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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... "
Cornell University Register and Catalogue - Page 101
by Cornell University - 1880
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The First Six Books of the Elements of Euclid, with a Commentary and ...

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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Annual Statement, Volumes 11-20

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...
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Elements of Plane and Solid Geometry

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...
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Elements of Plane and Solid Geometry

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...
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Elements of Plane and Solid Geometry

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'...
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Elements of Plane and Solid Geometry

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...
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Chauvenet's Treatise on Elementary Geometry

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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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 342 pages
...plane can be passed parallel to a given plane, and but one. PROPOSITION X. If two angles,, not in tlie same plane, have their sides respectively parallel...direction, they are equal and their planes are parallel. PROPOSITION XI. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular...
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