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" If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines. "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 168
by Benjamin Greenleaf - 1862 - 490 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...greater cuts off the greater distance from the foot of the perpendicular. PROPOSITION VII. THEOREM. 380. If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane of those lines. Given — PO perpendicular to AO and BO at their intersection 0. To Prove — PO perpendicular...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...position of this plane with respect to the line AB perpendicular to these two lines (197) ; we say — If a straight line is perpendicular to each of two straight lines drawn in a plane through its foot, it is perpendicular to every other straight line drawn through its...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...cannot but be a straight line.* Therefore, if two planes, &c. PROP. IV. THEOR. IF a straight line be perpendicular to each of two straight lines at their point of intersection, it is also perpendicular to the plane in which they are. Let the straight line EF be perpendicular to each...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...planes AB, BC, cannot but be a straight line.* Therefore, &c. Puor. IV. THEOR. — If a straight line be perpendicular to each of two straight lines at their point of intersection, it is also perpendicular to the plane in which they are. Let the straight lineEF be perpendicular to each...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...common section is a straight line. Recite def. 7,1. 4 Th. If a straight line stand at right angles to each of two straight lines, at their point of intersection, it will also be at right angles to the plane in which those straight lines are. Recite p 47 and 48 of...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...it is their common section. Hence, if two planes, &c. PROPOSITION IV. THEOREM. If a straight line be perpendicular to each of two straight lines at their point of intersection, it will be perpendicular to the plane in which these lines are. Through B draw any line BG, in the plane...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...be a right angle, the planes are said to be perpendicular to one another. 5. If a straight line be perpendicular to each of two straight lines at their point of intersection, it is said to be perpendicular to the plane passing through those two lines. Conversely, the plane is said...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 235 pages
...common to both of them ; that is, the intersection of the two planes is in a straight line. THEOREM Iv. If a straight line is perpendicular to each of two...of intersection^ it is perpendicular to the plane of these lines. Let AP be perpendicular to the two lines PB, PC, at their point of intersection P ;...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...it is their common section. Hence, if two planes, &c. PROPOSITION IV. THEOREM. If a straight line be perpendicular to each of two straight lines at their point of intersection, it will be perpendicular to the plane in which these lines are. Let the straight line AB be perpendicular...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 pages
...common to both of them ; that is, the intersection of the two planes is in a straight line. THEOREM IV. If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane of these lines. Let AP be perpendicular to the two* lines PB, PC, at their point of intersection P...
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