ' . = Proof . In ... Page 352

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**edge**of a cube having a surface equal to the sum of the surfaces of two cubes whose**edges**are 120 in . and 209 in ...**lateral**faces and the corre- sponding altitude . D ' CD R C B E Given R , the volume of a right parallelopiped , B one of ...### Other editions - View all

### Common terms and phrases

altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices

### Popular passages

Page 222 - 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 208 - The area of a rectangle is equal to the product of its base and altitude.

Page 183 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 160 - A line parallel to one side of a triangle divides the other two sides proportionally.

Page 82 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 70 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 188 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.

Page 409 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...

Page 333 - The sum of any two face angles of a trihedral angle is greater than the third face angle.

Page 193 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.