 | Robert Potts - 1868 - 434 σελίδες
...BD, the common section of the planes AB, BC, cannot but be a straight line. PROPOSITION IV. THEOREM. If a straight line stand at right angles to each of two straight lines in the point of their intersection, it shall also be at right angles to the plane which passes through... | |
 | Benjamin Greenleaf - 1868 - 340 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 - 392 σελίδες
...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 - 380 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 - 376 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.... | |
 | Manchester univ - 1872 - 380 σελίδες
...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... | |
 | William Chauvenet - 1872 - 382 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 - 1874 - 342 σελίδες
...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 - 400 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... | |
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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. 
