The Elements of EuclidJohnson and Warner, 1811 - 518 Seiten |
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Seite 197
... 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 ... cone , Book XI . XIX . The axis of a cone THE ELEMENTS 197.
... 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 ... cone , Book XI . XIX . The axis of a cone THE ELEMENTS 197.
Seite 198
Euclid Robert Simson. Book XI . XIX . The axis of a cone is the fixed straight line about which the triangle revolves ... cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is ...
Euclid Robert Simson. Book XI . XIX . The axis of a cone is the fixed straight line about which the triangle revolves ... cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is ...
Seite 269
... 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 is the third part of the ...
... 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 is the third part of the ...
Seite 270
... some segments of the cylinder which together are less 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 , € Lem . A H D G FC , CG , GD , 270 THE ELEMENTS.
... some segments of the cylinder which together are less 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 , € Lem . A H D G FC , CG , GD , 270 THE ELEMENTS.
Seite 271
... cone ; therefore 12 . the pyramid upon the base AEBFCGDH , having the same ver . tex with the cone , is greater than the cone , of which the base is the circle ABCD : but it is also less , for the pyramid is contained within the cone ...
... cone ; therefore 12 . the pyramid upon the base AEBFCGDH , having the same ver . tex with the cone , is greater than the cone , of which the base is the circle ABCD : but it is also less , for the pyramid is contained within the cone ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore