## Elements of Geometry and Trigonometry |

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Page 143

... the remaining solid ABCDE - d , is called a truncated pyramid , or the

... the remaining solid ABCDE - d , is called a truncated pyramid , or the

**frustum**of a pyramid . B A 12. The altitude of a pyramid is the perpendicular let fall from the vertex upon the plane of the base , produced if necessary . C 13. Page 147

The convex surface of the

The convex surface of the

**frustum**of a regular pyramid is equal to half the perimeters of its upper and lower bases multiplied by its slant height . For , since the section abcde is similar to the base ( Prop . III . ) ... Page 161

If a pyramid be cut by a plane parallel to its base , the

If a pyramid be cut by a plane parallel to its base , the

**frustum**that remains when the small pyramid is taken away , is equivalent to the sum of three pyramids having for their common altitude the altitude of the**frustum**, and for ... Page 162

S B Let FGH - hfg be the

S B Let FGH - hfg be the

**frustum**of a triangular pyramid , having parallel bases : through the three points F , g , H , pass the plane FgH ; it will cut off from the**frustum**the triangular pyramid g - FGH . This pyramid has for its base ... Page 163

But the pyramid K - FƒH may be regarded as having its vertex in f , and thus its altitude will be the same as that of the

But the pyramid K - FƒH may be regarded as having its vertex in f , and thus its altitude will be the same as that of the

**frustum**: as to its base FKH , we are now to show that this is a mean proportional between the bases FGH and fgh .### What people are saying - Write a review

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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |

### 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 produced 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