 | War office - 1861 - 714 pages
...circle is equal to both the rectangles contained by its opposite sides. 2. If two straight lines are at right angles to the same plane they shall be parallel to each other. 3. Prove the following formulae : ,,^ ... 3 tan A — tan 3A (1) tan 3 A = — -= — —... | |
 | Euclides - 1864 - 448 pages
...plane. Therefore, if three straight lines, &c. QED PROPOSITION VI. THEOREM. If two straight lines bs at right angles to the same plane, they shall be parallel...lines AB, CD be at right angles to the same plane. Then AB shall be parallel to CD. Let them meet the plane in the points 7?, D, and draw the straight... | |
 | Euclides - 1865 - 402 pages
...each of them in that point, these three straight lines are in one and the same plane .... Try. 5. 5. If two straight lines be at right angles to the same plane, they are parallel to one another ...... XI, 6. 6. If two straight lines be parallel, the straight line drawn... | |
 | Robert Potts - 1865 - 528 pages
...one and the same plane. Therefore, if three straight lines, &c. QED PROPOSITION VI. THEOREM. lf ttco straight lines be at right angles to the same plane, they shall bt parallel to one another. Let the straight lines AB, CD be at right angles to the same plane. Then... | |
 | Samuel H. Winter - 1867 - 468 pages
...triangle coincide, and the diameter of one is double that of the other. 19. If two straight lines are at right angles to the same plane, they shall be parallel to one another. 20. Solve the following equations : (a) x -- ?^- = 15. Find, by the aid of the tables, (a) The fifth... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...the plane, in which BD, BE are, and .'. BC, BD, BE are in one and the same plane. QED PROPOSITION VI. THEOREM. If two straight lines be at right angles to the same plane, they must be parallel to one another. Let the st. lines AB, CD be x to the same plane. Then must AB be II... | |
 | Euclides - 1874 - 342 pages
...plane of BD and BE; Therefore The three straight lines BC, BD, and BE are in the same plane. Therefore, if three straight lines, &c. QED PROPOSITION 6. —...straight lines be at right angles to the same plane, they are parallel. Let the straight lines AB and CD be at right angles to the same plane. Then AB is parallel... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...Prop.) but it is also j. to QX; (hyp-) which is impossible. .'. If a straight line, &c. PROPOSITION VII. If two straight lines be at right angles to the same...plane, they shall be parallel to one another. Let AB, Cfbe each jL to the plane BFG. Then shall AB be | | to Cf. Join BF and draw FG in the plane BFG... | |
 | Euclid - 1876 - 240 pages
...(6) XI. 4. ' ) XI. Def. 3. ) I. Ax. 9. PROPOSITION VI. THEOREM. — If two straight lines (AB, CD) be at right angles to the same plane, they shall be parallel to one another. DEMONSTRATION. Let them meet the plane in the points B, D, and draw the straight line BD, to which... | |
 | Samuel H. Winter - 1877 - 452 pages
...should vanish separately ; show that this is the case for the whole coefficient of x*. LXXXV. % 1. If two straight lines be at right angles to the same plane, they shall be parallel to one another. 2. If two straight lines be cut by parallel planes, they shall be cut in the same ratio. 3.' If two... | |
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If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane : AB is parallel to CD. 
