## Elements of Geometry and Trigonometry |

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Page 142

The

The

**prism**is a solid bounded by several parallelograms , which are terminated at both ends by equal and parallel polygons . K F B To construct this solid , let ABCDE be any polygon ; then if in a plane parallel to ABCDE , the lines FG ... Page 143

A

A

**prism**is right , when the sides AF , BG , CH , & c . are perpendicular to the planes of the bases ; and then each of them is equal to the altitude of the**prism**. In every other case the**prism**is oblique , and the altitude less than ... Page 144

The convex surface of a right

The convex surface of a right

**prism**is equal to the perimeter of its base multiplied by its altitude . Let ABCDE - K be a right**prism**: then will its convex surface be equal to ( AB + BC + CD + DE + EA ) x AF . Page 145

Every section in a

Every section in a

**prism**, if drawn parallel to the base , is also equal to the base . PROPOSITION III . THEOREM . If a pyramid be cut by a plane parallel to its base , 1st . The edges and the altitude will be divided proportionally . Page 146

The triangles , therefore , which form the convex surface of the

The triangles , therefore , which form the convex surface of the

**prism**are all equal to each other . But the area of either of these triangles , as ESA , is equal E F S B C to its base EA multiplied by half the perpendicular SF 146 ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole