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" If a straight line stand at right angles to each of two straight lines at the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 133
by Dennis M'Curdy - 1846 - 138 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 518 pages
...perp. to this plane. QED PROPOSITION 4. THEOREM. [Euclid's Proof.] If a straight line is perpendicular to each of two straight lines at their point of intersection, it shall also be perpendicular to the plane in which they lie. Let the st. line EF be perp. to each of...
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Yale Examination Papers

Yale University - 1892 - 139 pages
...area will be a maximum when these sides are at right angles. 7. If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of these lines. 8. Define symmetrical polyhedral angles. Illustrate the...
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - Geometry, Solid - 1893 - 148 pages
...straight line and a point without, 5. PROPOSITION II. THEOREM. 15. 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. Notation. Let m and n be two straight lines which determine...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...from the foot of the perpendicular. PROPOSITION IV.—THEOREM. 10. 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. Let AP be perpendicular to PB and PC, at their intersection...
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Examination Papers for the Academic Year ...

Examinations - 1893
...plane, surface vf revolution, oblique prism, sphere. 15 2 Prove that if a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of the two lines. 1 8 3 Prove that the sum of the face angles of any...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...plane is perpendicular to the line. PROPOSITION III. THEOREM 511. If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to Hie plane of those lines. GIVEN — the straight line BG perpendicular to each...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 374 pages
...plane is perpendicular to the line. PROPOSITION III. THEOREM 511. 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. GIVEN—the Straight line BG perpendicular to each of...
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Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 208 pages
...prism, a parallelopiped, a pyramid, a cone, a cylinder, a sphere. 2. 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. 3. If a pyramid is cut by a plane parallel to its base,...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898 - 212 pages
...prism, a parallelepiped, a pyramid, a cone, a cylinder, a sphere. 2. 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. 3. If a pyramid is cut by a plane parallel to its base,...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...from the foot of the perpendicular. PROPOSITION III. THEOREM. 337. 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. To prove that BA is perpendicular to EA and hence perpendicular...
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