## Elements of Geometry and Trigonometry |

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Page 143

A

A

**pyramid**is a solid formed by several triangular planes proceeding from the same point S , and terminating in the different sides of the same polygon ABCDE . The polygon ABCDE is called the base of the**pyramid**, the point S the vertex ... Page 145

If a

If a

**pyramid**be cut by a plane parallel to its base , 1st . The edges and the altitude will be divided proportionally . 2d . The section will be a polygon similar to the base . Let the**pyramid**S - ABCDE , of which SO is the altitude ... Page 146

Let S - ABCDE , S - XYZ be two

Let S - ABCDE , S - XYZ be two

**pyramids**, having a common vertex and the same altitude , or having their bases situated in the same plane ; if these**pyramids**are cut by a plane parallel to the plane of their bases , giving the sections ... Page 147

to its base EA multiplied by half the perpendicular SF , which is the slant height of the

to its base EA multiplied by half the perpendicular SF , which is the slant height of the

**pyramid**: hence the area of all the triangles , or the convex surface of the**pyramid**, is equal to the perimeter of the base multiplied by half ... Page 158

Two triangular

Two triangular

**pyramids**, having equivalent bases and equal altitudes , are equivalent , or equal in solidity . S πt 2 A D K N L H k m Let S - ABC , S - abc , be those two**pyramids**; let their equivalent bases ABC , abc , be situated in ...### 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 contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole