 | Benjamin Greenleaf - 1868 - 320 σελίδες
...AB, A CD is a straight line. PROPOSITION IV. — THEOREM. 401. If a straight line is perpendicular to each of two straight lines, at their point of intersection, it is perpendicular to the plane in which the two lines lie. Let the straight line AB be perpendicular... | |
 | Edinburgh univ - 1871
...for the base of a similar triangle whose area is threefourths of the former. 7. If a straight line be at right angles to each of two straight lines at their point of intersection, it is at right angles to their plane. 8. Prove the inequality — x* +y* + z*>xy + xz +yz. 9. Solve the... | |
 | William Chauvenet - 1871 - 368 σελίδες
...will be the required perpendicular. PROPOSITION V.— THEOREM. 13. 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... | |
 | Euclides, James Hamblin Smith - 1872 - 349 σελίδες
...MN. QED Note. — The Propositions which follow are numbered as in Euclid. PROPOSITION IV. THEOREM. If a straight line stand at right angles to each of two straight lines, at the point of their intersection, it must also be at right angles to the plane that passes through them.... | |
 | William Chauvenet - 1872 - 368 σελίδες
...will be the required perpendicular. PROPOSITION V.— THEOREM. 13. 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... | |
 | Manchester univ - 1872
...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... | |
 | Euclides - 1874
...AB and BC, must be in a straight line. Wherefore, if two planes, &c. QED PROPOSITION 4. — Theorem. If a straight line stand at right angles to each of two straight lines at. the point of their intersection, it is at right angles to the plane in which they are. Let the straight... | |
 | Francis Cuthbertson - 1874 - 349 σελίδες
...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... | |
 | Sir George Greenhill - 1876 - 236 σελίδες
...perpendiculars from B and D on FA are equal, and therefore FA bisects BD, and its parallel CE. •vi. 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... | |
 | Robert Potts - 1876 - 403 σελίδες
...and AFis perpendicular to DE; therefore AFis perpendicular to each of the straight lines GH, DE. But if a straight line stand at right angles to each of two straight lines in the point of their intersection, it is also at right angles to the plane passing through them :... | |
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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. 
