| Adrien Marie Legendre - Geometry - 1874 - 512 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... | |
| 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... | |
| William Chauvenet - Geometry - 1875 - 468 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... | |
| 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... | |
| 1876 - 646 pages
...area will be a maximum when these sides are at right angles. II.— SOLID AND SPHERICAL GEOMETRY. 7. **If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane** of these lines. 8. Define symmetrical polyhedral angles. Illustrate the definition by a figure. 9.... | |
| William Guy Peck - Conic sections - 1876 - 394 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... | |
| Elias Loomis - Geometry - 1877 - 458 pages
...is their common section. Hence, if two planes, etc. PROPOSITION IV. THEOREM. If a straight line be **perpendicular to each of two straight lines at their point of intersection, it** will be perpendicular to the plane in which these lines are. Let the straight line AB be perpendicular... | |
| J. B. Millar - Geometry, Descriptive - 1878 - 264 pages
...planes out one another, their common section is a straight line 2 Theorem III. If a straight line be **perpendicular to each of two straight lines at their point of intersection, it** shall also be perpendicular to their plane 3 Theorem IV. Every plane which contains the normal to another... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...is therefore their common section. Proposition 4. Theorem.—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 the plane in which these straight lines are. Let AB be at right angles to each of... | |
| Cornell University - 1880 - 868 pages
...symmetrical triedral angles, a segment of a sphere, the axis of a parabola. 2. If a straight line be **perpendicular to each of two straight lines at their...of intersection, it is perpendicular to the plane** of those lines. 3. Two prisms are equal, if three faces including a triedral angle of one be respectively... | |
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