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" Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular. "
The Elements of Plane and Solid Geometry ... - Σελίδα 253
των Edward Albert Bowser - 1890 - 393 σελίδες
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 σελίδες
...which a line makes with the perpendicular, the greater the line is, and vice versa. 4°. Lines which meet the plane at equal distances from the foot of the perpendicular are equal, and vice versa. 5°. The more distant the point where a line meets the plane is from the...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 σελίδες
...other straight lines which are drawn from the point to the plane, such as are equal to one another, cut the plane at equal distances from the foot of the perpendicular; and such as are unequal, cut the plane at unequal distances from the foot, the greater being always further...

Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...other straight lines which are drawn from the point to the plane, such as are equal to one another cut the plane at equal distances from the foot of the perpendicular ; and such as are unequal cut the plane at unequal distances from the foot, the greater being always further...

Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1860 - 453 σελίδες
...perpendicular to a plane, oblique lines be drawn to different points in the plane, those oblique lines which meet the plane at equal distances from the foot of the perpendicular are equal ; and those which meet the plane at unequal distances from the foot of the perpendicular...

ELEMENTS OF GEOMETRY AND TRIGONOMETRY

CHARLES DAVIES, LL.D. - 1863
...plane : • 1°. The perpendicular will be shorter than any oblique line : 2°. Oblique lines which meet the plane at 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...

Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1864 - 276 σελίδες
...without a plane, a perpendicular and oblique lines be extended to the plane, then two oblique lines which meet the plane at equal distances from the foot of the perpendicular, are equal. Let AB be perpendicular, and AC and AD oblique to the plane MN, and the distances BC and...

Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1868 - 420 σελίδες
...without a plane, a perpendicular and oblique lines be extended to the plane, then two oblique lines which meet the plane at equal distances from the, foot of the perpendicular, are equal. Let AB be perpendicular, and AC and AD oblique to the plane MN, and the distances BC and...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...Corollary I. Conversely, equal oblique lines from a point to a plane meet the plane at equal distances from the perpendicular; and of two unequal oblique lines,...greater meets the plane at the greater distance from the perpendicular. 12. Corollary II. Equal straight lines from a point to a plane meet the plane in the...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...PB = PC, and join AB: thenAD>^.B (L 35); but AB = AC; therefore, AD>AC. 11. Corollary I. Conversely, equal oblique lines from a point to a plane meet the plane at equal distances from the perpendicular; land of two unequal oblique lines, the greater meets the plane at the Beater distance...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1872 - 368 σελίδες
...PC, and join AB: then AD> AB (I. 35); but AB = AC; therefore, AD > A C. 11. Corollary I. Conversely, equal oblique lines from a point to a plane meet the plane at equal distances from the perpendicular; and of two unequal oblique lines, the greater meets the plane at the greater distance...




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