Theorem. The acute angle which a line makes with its own projection on a plane is the least angle which it makes with any line in that plane. Given the line AB, cutting plane P at 0, A'B' the projection of AB on P, and XX' any other line in P, through... Solid Geometry - Page 260by Wooster Woodruff Beman, David Eugene Smith - 1903Full view - About this book
| William Chauvenet - Geometry - 1871 - 380 pages
...PROPOSITION XXIII.— THEOREM. 59. The acute angle which a straight line makes with its own projection upon a plane, is the least angle which it makes with any line of that plane. Let Ba be the projection of the straight line BA upon the plane MN, the point B being... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...PROPOSITION XXIII.— THEOREM. 59. The acute angle which a straight line makes with its own projection upon a plane, is the least angle which it makes with any line of that plane. Let Ba be the projection of the straight line BA upon the plane MN, the point B being... | |
| Aaron Schuyler - Geometry - 1876 - 384 pages
...equally distant from two given points. 3. The angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of that plane. 5. Find the locus of the points which are equally distant from two given straight lines... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...ANGLES. SUPPLEMENTARY PROPOSITIONS. PROPOSITION XXI. THEOREM. 478. The acute angle which a straight line makes with its own projection on a plane is the least angle which it makes with any line of that plane. Let BA meet the plane MN at B, and let B A' be its projection upon the plane MN, and... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...ANGLES. SUPPLEMENTARY PROPOSITIONS. PROPOSITION XXI. THEOREM. 478. The acute angle which a straight line makes with its own projection on a plane is the least angle winch it makes with any line of that plane. Let BA meet the plane MN at B, and let B A' be its projection... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...parallel to one plane and perpendicular to another, the planes are at right angles to each other. 6. The acute angle which a line makes with its own projection...plane, is the least angle which it makes with any line on the plane. See Def. of projection, and use the last Ex. and (I. 23). 7. If a plane be passed through... | |
| Education - 1902 - 730 pages
...same plane have one, and only one, common perpendicular. 2. Prove: The acute angle that a straight makes with its own projection on a plane is the least angle it makes with any line in that plane. 3. (a) Prove: The sum of the face angles of any convex polyhedral... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...PROPOSITION XIX.—THEOREM. 44. The acute angle which a straight line makes with its own projection upon a plane is the least angle which it makes with any line of that plane. Let Ba be the projection of the straight line BA upon the plane MN, the point B being... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...as steps 6, 7, 8 under converse of 4. 6. .'. OA < OX, or its equal OY. SOLID GEOMETRY. Theorem 12. The acute angle which a line makes with its own projection...angle which it makes with any line in that plane. Given the line AB, cutting plane P at 0, A'B' the projection of AB on P, and XX' any other line in... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...perpendicular from a point to a plane is called the distance from that point to the plane. Theorem 12. The acute angle which a line makes with its own projection...angle which it makes with any line in that plane. Given the line AB, cutting plane P at 0, A'B' the projection of AB on P, and XX' any other line in... | |
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