 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...planes are equal, and therefore parallel planes are equidistant. PROPOSITION XXI. (44) If two angles have their sides respectively parallel and lying in the same direction, they will be equal, and their planes will be parallel. If they be in the same plane, the proposition has... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...plane, the plane of these lines is parallel to the given plane. v, PROPOSITION XIII.— THEOREM. 32. If two angles, not in the same plane, have their sides...direction, they are equal and their planes are parallel. Let BA C, B'A'C', be two angles lying in the af planes MN, M'N'; and let AB, AC, be parallel respectively... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...given plane, the plane of these lines is parallel to the given plane. PROPOSITION XIII— THEOREM. 32. If two angles, not in the same plane, have their sides...direction, they are equal and their planes are parallel. Let BA C,B'A' C', be two angles lying in the planes MN, M'N'; and let AB, AC, be parallel respectively... | |
 | 1876 - 646 pages
...area of a trapezoid ? how, that of a regular polygon ? • II. — Solid and Spherical Geometry. 6. If two angles, not in the same plane, have their sides...direction, they are equal and their planes are parallel. 7. If a pyramid be cut by a plane parallel to its base : 1st, the edges and the altitude will be divided... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...are II if all the points of either be equally distant from the other). PROPOSITION X. THEOREM. 462. If two angles not in the same plane have their sides...parallel and lying in the same direction, they are equal. M Let AA and A' be respectively in the planes MN and PQ and have AD parallel to A' D' and AC parallel... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...of either be equally distant from the other). GEOMETIiY. — BOOK VI. PROPOSITION X. THEOREM. 462. If two angles not in the same plane have their sides...parallel and lying in the same direction, they are ctfital. M Let AA and A' be respectively in the planes MN ana PQ and have AD parallel to A' D' and... | |
 | Cornell University - 1880 - 868 pages
...polyedrons, a spherical triangle, the ordinate of a point on a curve, the subtangent of a parabola. 2. If two angles not in the same plane have their sides...direction, they are equal, and their planes are parallel. 3. Two triangular pyramids, having equvialent bases and equal altitudes, are equivalent. 4. The area... | |
 | George Albert Wentworth - Geometry - 1882 - 442 pages
...ofeither be equally distant from the other). QED 262 GEOMETRY. — BOOK VI. PROPOSITION X. THEOREM. 462. If two angles not in the same plane have their sides...respectively parallel and lying in the same direction, thetj are equal. M Let AA and A' be respectively in the planes MN and PQ and have AD parallel to A'... | |
 | George Albert Wentworth - Geometry - 1884 - 422 pages
...D A L GEOMETRY. BOOK VI. PROPOSITION X. THEOREM. 462. If two angles not in the same plane have then sides respectively parallel and lying in the same direction, they are equal. M Let AA and A' be respectively in the planes MN and PQ and have AD parallel to A' D' and AC parallel... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...and then pass a plane through the point perpendicular to this line. PROPOSITION X.— THEOREM. 23. If two angles, not in the same plane, have their sides...parallel and lying in the same direction, they are eaual and their planes are parallel. Let BAG, B'A'C', be two angles lying in the planes MN, M'N'; and... | |
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If two angles, not in the same plane, have their sides respectively parallel and lying in the same direction, they are equal and their planes are parallel. Let BA C,B'A... 
