## The Elements of Euclid |

### From inside the book

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Page 197

A

A

**pyramid**is a solid figure contained by planes that are constituted betwixt one plane and one point above it in which they meet . XIII . A prism is a solid figure contained by plane figures , of which two that are opposite are equal ... Page 257

THEOR , EVERY

THEOR , EVERY

**pyramid**having a triangular base , may See Note , be divided into two equal and similar**pyramids**having triangular bases , and which are similar to the whole**pyramid**; and into two equal prisms which together are greater ... Page 258

Therefore the

Therefore the

**pyramid**of which the base is the triangle AEG , and of which the vertex 1 C , 11 . is the point H , is equals and similar to the**pyramid**the base of which is the triangle KHL , and vertex the point D : and because HK is ... Page 259

HKL : and it is manifest that each of these prisms is greater sind than either of the

HKL : and it is manifest that each of these prisms is greater sind than either of the

**pyramids**of which the ... is greater than the**pyramid**of which the base is the triangle EBF , and ver , tex the point K ; but this**pyramid**is equal ... Page 260

IF there be two

IF there be two

**pyramids**of the same altitude , upon triangular bases , and each of them be divided into two equal**pyramids**similar to the whole**pyramid**, and also into two equal prisms ; and if each of these**pyramids**be divided in the ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole