 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...them. Therefore, the common section of the two planes AB, CD is a straight line. PROPOSITION IY. — THEOREM. 401. If a straight line is perpendicular...intersection, it is perpendicular to the plane in ivhich the two lines lie. Let the straight line AB be perpendicular to each of the straight lines CD,... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...straight line ; which was to be proved. PROPOSITION IY. 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 line of the plane which pusses through P, and consequently,... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...points are all in one straight line (59). PERPENDICULAR LINES. 517. 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... | |
 | James Robert Christie - Mathematics - 1866 - 426 pages
...through the point of contact will cut off similar segments. 4. If a straight line stand at right angles to each of two straight lines at their point of intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...are all in one straight line (59). 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... | |
 | William Chauvenet - Geometry - 1871 - 380 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...of 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 perpendicular... | |
 | Edinburgh univ - 1871 - 392 pages
...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 equations... | |
 | 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...of 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.... | |
 | 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... | |
 | 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... | |
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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. 
