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" A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane. "
A Course of Mathematics: In Two Volumes. For the Use of Academies, as Well ... - Page 306
by Charles Hutton - 1818
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...the diameter to the circumference. BOOK VI. PLANES AND POLYEDRAL ANOLKS. DEFINITIONS. 1. A straight line is PERPENDICULAR TO A PLANE, when it is perpendicular to every straight line of the plane which passes through its FOOT; that is, through the point in which it meets...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 394 pages
...an infinite distance in all directions ; its position is indicated by two or more of its lines. 89. A line is perpendicular to a plane, when it is perpendicular to all the lines of the plane that pass through its foot ; that is, through the point in which it meets...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...revolving on AB as an axis, occupies an infinite number of positions. DEFINITIONS. ;. A straight line is perpendicular to a plane when it is perpendicular to every straight line of the plane which it meets. Conversely, the plane, in this case, is perpendicular to...
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Elements of geometry, tr. by J. Kaines

Alexis Claude Clairaut - 1881 - 180 pages
...perpendicular meets the plane 82 8. Simple modes of erecting or letting fall perpendiculars to planes . 83 9. A line is perpendicular to a plane when it is perpendicular to two lines on that plane drawn from the point where it meets the plane 83 1 0. Method of erecting a...
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The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...points be connected by a straight line, the line will lie wholly within the surface. 3. A straight line is perpendicular to a plane when it is perpendicular to every straight line of that plane which it can meet. The plane is also perpendicular to the line. 4. The...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...hexagon inscribed in the same circle. BOOK VI. PLANE8 AND POLYEDRAL ANGLE8. DEFINITIONS. 1. A straight line is PERPENDICULAR TO A PLANE, when it is perpendicular to every straight line of the plane which passes through its FOOT; that is, through the point in which it meets...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 331 pages
...intersection of the two planes. PERPENDICULARS AND OBLIQUE LINES TO PLANES. 6. Definition. A straight line is perpendicular to a plane when it is perpendicular to every straight line drawn in the plane through its foot; that is, through the point in which it meets the...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...contains either of these parallels / / and any point in the other, it is determined. (483) 487. A straight line is, perpendicular to a plane when it is perpendicular to every straight line which it meets in that plane. Conversely, the plane in this case is said to be perpendicular...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 428 pages
...any two of its points are joined by a straight line, that line will lie wholly in the surface. 426. A line is perpendicular to a plane when it is perpendicular to every line in the plane drawn through its foot. The line AB is perpendicular to the plane 12; it is perpendicular...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...not planes, and of lines which can not be drawn on a plane surface. LINES AND PLANES. 1. A straight line is perpendicular to a plane when it is perpendicular to every straight line which meets it in that plane. NOTE. It will be proved in Proposition 4 that if a straight...
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