## Elements of Geometry and Trigonometry |

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Page 143

A prism whose base is a parallelogram , and which has all its faces parallelograms , is named a

A prism whose base is a parallelogram , and which has all its faces parallelograms , is named a

**parallelopipedon**. The**parallelopipedon**is rectangular when all its faces are rectangles . 9. Among rectangular**parallelopipedons**, we ... Page 148

In every

In every

**parallelopipedon**the opposite planes are equal and parallel . By the definition of this solid , the bases ABCD , EFGH , are equal parallelograms , and their sides are parallel : it remains only to show , that the same is true ... Page 149

Since the

Since the

**parallelopipedon**is a solid bounded by six planes , whereof those lying opposite to each other are equal and parallel , it follows that any face and the one opposite to it , may be assumed as the bases of the**parallelopipedon**... Page 150

Let the

Let the

**parallelopipedon**ABCD - H be divided by the plane BDHF passing through its diagonal edges : then will the triangular prism ABD - H be equivalent to the triangular prism BCD - H . E G F a Through the vertices B and F , draw the ... Page 151

Every triangular prism ABD - HEF is half of the

Every triangular prism ABD - HEF is half of the

**parallelopipedon**AG described with the same solid angle A , and the same edges AB , AD , AE . PROPOSITION VIII . THEOREM . If two**parallelopipedons**have a common base , and their upper ...### What people are saying - Write a review

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### Other editions - View all

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