## The Elements of Euclid |

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Page 198

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A

**cylinder**is a solid figure described by the revolution of a right angled parallelogram about one of its sides , which re . mains fixed . XXII . The axis of a**cylinder**is the fixed straight line about which the parallelogram revolves . Page 269

EVERY cone is the third part of a

EVERY cone is the third part of a

**cylinder**which has the same base , and is of an equal altitude with it . Let a cone have the same base with a**cylinder**, viz . the circle ABCD , and the såme altitude . The cone is the third part of the ... Page 270

1 270 THE ELEMENTS Book XI1 Upon the square ABCD erect a prism of the same altitude with the cylindçr ; this prism is greater than half of the

1 270 THE ELEMENTS Book XI1 Upon the square ABCD erect a prism of the same altitude with the cylindçr ; this prism is greater than half of the

**cylinder**; because if a square be described about the circle , and å prism erected upon the ... Page 271

Book XII . der , that is , the prism of which the base is the polygon AEBFCGDH , and of which the altitude is the same with that of the

Book XII . der , that is , the prism of which the base is the polygon AEBFCGDH , and of which the altitude is the same with that of the

**cylinder**, is greater than the triple of the cone ; but this prism is tripled of the pyramid upon ... Page 272

H ? " Book XII . the third part of the

H ? " Book XII . the third part of the

**cylinder**. Let these be the segments opend upon AE , EB , BF , FC , CG , GD , DH , HA . Therefore the rest of the cone , that is , the pyramid , ' of which the base is the polygon AEBFCGDH , and of ...### 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