 | Yale University - 1892 - 200 pages
...other in what ratio? Of all plane figures having the same area what one has the least perimeter ? 5. If a straight line is perpendicular to each of two...intersection, it is perpendicular to the plane of those lines. 6. A triangular pyramid is one-third of a triangular prism of the same base and altitude.... | |
 | Euclid - Geometry - 1892 - 460 pages
...the plane of AB, AC ; .'. DA is perp. to this plane. QED PROPOSITION 4. THEOREM. [Euclid's Proof.] If a straight line is perpendicular to each of two straight lines at their point of intersection, it shall also be perpendicular to the plane in which they lie. Let the st. line EF be perp. to each of... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...AND PLANES. PROPOSITION II. THEOREM. 472. If a straight line is perpendicular to each of two otJier straight lines at their point of intersection, it is perpendicular to the plane of the two lines. A Let AB be perpendicular to BC and BD at B. To prove AB perpendicular to the plane... | |
 | William Chauvenet - 1893 - 340 pages
...At a given point in a plane one perpendicular can be erected to the plane, and but one. PROPOSITION IV. If a straight line is perpendicular to each of...intersection, it is perpendicular to the plane of those lines. Corollary I. At a given point of a straight line, one plane can be drawn perpendicular... | |
 | Examinations - 1893 - 408 pages
...angle of a diedral angle, tangent plane, surface vf revolution, oblique prism, sphere. 15 2 Prove that if a straight line is perpendicular to each of two...intersection, it is perpendicular to the plane of the two lines. 1 8 3 Prove that the sum of the face angles of any convex polyedral angle is less than... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...only one plane can contain a straight line and a point without, § 5. PROPOSITION II. THEOREM. 15. If a straight line is perpendicular to each of two...of intersection it is perpendicular to the plane of those lines. Notation. Let m and n be two straight lines which determine the plane M, and p another... | |
 | 1893 - 760 pages
...Shew that similar triangles are to one another in the duplicate ratio of corresponding medians. 4. If a straight line is perpendicular to each of two straight lines at their point of intersection, it shall also be perpendicular to the plane in which they lie. The locus of points equidistant from two... | |
 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...passed perpendicular to the line. PROPOSITION IV. 16. THEOREM. If a line is perpendicular to each of two lines at their point of intersection, it is perpendicular to the plane of the two lines. By our hypothesis BG and BD are perpendiculars to AB, at a common point B ; therefore... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...drawn.] (§ 28.) Hence, but one perpendicular can be drawn to MN at P. 400. COR. I. A straight line perpendicular to each of two straight lines at their point of intersection is perpendicular to their plane. 401. COR. II. From a given point without a plane, one perpendicular... | |
 | United States. War Department - 1896 - 1256 pages
...between the secant and its external segment. [Weight, 2.] 3. If a straight line is perpendicular to two straight lines at their point of intersection it is perpendicular to the plane of those lines. [Weight, 4.] 4. Given an equilateral triangle inscribed in a circle, and a similar circumscribed... | |
| |
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. 
