The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Seite 140
... Parallel planes are such as , however far produced in all possible directions , they will never meet . 2. A line and plane are parallel when , however far ... planes passing through a point without a plane 140 GEOMETRY OF PLANES AND SOLIDS .
... Parallel planes are such as , however far produced in all possible directions , they will never meet . 2. A line and plane are parallel when , however far ... planes passing through a point without a plane 140 GEOMETRY OF PLANES AND SOLIDS .
Seite 141
... parallel to its first position , it generates a cylindrical surface . If this surface be cut by two planes parallel to the circle , the inter- cepted portion is a cylinder . These two planes are called the ends or bases of the cylinder ...
... parallel to its first position , it generates a cylindrical surface . If this surface be cut by two planes parallel to the circle , the inter- cepted portion is a cylinder . These two planes are called the ends or bases of the cylinder ...
Seite 142
Royal Military Academy, Woolwich. CHAPTER I. PARALLELISM OF LINES AND PLANES . PROPOSITION I. If two parallel planes be cut by a third plane , the sections will be parallel . Let the parallel planes MN , PQ be cut by the plane AD in the ...
Royal Military Academy, Woolwich. CHAPTER I. PARALLELISM OF LINES AND PLANES . PROPOSITION I. If two parallel planes be cut by a third plane , the sections will be parallel . Let the parallel planes MN , PQ be cut by the plane AD in the ...
Seite 143
... parallel to AB . ( 2. ) The planes AD , AD ' intersecting in the line AB , they cannot meet in any point out of that line ; and hence the lines CD , C'D ' in them , and parallel to AB , can never meet : but they are in one plane MN ...
... parallel to AB . ( 2. ) The planes AD , AD ' intersecting in the line AB , they cannot meet in any point out of that line ; and hence the lines CD , C'D ' in them , and parallel to AB , can never meet : but they are in one plane MN ...
Seite 144
... plane , draw a plane through AB and E to cut the plane CF in EF ' . Then since through AB and CD the planes AF ' , CF ' are drawn , intersecting in EF ' , the line EF ' is parallel to CD ( Prop . Iv . ) . But ( Hypoth . ) EF is parallel ...
... plane , draw a plane through AB and E to cut the plane CF in EF ' . Then since through AB and CD the planes AF ' , CF ' are drawn , intersecting in EF ' , the line EF ' is parallel to CD ( Prop . Iv . ) . But ( Hypoth . ) EF is parallel ...
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ABC is equal ABCD adjacent angles angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone construction coordinate planes described Descriptive Geometry diameter dicular dihedral angles draw edges ellipse equal angles equiangular equimultiples given line given point given straight line greater hence horizontal hyperbola inclination intersection join less Let ABC Let the plane line BC lines drawn magnitudes meet multiple orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular perpendicular to MN plane MN plane of projection plane parallel plane PQ prisms profile angles profile plane projecting plane Prop Q. E. D. PROPOSITION ratio rectangle rectangle contained rectilineal figure remaining angle respectively right angles SCHOLIUM segment sides six right sphere spherical angle tangent THEOR trace triangle ABC trihedral vertex Whence Wherefore