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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. "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 139
by George Roberts Perkins - 1856 - 235 pages
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...these points; the straight line AP will be the required perpendicular. PROPOSITION V.— THEOREM. 13. If a straight line is perpendicular to each of two...intersection, it is perpendicular to the plane of those lines. Let AP be perpendicular to PB and PC, at their intersection P; then, AP is perpen. dicular...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...line ; which, was to be proved. • PROPOSITION IV. THEOREM. If a straight line is perpendicular to two straight lines at their point of intersection, it is perpendicular to the plane of those lines. AP be perpendicular to every straight line of the plane which passes through P, and consequently,...
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The Calendar of Owens college, Manchester

Manchester univ - 1872 - 380 pages
...circumscribing circle, one of these lines is equal to the sum of the other two. 6. 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. 7. Define parallel planes. Prove that two planes...
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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - Geometry - 1873 - 288 pages
...all in one straight line (59). — E PERPENDICULAR LINES. *»17. Theorem — A straight line which is perpendicular to each of two straight lines at their point of intersection, is perpendicular to every other straight line which lies in the plane of the two, and passes through...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...straight line ; which was to be proved. PROPOSITION IV. THEOREM. Jf a straight line is perpendicular to two straight lines at their point of intersection, it is perpendicular to the plane of those lines. Let JOT be the plane of the two lines BB, (7(7, and let AP be perpendicular to these lines...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...DEFINITION. A straight line is said to be perpendicular to a plane PROPOSITION VI. . If a straight line be perpendicular to each of two straight lines at their point of intersection, it shall be perpendicular to the plane passing through them. Let PQ be j . to QA and QC. Then shall PQ...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1875 - 466 pages
...will be the required perpendicular. PROPOSITION V.—THEOREM. 13. If a etraight line isperpendicular to each of two straight lines at their point of intersection., it is perpendicular to the plane of Uiose lines. Let AP be perpendicular to PR and PC, at their intersection P; then, AP is perpendicular...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1875 - 390 pages
...these points; the straight line AP will be the required perpendicular. PROPOSITION V.— THEOREM. ^ 13. If a straight line is perpendicular to each of two straight lines at thttir point of intersection, it is perpendicular to the plane of those lines. Let AP be perpendicular...
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Annual Statement, Volumes 11-20

1876 - 646 pages
...other in what ratio ? Of all plane figures having the same area what one has the least perimeter? 5. If a straight line is perpendicular to each of two...intersection, it is perpendicular to the plane of those lines. 6. A triangular pyramid is one-third of a triangular prism of tbe same base and altitude....
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 412 pages
...a plane. PROPOSITION III. THEOREM. If a straight line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane of those lines. Let AQ and DQ be two lines in the plane KL, and let PQ be perpendicular to both ; then...
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