 I, prop. XII 3. .'.by folding A ACP over AC as an axis, it can be brought to coincide with A ACP'. § 57 339. Definitions. A line is said to be perpendicular to a plane when it is perpendicular to every line in that plane which passes through its foot,...  Solid Geometry - Page 252by Wooster Woodruff Beman, David Eugene Smith - 1903Full view - About this book
 | 1893 - 760 pages
...lines at their point of intersection, it shall also be perpendicular to the plane in which they lie. The locus of points equidistant from two given points is the plane that bisects at right angles the line joining the points. 6. The sum of the roots of the equation a?... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...prop. XII 3. .'.by folding A ACP over AC as an axis, it can be brought to coincide with A ACP'. § 57 339. Definitions. A line is said to be perpendicular...of concurrence, the three lines are coplanar. Given To prove that OY±OA, OB, OC. OA, OB, OC are coplanar. Proof. 1. Suppose M the plane determined by... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 412 pages
...1. If a line is perpendicular to each of two intefsecting lines, it is perpendicular to their plane. The locus of points equidistant from two given points...of concurrence, the three lines are coplanar. Given OY±OA, OB, 0C. To prove that OA, OB, 0C are coplanar. Proof. 1. Suppose M the plane determined by... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Solid - 1900 - 160 pages
...with A, B, C. Then AP = A P', and CP = CP'. I, prop. XX, cor. 5 2. And ..' AC = AC, .'.AACP^AACP'. I, prop. XII 3. .'.by folding A ACP over AC as an...of concurrence, the three lines are coplanar. Given OY±OA, OB, OC. To prove that OA, OB, OC are coplanar. Proof. 1. Suppose M the plane determined by... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1900 - 395 pages
...with A ACP1. § 57 4. /.A BOP ^ A BOP', and ZP 01> is a rt. Z., and w -L y. SOLID GEOMETRY. [BK. Vic 339. Definitions. A line is said to be perpendicular...of concurrence, the three lines are coplanar. Given OY±OA, OB, OC. To prove that OA, OB, OC are coplanar. Proof. 1. Suppose M the plane determined by... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1900 - 400 pages
...prop. XII 3. .'.by folding A ACP over AC as an axis, it can be brought to coincide with A ACP'. § 57 339. Definitions. A line is said to be perpendicular...point of concurrence, the three lines are coplanar. _Y Given OY±OA, OB, OC. To prove that OA, OB, OC are coplanar. Proof. 1. Suppose M the plane determined... | |
 | Geometry, Plane - 1911 - 192 pages
...other as the squares of their distances from the vertex. 14. Prove that the locus of points in space equidistant from two given points is the plane bisecting at right angles the straight line joining the given points. 16. Prove that the area generated by a straight line revolving... | |
 | Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...dihedral angle cuts these faces in two points equally distant from the edge of the angle. 130. THEOREM. The locus of points equidistant from two given points is the plane perpendicular to the line segment joining the points at its midpoint. Given A and B, two points ; ma... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 pages
...consists of two planes parallel to the given plane and at the given distance from it. Call this Locus 1. 2. The locus of points equidistant from two given points is the plane perpendicular to and bisecting the segment between the two points. Call this Locus 2. 3. The desired... | |
 | David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...rt. A. Hence OP is J. to m at O (§ 33), and since OP is part of OF (§41), Pis on OF. 46. Corollary. The locus of points equidistant from two given points is the plane perpendicular at the midpoint to the line segment joining the points. We have first to prove (§ 19,... | |
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