The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 255
... 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. Also ...
... 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. Also ...
Page 256
... 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 demon- strated . From the point A draw AI ...
... 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 demon- strated . From the point A draw AI ...
Page 257
... sphere . There- fore in the greater of two spheres , which have the same centre , a solid polyhedron is inscribed , the superficies of which does not meet the lesser sphere . Which was to be done . But the straight line AZ may be ...
... sphere . There- fore in the greater of two spheres , which have the same centre , a solid polyhedron is inscribed , the superficies of which does not meet the lesser sphere . Which was to be done . But the straight line AZ may be ...
Page 258
... 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 super- ficies 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 super- ficies of the ...
Page 259
... spheres , of which the diame- ters are BC , EF . The sphere ABC shall have to the sphere DEF the triplicate ratio of that which BC has to EF . For , if it has not , the sphere ABC must have to a sphere either less or greater than DEF ...
... spheres , of which the diame- ters are BC , EF . The sphere ABC shall have to the sphere DEF the triplicate ratio of that which BC has to EF . For , if it has not , the sphere ABC must have to a sphere either less or greater than DEF ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore