The Essentials of Geometry (solid) |
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Page 233
... plane is said to be determined by certain lines or points when one plane , and only one , can be drawn through these lines or points . PROP . I. THEOREM . 395. A plane is determined I. By a straight line and a point without the line ...
... plane is said to be determined by certain lines or points when one plane , and only one , can be drawn through these lines or points . PROP . I. THEOREM . 395. A plane is determined I. By a straight line and a point without the line ...
Page 234
... plane is determined by A , B , and C. Proof . Draw line AB ; then a plane , and only one , can be drawn through line AB and point C. [ A plane is determined by a str . line and a point without the line . ] ( § 395 , I ) Then , a ...
... plane is determined by A , B , and C. Proof . Draw line AB ; then a plane , and only one , can be drawn through line AB and point C. [ A plane is determined by a str . line and a point without the line . ] ( § 395 , I ) Then , a ...
Page 235
Webster Wells. And only one plane can be drawn through AB and point C. [ A plane is determined by a str . line and a point without the line . ] ( § 395 , I ) Then , a plane , and only one , can be drawn through AB and CD . PROP . II ...
Webster Wells. And only one plane can be drawn through AB and point C. [ A plane is determined by a str . line and a point without the line . ] ( § 395 , I ) Then , a plane , and only one , can be drawn through AB and CD . PROP . II ...
Page 236
... plane determined by AC and AD . Let AE be any other str . line drawn through point A in plane RS ; and draw line CD intersecting AC , AE , and AD at C , E , and D , respectively . : Produce BA to B ' , making AB ' = AB , and draw lines ...
... plane determined by AC and AD . Let AE be any other str . line drawn through point A in plane RS ; and draw line CD intersecting AC , AE , and AD at C , E , and D , respectively . : Produce BA to B ' , making AB ' = AB , and draw lines ...
Page 237
... plane MN at P ; and let the plane determined by PQ and PT intersect MN in line HK . Then , both PQ and PT are 1 HK . [ A to a plane is to every str . line drawn in the plane through its foot . ] ( § 398 ) But this is impossible ; for , in ...
... plane MN at P ; and let the plane determined by PQ and PT intersect MN in line HK . Then , both PQ and PT are 1 HK . [ A to a plane is to every str . line drawn in the plane through its foot . ] ( § 398 ) But this is impossible ; for , in ...
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Common terms and phrases
ABCD Algebra altitude approaches the limit area ABC axis bisecting centre cents circle circular cone circular cylinder circumference circumscribed cone of revolution conical surface convex polyedron cube cylinder of revolution diameter diedral angle distance Draw lines entire surface equal parts occur equal spheres equally distant Find the area Find the volume frustum Geometry Given line given point homologous inscribed intersection lateral area lateral edges lateral faces lateral surface line drawn lune O-ABC parallel planes perimeter perpendicular plane determined Plane Geometry plane MN pole polyedral angle proof is left PROP Prove pupil radii radius rectangular parallelopiped regular polygon respectively sector sides slant height solid Solid Geometry spherical angle spherical polygon spherical pyramid spherical triangle straight line tangent tetraedron THEOREM total surface tri-rectangular triangular prism triedral vertex vertices Wells's Whence