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" ... of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater. "
Elements of Solid Geometry - Page 4
by William Herschel Bruce, Claude Carr Cody - 1912 - 110 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...equal distances from the foot of the perpendicular, will be equal: 3.° Of two oblique lines which meet the plane at unequal distances from the foot of the perpendicular, the one which meets it at the greater distance will be the longer. Let A be a point without the plane MN...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...meeting the plane at equal distances from the •foot of the perpendicular; and let AC and AE be any two oblique lines meeting the plane at unequal distances from the foot of the perpendicular : 1°. AP will be shorter than any oblique line AC. For, draw PC', then will I— \^± N AP be less...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...meeting the plane at equal distances from the foot of the perpendicular ; and let AC and AE be any two oblique lines meeting the plane at unequal distances from the foot of the perpendicular : 1°. AP will be shorter ^ than any oblique line AC. For, draw PC; then will AP be less than AC (B....
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...PROPOSITION VI. THEOREM. 55. Of two oblique lines drawn from Ihe »ame point in a perpendicular, cutting off unequal distances from the foot of the perpendicular , the more remote is the greater. C Г • E Let С F be perpendicular to AB, and CK and С Н two oblique lines cutting off unequal...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...distances from the foot of the perpendicular are equal ; and of two oblique lines unequally distant from the foot of the perpendicular the more remote is the greater. Iden. IIypLet the oblique lines BC, BD, and BE, be drawn at equal distances, AC, AD, and AE, from the...
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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...point A from the plane MN. III. Theorem. All oblique lines drawn from the same point, and meeting a plane at equal distances from the foot of the perpendicular,...the perpendicular, the more remote is the greater. HYPOTH. 1. AB1MN, and BC = BD = BE, = , &c. ELEMENTS OF GEOMETRY. [BOOK V. PROOF. A ABC ^ ABD ^ ABE...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 332 pages
...from the foot of the perpendicular let fall from the point are equal ; and that of two lines drawn to unequal distances from the foot of the perpendicular, the more remote is the greater. 6. Prove the converse of the first part of the last exercise. 7. Find the locus of points in a plane...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...PROPOSITION VI. THEOREM. 55. 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. С E Let С F be perpendicular to AB, and С К and СH two oblique lines cutting oil unequal distances...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...Oblique lines meeting the plane at equal distances from the foot of the perpendicidar, will be equal. 3. Of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular, the one which meets it at the greater distance is the longer. Let P be the point; MN, the plane; PC, the...
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Annals of Mathematics

Electronic journals - 1902 - 232 pages
...straight line. 5. If oblique lines drawn from a point in a perpendicular to a straight line cut off unequal distances from the foot of the perpendicular, the more remote is the greater. To prove our theorem it is sufficient to prove that if the triangle ABC is not isosceles, the lines...
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