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

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Page 216

A

A

**sphere**is a solid figure described by the revolution of a semicircle about its diameter , which remains unmoved . XV . The axis of a**sphere**is the fixed straight line about which the semicircle revolves . XVI . The centre of a**sphere**... Page 319

Let there be two

Let there be two

**spheres**about the same centre A : it is required to inscribe in the greater a solid polyhedron , the superficies of which shall not meet the lesser**sphere**. Let the**spheres**be cut by a plane passing through BOOK XII . Page 320

Let the

Let the

**spheres**be cut by a plane passing through the centre ; the common sections of it with the**spheres**shall be circles ; because the**sphere**is described by the revolution of a semicircle about the diameter remaining unmoveable ... Page 322

... has been done upon BK , and the like be done also in the other three quadrants , and in the other hemisphere ; there will be formed a solid polyhedron inscribed in the

... has been done upon BK , and the like be done also in the other three quadrants , and in the other hemisphere ; there will be formed a solid polyhedron inscribed in the

**sphere**, composed of pyramids , the bases of 322 EUCLID'S ELEMENTS . Page 323

the

the

**sphere**, composed of pyramids , the bases of which are the aforesaid quadrilateral figures , and the triangle YRX , and those formed in the like manner in the rest of the**sphere**, the common vertex of them all being the point A.### 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 equimultiples 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 Q. E. D. PROP ratio reason 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