 | Henry Barnard - Military education - 1862 - 410 pages
...angle.—How to measure the ratio of any dihedral angle to the right dihedral angle. Parallel planes.—When two parallel planes are cut by a third plane the intersections are parallel.—Two parallel planes have their perpendiculars common to both. Two right lines comprised... | |
 | Henry Barnard - Military education - 1872 - 988 pages
...planes perpendicular to a third plane, is perpendicular to this third plane. Parallel planes. — when two parallel planes are cut by a third plane the intersections are parallel. — Two parallel planes have their perpendiculars common to both. The shortest distance between two... | |
 | Webster Wells - Geometry - 1894 - 398 pages
...determined by AC and BD intersect MN and PQ in the lines AB and CD. Then, AB and CD are parallel. [If two parallel planes are cut by a third plane, the intersections are parallel.] (§417.) Therefore, AC = BD. [Parallel lines included between parallel lines are equal.] (§ 105.)... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...lines is parallel to a plane, what is true of the other? Prove it. PROPOSITION XV. THEOREM. 893. // two parallel planes are cut by a third plane, the intersections are parallel. Given—The parallel planes MN and PQ cut by the plane AD in the lines CD and AB respectively. To Prove—AB... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...through a given point || to a given str. line.] (§ 53) Whence, CD lies in MN. PROP. X. THEOREM. 414. If two parallel planes are cut by a third plane, the intersections are parallel. Given II planes MN and PQ cut by plane AD in lines AB and CD, respectively. To Prove AB II CD. (AB and CD... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...through a given point || to a given str. line.] (§63) Whence, CD lies in MN. PROP. X. THEOREM. 414. If two parallel planes are cut by a third plane, the intersections are parallel. Given II planes MN and PQ cut by plane AD in lines AB and CD, respectively. To Prove AB II CD. (AB and CD... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...given line, which is impossible. Art, 513. .*. MN and PQ are parallel. PROPOSITION X. THEOREM 531. If two parallel planes are cut by a third plane, the intersections are parallel lines. Given MN and PQ two || planes intersected by the R8 in the lines AB and CD. To prove AB \\ CD.... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...which is impossible. Art. 513. .'. MN and PQ are parallel. Art. 507. • PROPOSITION X. THEOREM 531. // two parallel planes are cut by a third plane, the intersections are parallel lines. V Given MN and PQ two 1 1 planes intersected by the plan* RS in the lines AB and CD. To prove... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...through a given point II to a given str. line.] Whence, b lies in MN. (§ 69) PROP. XII. THEOREM 364. If two parallel planes are cut by a third plane, the intersections are parallel. Given II planes MN and PQ cut by plane AB in lines a and b, respectively. To Prove « II 6. SOLID GEOMETRY... | |
 | Webster Wells - Geometry - 1908 - 329 pages
...through a given point I! to a given str. line. ] Whence, b lies in MN. (§ PROP. XII. THEOREM 364. If two parallel planes are cut by a third plane, the intersections are parallel. Givfen II planes MN and PQ cut by plane AB in lines a and b, respectively. To Prove a II b. SOLID GEOMETRY... | |
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If two parallel planes are cut by a third plane, the intersections are parallel. Given II planes MN and PQ cut by plane AD in lines AB and CD, respectively. 
