...would PD<PC. § 99 [Of two oblique lines drawn from the same point in a perpendicular and cutting off unequal distances from the foot of the perpendicular, the more remote is the greater.] But both these conclusions contradict the hypothesis. Therefore OD>OC. QED 1O1. COR. Two right triangles...

...Converse o/§ 82. PROPOSITION XVI. THEOREM. 84. Jf two oblique lines from a point to a line meet that line at unequal distances from the foot of the perpendicular, the more remote is the greater. It is to be proved that PA is greater than PB. Extend PD to Q, making DQ = PD. Draw QA, QB, extending...

...oblique lines meeting the plane at equal distances from the foot of the perpendicular are equal. (2) Of two oblique lines meeting the plane at unequal...foot of the perpendicular, the more remote is the longer. Let OP be perpendicular to the plane MN, and PA = PB, but PC > PA. To prove that OA = OB, but...

...to FG, and consequently to MN. § 503 Therefore, AB is the only _L from A to MN. QE D 512. COR. The perpendicular is the shortest line from a point to...the perpendicular the more remote is the greater. Let AC and AD cut off the equal distances EC and BD from the foot of the perpendicular AB, and let...

...perpendicular drawn from the point to the plane ; and of two oblique lines drawn from a point to a plane, and meeting the plane at unequal distances from the foot...the perpendicular, the more remote is the greater. THEOREM VI. The intersections of two parallel planes with any third plane are parallel. THEOREM VII....

...distances from the foot of the perpendicular are equal. 2. Of oblique lines which meet the given line at unequal distances from the foot of the perpendicular the more remote is the greater. Data : Any straight line, as AB ; any perpendicular to AB, as PD ; and any point in PD, as C, from...

...Theorem. 24. If from the same point in a perpendicular to a line two oblique lines are drawn cutting off unequal distances from the foot of the perpendicular, the more remote is the greater. CASE I. When the two oblique lines are on the same side of the perpendicular. F\E\ D Hypothesis. CD...

...equal distances from the foot of the perpendicular are equal. II. Of two oblique lines cutting off unequal distances from the foot of the perpendicular, the more remote is the greater. I. Given line AB _L to plane MN at B, and AC and AD oblique lines meeting MN at equal distances from...

...equal distances from the foot of the perpendicular are equal. II. Of two oblique lines cutting off unequal distances from the foot of the perpendicular, the more remote is the greater. 1. Given line AB _L to plane MN at B, and AC and AD oblique lines meeting MN at equal distances from...

...drawn from the same point in a perpendicular to a given line, cutting off on the line unequal segments from the foot of the perpendicular, the more remote is the greater. E Let OC be perpendicular to AB, OG and OE two straight lines to AB, and CE greater than CG. To prove...