 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...Therefore, the common section of the two planes AB, CD is a straight line. PROPOSITION IY. — THEOREM. 401. If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane in which the two lines lie. Let the straight line AB be perpendicular to each of the straight lines... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...AB, CD is a straight line. B 1> PROPOSITION IV. — THEOREM. 401. If a straight line is pcrpemlicular 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 to each of the straight lines... | |
 | 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 - 288 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... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...Therefore, the common section of the two planes AB, CD is a straight line. PROPOSITION IV. — THEOREM. 401. If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane in which the two lines lie. Let the straight line AB be perpendicular to. each of the straight lines... | |
 | James Robert Christie - Mathematics - 1866 - 428 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... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...the common section of the two planes AB, A CD is a straight line. PROPOSITION IV. — THEOREM. 401. If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane in which the two lines lie. Let the straight line AB be perpendicular to each of the straight lines... | |
 | 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...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... | |
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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. 
