 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, with Problems and Applications - Page 33by Herbert Ellsworth Slaught, Nels Johann Lennes - 1919 - 211 pagesFull 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
...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 M If, and... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...perpendicular to another, the planes are at right angles to each other. 6. The acute angle which a line makes with its own projection on a 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... | |
 | 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
...4. 6. .'. OA < OX, or its equal OY. SOLID GEOMETRY. Theorem 12. 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... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...is called the distance from that point to the plane. Theorem 12. 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... | |
 | John Macnie - Geometry - 1895 - 386 pages
...AC < AD, (432) (since AC is _L to plane MN;) (Hyp.) .-. Z ABC < Z ABD. QED (91) *. 483. DEFINITION. The acute angle formed by a straight line with its own projection on a plane is called the inclination of the line to the plane, or the angle of the line and plane. EXERCISE 667.... | |
 | John Macnie - Geometry - 1895 - 390 pages
...but AC < AD, (432) (since AC is _L to plane MN;) (Hyp.) ... Z ABC<Z ABD. QEI>. (91) 483. DEFINITION. The acute angle formed by a straight line with its own projection 0ii a plane is called the inclination of the line to the plane, or the angle of the line and plane.... | |
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