| George Washington Hull - Geometry - 1807 - 408 pages
...greater cuts off the greater distance from the foot of the perpendicular. PROPOSITION VII. THEOREM. 380. **If a straight line is perpendicular to each of two...intersection, it is perpendicular to the plane of** those lines. Given — PO perpendicular to AO and BO at their intersection 0. To Prove — PO perpendicular... | |
| James Hayward - Geometry - 1829 - 218 pages
...position of this plane with respect to the line AB perpendicular to these two lines (197) ; we say — **If a straight line is perpendicular to each of two straight lines** drawn in a plane through its foot, it is perpendicular to every other straight line drawn through its... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...cannot but be a straight line.* Therefore, if two planes, &c. PROP. IV. THEOR. IF a straight line be **perpendicular to each of two straight lines at their point of intersection, it is** also perpendicular to the plane in which they are. Let the straight line EF be perpendicular to each... | |
| Euclides, James Thomson - Geometry - 1845 - 382 pages
...planes AB, BC, cannot but be a straight line.* Therefore, &c. Puor. IV. THEOR. — If a straight line be **perpendicular to each of two straight lines at their point of intersection, it is** also perpendicular to the plane in which they are. Let the straight lineEF be perpendicular to each... | |
| Dennis M'Curdy - Geometry - 1846 - 166 pages
...common section is a straight line. Recite def. 7,1. 4 Th. If a straight line stand at right angles **to each of two straight lines, at their point of intersection, it** will also be at right angles to the plane in which those straight lines are. Recite p 47 and 48 of... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...it is their common section. Hence, if two planes, &c. PROPOSITION IV. THEOREM. If a straight line be **perpendicular to each of two straight lines at their point of intersection, it** will be perpendicular to the plane in which these lines are. Through B draw any line BG, in the plane... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...be a right angle, the planes are said to be perpendicular to one another. 5. If a straight line be **perpendicular to each of two straight lines at their point of intersection, it is** said to be perpendicular to the plane passing through those two lines. Conversely, the plane is said... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...it is their common section. Hence, if two planes, &c. PROPOSITION IV. THEOREM. If a straight line be **perpendicular to each of two straight lines at their point of intersection, it** will be perpendicular to the plane in which these lines are. Let the straight line AB be perpendicular... | |
| George Roberts Perkins - Geometry - 1860 - 472 pages
...secant EF, the plane of the two straight lines AB, EF is that of the parallels AB, CD. ) THEOREM 1IIThe **intersection of two planes is a straight line. Let...intersection P ; then will it be perpendicular to** MN the plane of the lines. Through P draw in the plane MN any line, as PQ ; and through any point of... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...Therefore, the common section of the two planes AB, CD is a straight line. PROPOSITION IV. — THEOREM. 401. **If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane** in which the two lines lie. Let the straight line AB be perpendicular to each of the straight lines... | |
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