 | George Washington Hull - 1807 - 408 σελίδες
...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 - 1829 - 218 σελίδες
...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 - 1837 - 410 σελίδες
...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... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...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 - 1846 - 166 σελίδες
...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 - 1849 - 252 σελίδες
...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 - 1853 - 400 σελίδες
...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... | |
 | George Roberts Perkins - 1856 - 460 σελίδες
...secant EF, the plane of the two straight lines AB, EF is that of the parallels AB, CD. THEOREM HI. The intersection of two planes is a straight line. Let...intersection P ; then will it be perpendicular to MIST the plane of the lines. Through P draw in the plane MN" any line, as PQ ; and through any point... | |
 | Elias Loomis - 1858 - 256 σελίδες
...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... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...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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If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines. 
