...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...of 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...

...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...

...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...

...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...

...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...

...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...

...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...

...common to both of them ; that is, the intersection of the two planes is in a straight line. THEOREM Iv. If a straight line is perpendicular to each of two...of intersection^ it is perpendicular to the plane of these lines. Let AP be perpendicular to the two lines PB, PC, at their point of intersection P ;...

...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...

...common to both of them ; that is, the intersection of the two planes is in a straight line. THEOREM IV. If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane of these lines. Let AP be perpendicular to the two* lines PB, PC, at their point of intersection P...