## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 173

A

A

**cylinder**is a solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed . XXII . The axis of a**cylinder**is the fixed straight line about which the parallelogram revolves . Page 174

Similar cones and

Similar cones and

**cylinders**are those which have their axes and the diameters of their bases proportionals . XXV . A cube is a solid figure contained by six equal squares . XXVI . A tetrahedron is a solid figure contained by four equal ... Page 238

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 same altitude . The cone shall be the third part of ... Page 239

7 . of the

7 . of the

**cylinder**which are upon the segments of the 12 . circle cut off by AB , BC , CD , DA , are less than the solid parallelopipeds which contain thenı ; therefore the prisms upon the triangles AEB , BFC , CGD , DHA , are greater ... Page 240

And it has been demonstrated that neither is it greater than the triple : therefore the

And it has been demonstrated that neither is it greater than the triple : therefore the

**cylinder**is triple of the cone , or , the cone is the third part of the**cylinder**. Wherefore , every cone , & c . Q. E.D. EX B В PROP . XI . THEOR .### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

### Common terms and phrases

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