## The Essentials of Geometry (solid) |

### From inside the book

Results 1-5 of 31

Page 233

... plane is determined by AB and C. Proof . If any

... plane is determined by AB and C. Proof . If any

**plane MN**be drawn through AB , it may be revolved about AB as an axis until it contains point C. Hence , a plane can be drawn through line AB and point C ; and it is evident that but one such ... Page 235

... planes is a straight line . P B M N A Given line AB the intersection of

... planes is a straight line . P B M N A Given line AB the intersection of

**planes MN**and PQ . To Prove AB a str . line . Proof . Draw a str . line between points A and B. This str . line lies in**plane MN**, and also in plane PQ . [ A plane ... Page 236

... plane is perpendicular to every straight line drawn in the plane through its foot . PROP . III . THEOREM . 399. At a given point in a plane , one perpendicular to the plane can be drawn , and but one . M H N B C Given point P in

... plane is perpendicular to every straight line drawn in the plane through its foot . PROP . III . THEOREM . 399. At a given point in a plane , one perpendicular to the plane can be drawn , and but one . M H N B C Given point P in

**plane MN**... Page 237

... MN so that point A shall fall at point P ; and let AB take the position PQ . Then , PQ will be 1 MN . Hence , a can be drawn to MN at P. If possible , let PT be another to

... MN so that point A shall fall at point P ; and let AB take the position PQ . Then , PQ will be 1 MN . Hence , a can be drawn to MN at P. If possible , let PT be another to

**plane MN**at P ; and let the plane determined by PQ and PT intersect ... Page 238

... plane to AB . Proof . Let MN be the plane determined by AC and AD . Then ,

... plane to AB . Proof . Let MN be the plane determined by AC and AD . Then ,

**plane MN**is LAB . [ A str . line to each of two str . lines at their point of intersection is to their plane . ] ( § 400 ) Let the plane determined by AB and AE ...### Other editions - View all

### 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