Books Books Theorem: If a straight line is perpendicular to one of two parallel planes, it is perpendicular, also, to the other plane. The Elements of Solid Geometry - Page 6
by William C. Bartol - 1893 - 95 pages ## Cyclomathesis: Or, An Easy Introduction to the Several Branches of ..., Volume 2

William Emerson - Mathematics - 1763 - 268 pages
...whence IKLD is a parallelogram, and IK = DL, therefore AC is parallel to EG (Def. io). Cor. If a right line is perpendicular to one of two parallel planes , it is perpendicular to the other. " • „ . . ". PROP. XI. 145. If two parallel planes AC, EG, he cut by a third IL •, their common... ## The Elements of Geometry: In which the Principal Propositions of Euclid ...

William Emerson - Geometry - 1794 - 274 pages
...whence 1KLD is a parallelogram, and IK = DL, therefore AC is parallel to EG (Def. 10). Cor. If a right line is perpendicular to one of two parallel planes, it is perpendicular to the otfher. PROP. XI. "145. If tivo parallel planes AC, EG, be cut by a third IL; their- common feclions... ## An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...316, perpendicular to AB, it is, by art. 327, parallel to MN; and, therefore, CD is equal to AB. 330. Theorem. If a straight line is perpendicular - to one of two parallel planes, it must also be perpendicular to the other. Demonstration. Thus, if AB (fig. 155) is perpendicular to... ## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 pages
...meet ; therefore EF and GH are parallel (Euc. 35. Def. 1.). QED PROP. XV. THEOR. IF a straight line be perpendicular to one of two parallel planes : it is perpendicular to the other. Let the plane CD be parallel to the plane AB, and the straight line EF perpendicular to the plane AB:... ## Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...line BC drawn through its foot in the plane PQ, is consequently perpendicular to that plane. Hence, If a straight line is perpendicular to one of two parallel planes, it is also perpendicular to the other. PROPOSITION XII. THEOREM. The parallels EG, FH, comprehended between... ## An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...317, perpendicular to AB, it is, by § 329, parallel to MN; and, therefore, CD is equal to AB. 331. Theorem. If a straight line is perpendicular to one of two parallel planes, it must also be perpendicular to the other. Proof. Thus, if AB (fig. 155) is perpendicular to the plane... ## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...and GH cannot meet ; they are, therefore, parallel ; which was to be proved. M E 7 PROPOSITION XI. THEOREM. If a straight line is perpendicular to one of two parallel planes^ it is also perpendicular to the other. 168 B For, through AB pass any plane ; its intersections with MN and... ## The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 294 pages
...sides of the figure AC being parallel, it is a parallelogram, and hence AD equals BC, THEOREM VII. If a straight line is perpendicular to one of two...perpendicular to the other also. Let MN and PQ be two parallel planes, and let the line AB be perpendicular to PQ; then will it also be perpendicular... ## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...GH cannot meet ; they are, therefore, parallel ; which was to be proved. PROPOSITION XI. THEOREM. Zf a straight line is perpendicular to one of two parallel planes, it is also perpendicular to the other. For, through AB pass any plane ; its intersections with MN and PQ... 