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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
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

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

William Chauvenet - 1872 - 368 σελίδες
...AB, CD; therefore, the figure ABDCia a parallelogram, and AC '= BD. PROPOSITION XI— THEOREM. 27. A straight line perpendicular to one of two parallel planes is perpendicular to the other. Let MN and PQ be parallel planes, and let the straight line AB be perpendicular to PQ ; then, it will...

A Treatise on Special Or Elementary Geometry, Τόμοι 1-2

Edward Olney - 1872
...figure ABDC is a parallelogram ; whence AC = BD (?). PROPOSITION XI. 412. Theorem. — A line which, is perpendicular to one of two parallel planes, is perpendicular to the other also. •?»• ELEMENTARY SOLID GEOMETRY. M,'C' DEM.— Let AB be perpendicular to MN ; then is it perpendicular...

Elements of geometry, with ... trigonometry

André Darré - 1872
...through B and C (139), and consequently must coincide with MN (123). THEOREM. 140. A straight tine perpendicular to one of two parallel planes is perpendicular to the other. Let MN and DE (Fig. 120) be two parallel planes, and AP a straight line perpendicular to the plane...

Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - 1876 - 364 σελίδες
...whose opposite sides are equal (82). Hence, the lines are equal. 348. Proposition XII.— Theorem. A straight line perpendicular to one of two parallel planes is perpendicular to the otlier. Let MN, PQ, be parallel planes, and yr, , let AB be perpendicular to PQ ; then, , AB is perpendicular...

A Treatise on Special Or Elementary Geometry: Including an Elementary, and ...

Edward Olney - 1879 - 440 σελίδες
...figure AB DC is a parallelogram ; whence AC = BD (?). PROPOSITION XI. 412. Theorem. — A line which is perpendicular to one of two parallel planes, is 'perpendicular to the other also. C' DEM. — Let AB be perpendicular to MN ; then is it perpendicular to PQ, parallel to MN. For, pass...

Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - 1883 - 333 σελίδες
...figure ABDC is a parallelogram; whence, AC — BD (?). PROPOSITION XIX. 490. Theorem.—A line which, is perpendicular to one of two parallel planes, is perpendicular to the other also. DEMONSTRATION. Let MN and PQ be two parallel planes, and let AB be perpendicular to PQ. Then is AB...

The Eclectic School Geometry

Evan Wilhelm Evans - 1884 - 149 σελίδες
...Cor. — The perpendicular distance between two parallel planes is everywhere the same. THEOREM III. A straight line perpendicular to one of two parallel planes is perpendicular to the other. Let MS and DP be parallel planes, and let the straight line AO be perpendicular to MS ; then it will...

CHAUVENETS TREATISE ON ELEMENTARY GEOMETRY

W. E. BYERLY - 1887
...are lines in the same plane AD; therefore they are parallel. EXERCISE. PROPOSITION IX.—THEOREM. 21. A straight line perpendicular to one of two parallel planes is perpendicular to the other. Let MN and PQ be parallel planes, and let the straight line AB be perpendicular to PQ; then it will...

A Primary Geometry: With Simple and Practical Examples in Plane and ...

Samuel Edward Warren - 1887 - 178 σελίδες
...perpendicular to the axis of the cage) . 2d, A line, like the plumb-line in the last case, which is perpendicular to one of two parallel planes, is perpendicular to the other one (see also the axle of a pair of locomotive drivingwheels, which is perpendicular to the face of...

The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 393 σελίδες
...true of polygons of more than three sides situated in any way in space. Proposition 1O. Theorem. 521. A straight line perpendicular to one of two parallel planes is perpendicular to the other. Hyp. Let MN and PQ be || planes, M/ -, and let AB be J_ to PQ. / Ar C / To prove AB J_ to MN. >- '...




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