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" A straight line perpendicular to one of two parallel planes is perpendicular to the other also. "
Plane and Solid Geometry - Σελίδα 250
των Arthur Schultze, Frank Louis Sevenoak - 1902 - 370 σελίδες
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Plane and Solid Geometry

Isaac Newton Failor - 1906 - 418 σελίδες
...ACDB is a £7 (§ 195), and AC = BD (§ 200). SOLID GEOMETRY — BOOK VI PROPOSITION XII. THEOREM 545 A straight line perpendicular to one of two parallel planes is perpendicular to the other. M V A HYPOTHESIS. MN and PQ are parallel planes, and AB is -L to MN. CONCLUSION AB is -L to PQ. PROOF...

Plane and Solid Geometry

Edward Rutledge Robbins - 1907 - 412 σελίδες
...AB. M ... MN is -L to CD and to EF(?) (509). .-. CD is II to EF (?) (510). QED B -N 512. THEOREM. A line perpendicular to one of two parallel planes is perpendicular to the other also. Given : Plane MN II to plane ^ - s - v US ; AP _L to plane ES. To Prove : AP J- to MN. Proof : Through...

New Plane and Solid Geometry

Webster Wells - 1908 - 298 σελίδες
...locus of points equidistant from all points in the circumference of a circle. PROP. XVIII. THEOREM 373. A straight line perpendicular to one of two parallel planes is perpendicular to the other also. Given planes MN and PQ II, and line a -L PQ. To Prove a -L MN. Proof. 1. Let two planes through a intersect...

Key to the Exercises in Wells's New Geometry

Webster Wells - 1909
...parallel to MN. To Prove PQ II ItS. / Proof. 1. Draw a line AB _L MN; / then, AB _L PQ, and AB JL RS. * (A straight line perpendicular to one / of two parallel planes is perpendicular / to the other also.) § 373. p/ 2. Hence, PQ II RS. / (Two planes perpendicular to the / same straight line are parallel)....

The Elements of Geometry

Walter Nelson Bush, John Bernard Clarke - 1909 - 355 σελίδες
...any of its dihedrals, the sum of the angles about angle F might exceed four right angles. XXII. 5. A line perpendicular to one of two parallel planes is perpendicular to the other, and conversely. Hyp. If plane MQ is parallel to plane RS and AB±RS, Cone. : then .4B J_ M Q. Dem....

The Teaching of Geometry

David Eugene Smith - 1911 - 339 σελίδες
...through an ordinary board (with rectangular cross section) the section is a parallelogram. THEOREM. A straight line perpendicular to one of two parallel planes is perpendicular to the other also. Notice (1) the corresponding proposition in plane geometry ; (2) the proposition that results from...

Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - 1912 - 488 σελίδες
...AC. 5. AE AF , — and CH _AF " EB~ FD HD ~ FD' 6. AE _ CH " EB~ HD' PROPOSITION XVII. THEOREM 651. A straight line perpendicular to one of two parallel planes is perpendicular to the other also. A ,N / ' y M' _y E R ' y S B Given plane MN II plane BS and line AB _L plane BS. To prove line AB _L...

Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - 1912 - 188 σελίδες
...more parallel planes, their corresponding segments are proportional. PROPOSITION XVII. THEOREM 651. A straight line perpendicular to one of two parallel planes is perpendicular to the other also. A 7^ ^_CL..^ M* E R * B Given plane MN II plane RS and line AB _L plane RS. To prove line AB ± plane...

Elements of Solid Geometry

William Herschel Bruce, Claude Carr Cody - 1912 - 110 σελίδες
...550. COR. 1. Parallel lines included between parallel planes are equal. PROPOSITION XI. THEOREM. 552. A straight line perpendicular to one of two parallel planes is perpendicular to the other, also. Given MN and PQ, II planes, and AB _L plane PQ. To prove AB ± plane MN. 'Q Proof. Draw BE and BF,...

Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - 1912 - 376 σελίδες
...to plane N? Auth. 6. What relation does N bear to M? Auth. Therefore — PROPOSITION XVIII. 476. A line perpendicular to one of two parallel planes is perpendicular to the other. Given plane M II plane N and line a 1Jf at 0. To Prove aLN. Proof. SUG. 1. Through any point in plane...




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