The Elements of Euclid |
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Page 215
... angles . But all the angles at the bases of the triangles are greater than all the angles of the polygon , as has been proved . Where- fore the remaining angles of the triangles , viz . those at the vertex , which contain the solid angle ...
... angles . But all the angles at the bases of the triangles are greater than all the angles of the polygon , as has been proved . Where- fore the remaining angles of the triangles , viz . those at the vertex , which contain the solid angle ...
Page 216
Euclid Robert Simson. Book XI . angle ABL equal to the angle GHK , and make BL equal to one of the straight lines AB ... solid angle which shall be contained by three given plane angles , any two of them being greater than the third , and ...
Euclid Robert Simson. Book XI . angle ABL equal to the angle GHK , and make BL equal to one of the straight lines AB ... solid angle which shall be contained by three given plane angles , any two of them being greater than the third , and ...
Page 220
... angle LRM is equal to the angle ABC . For the same reason , the angle MRN is equal to the angle DEF , and NRL to GHK . Therefore there is made a solid angle at R , which is contained by three plane angles LRM , MRN , NRI , which are ...
... angle LRM is equal to the angle ABC . For the same reason , the angle MRN is equal to the angle DEF , and NRL to GHK . Therefore there is made a solid angle at R , which is contained by three plane angles LRM , MRN , NRI , which are ...
Page 221
... solid angles be contained by three See Note . plane angles equal to one another , each to each ; the planes in which ... angle at A be contained by the three plane angles CAD , CAE , EAD ; and the angle at B by the three plane angles FBG ...
... solid angles be contained by three See Note . plane angles equal to one another , each to each ; the planes in which ... angle at A be contained by the three plane angles CAD , CAE , EAD ; and the angle at B by the three plane angles FBG ...
Page 222
... solid angles be contained , each by three plane angles which are equal to one another , each to each , and alike situated ; these solid angles are equal to one another . Let there be two solid angles at A and B , of which the solid angle ...
... solid angles be contained , each by three plane angles which are equal to one another , each to each , and alike situated ; these solid angles are equal to one another . Let there be two solid angles at A and B , of which the solid angle ...
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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