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" ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater. "
The Elements of Solid Geometry - Page 9
by William C. Bartol - 1893 - 95 pages
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1895 - 468 pages
...distances from the foot of the perpendicular, are equal; and of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater. Let AC and AD cut oft the equal distances BC and BD from the foot of the perpendicular AB, and let AD and...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 390 pages
...drawn to equal distances from the foot of the perpendicular are equal. 0°. Of oblique lines drawn to unequal distances from the foot of the perpendicular, the more remote is the greater. IT Given : PD _L to MN, and PA, PB, PC, drawn oblique to MN, so that AD is equal to BD, but CD is greater...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...OD<OC, then 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 101, COR. Two right triangles...
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...drawn, but included by them. 119. Of two oblique lines drawn from the same point in a perpendicular, cutting off unequal distances from the foot of the perpendicular, the more remote is the greater. 120. Cor. Only two equal straight lines can be drawn from a point to a straight line ; and of two unequal...
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Elements of Geometry: Plane geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...OD<OC, then 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 101, COR. Two right triangles...
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 254 pages
...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...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...distances from the foot of the perpendicular are equal. (2) Of two oblique lines meeting the plane at unequal distances from the 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...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 pages
...DF. If we suppose DE > DF, CE would be > CF. [If oblique lines be drawn from a point to a str. line, of two oblique lines cutting off unequal distances from the foot of the .L from the point to the line, the more remote is the greater.] (§ 49) But this is contrary to the...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...Proposition 14. 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...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...distances from the foot of the perpendicular, are equal; and of two oblique lines meeting the plane at unequal distances from the foot of 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 AD and...
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