The Elements of Euclid |
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Page 289
... sphere , the common vertex . of them all being the point A : and the superficies of this so- lid polyhedron does not meet the lesser sphere in which is the circle FGH ; for , from the point A draw AZ perpendicular a 11. 11 . to the ...
... sphere , the common vertex . of them all being the point A : and the superficies of this so- lid polyhedron does not meet the lesser sphere in which is the circle FGH ; for , from the point A draw AZ perpendicular a 11. 11 . to the ...
Page 290
... sphere to that plane . Therefore the plane KBOS does not meet the lesser sphere . And that the other planes between the quadrants BX , KX fall without the lesser sphere , is thus demonstrated : from the point A draw AI perpendicular to ...
... sphere to that plane . Therefore the plane KBOS does not meet the lesser sphere . And that the other planes between the quadrants BX , KX fall without the lesser sphere , is thus demonstrated : from the point A draw AI perpendicular to ...
Page 291
... sphere drawn to all the angles of the solid polyhedron in the greater sphere meet the superficies of the lesser ; in the same order in which are joined the points in which the same lines from the centre meet the superficies of the ...
... sphere drawn to all the angles of the solid polyhedron in the greater sphere meet the superficies of the lesser ; in the same order in which are joined the points in which the same lines from the centre meet the superficies of the ...
Page 292
... spheres , of which the diameters are BC , EF . The sphere ABC has to the sphere DEF the tri- plicate ratio of that which BC has to EF . For , if it has not , the sphere ABC shall have to a sphere either less or greater than DEF , the ...
... spheres , of which the diameters are BC , EF . The sphere ABC has to the sphere DEF the tri- plicate ratio of that which BC has to EF . For , if it has not , the sphere ABC shall have to a sphere either less or greater than DEF , the ...
Page 293
... sphere LMN has to the sphere ABC the triplicate ratio of that which the diameter EF has to the diameter BC . But , as the sphere LMN to ABC , so is the sphere DEF to some sphere , which must be less that the sphere ABC , because a 14 , 5 .
... sphere LMN has to the sphere ABC the triplicate ratio of that which the diameter EF has to the diameter BC . But , as the sphere LMN to ABC , so is the sphere DEF to some sphere , which must be less that the sphere ABC , because a 14 , 5 .
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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