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

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Page 173

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**cone**is a solid figure described by the revolution of a right angled triangle about one of the sides containing the right angle , which side remains fixed . If the fixed side be equal to the other side containing the right angle ... Page 174

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**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 237

... and the pyramid DEFH is the sixth part of the solid EHPO ; therefore the pyramid ABCG is equal to the pyramid DEFH . There- 2 Ax , 5 . fore the bases , & c . Q. E. D. PROP . X. THEOR . Every

... and the pyramid DEFH is the sixth part of the solid EHPO ; therefore the pyramid ABCG is equal to the pyramid DEFH . There- 2 Ax , 5 . fore the bases , & c . Q. E. D. PROP . X. THEOR . Every

**cone**is the third BOOK XII . PROP . IX . Page 238

Every

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 . upon the same base , of which the vertex is the same with the vertex of the

7 . upon the same base , of which the vertex is the same with the vertex of the

**cone**; therefore the pyramid upon the base AEBFCGDH , having the same vertex with the**cone**, is greater than the**cone**, of which the base is the circle ABCD ...### 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