| Robert Potts - 1868 - 410 pages
...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 - 338 pages
...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 - Geometry - 1871 - 380 pages
...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 - Geometry - 1872 - 349 pages
...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 - Geometry - 1872 - 382 pages
...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 - 342 pages
...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 - Euclid's Elements - 1874 - 349 pages
...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 - Mathematics - 1876 - 318 pages
...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... | |
| |