 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...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 - 1871 - 380 σελίδες
...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 - 1872 - 382 σελίδες
...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 σελίδες
...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 - 1877 - 416 σελίδες
...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 - 1877 - 416 σελίδες
...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 σελίδες
...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 - 1882 - 442 σελίδες
...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 - 1884 - 422 σελίδες
...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 - 1887 - 331 σελίδες
...plane, 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 ec/ual and their planes are parallel. Let BAC, B'A'C', be two angles lying in the planes MN, M'N';... | |
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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... 
