The Elements of Euclid |
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Page 213
... solid angle at A be contained by the three plane angles BAC , CAD , DAB . Any two of them are greater than the third ... solid angle , & c . Q. E. D. PROP . XXI . THEOR . EVERY solid angle is contained by plane angles which together are ...
... solid angle at A be contained by the three plane angles BAC , CAD , DAB . Any two of them are greater than the third ... solid angle , & c . Q. E. D. PROP . XXI . THEOR . EVERY solid angle is contained by plane angles which together are ...
Page 214
... solid angle at B is contained by the three plane angles CBA , ABD , DBC , any two of them are greater than the third ... solid angle at A , are less than four right angles . : B Next , let the solid angle at A be contained by any number ...
... solid angle at B is contained by the three plane angles CBA , ABD , DBC , any two of them are greater than the third ... solid angle at A , are less than four right angles . : B Next , let the solid angle at A be contained by any number ...
Page 215
... solid angle at A , are less than four right angles . Therefore every solid angle , & c . Q. E. D. PROP . XXII . THEOR . IF every two of three plane angles be greater than See Note . the third , and if the straight lines which contain ...
... solid angle at A , are less than four right angles . Therefore every solid angle , & c . Q. E. D. PROP . XXII . THEOR . IF every two of three plane angles be greater than See Note . the third , and if the straight lines which contain ...
Page 216
... solid angle which shall be contained by three given plane angles , any two of them being greater than the third , and all three together less than four right angles . Let the three given plane angles be ABC , DEF , GHK , any two of ...
... solid angle which shall be contained by three given plane angles , any two of them being greater than the third , and all three together less than four right angles . Let the three given plane angles be ABC , DEF , GHK , any two of ...
Page 221
... solid angles be contained by three See Note . plane angles equal to one another , each to each ; the planes in which the equal angles are , have the same inclination to one another . Let there be two solid angles at the points A , B ...
... solid angles be contained by three See Note . plane angles equal to one another , each to each ; the planes in which the equal angles are , have the same inclination to one another . Let there be two solid angles at the points A , B ...
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Common terms and phrases
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