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

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Page 217

A

A

**cylinder**is a solid figure described by the revolution of a right - angled parallelogram about one of its sides which remains fixed . a XXII . The axis of a**cylinder**is the fixed straight line about which the parallelogram revolves . Page 300

Every cone is the third part of a

Every cone is the third part of a

**cylinder**which has the same base und 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 301

therefore the prism upon the square ABCD is the half of the prism upon the square described about the circle ; because they are to one another * as their bases : and the

therefore the prism upon the square ABCD is the half of the prism upon the square described about the circle ; because they are to one another * as their bases : and the

**cylinder**is less than * 32. 11 . the prism upon the square ... Page 302

12 , than the excess of the

12 , than the excess of the

**cylinder**above the triple of the cone : let them be those upon the segments of the circle AE , EB , BF , FC , CG , GD , DH , HA ; therefore the rest of the**cylinder**, that is , the prism of which the base is ... Page 303

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 , DD 2 BOOK XII . 303 PROP .### 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

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole