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" 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
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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...
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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...
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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...
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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:...
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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...
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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...
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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...
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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...
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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...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...lines EF and GH cannot meet ; they are, therefore, parallel ; which was to be proved. PROPOSITION XI. THEOREM. If a straight line is perpendicular to one of two parallel planes, it is also perpendicular to the other. Let MN and PQ be two parallel planes, and let the line AB be perpendicular...
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