 | Ferdinand Rudolph Hassler - Geometry - 1828 - 180 pages
...demonstrated. CHAPTER III. Of Solid Angles and the equality of Solids. § 15. THEOREM. If a solid angle be contained by three plane angles, any two of them are together greater than the third. APPLIC. Let the solid angle at A, (fig. 98,) be contained by the three plane angles, GAF, GAH, and... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...&c. Solid angle, def. (also its "edges") . 125 When said to be a right angle >ch. 203 (а) If a solid angle is contained by three plane angles, any two of them are together greater than the third ; and any one is greater than the difference of the other two . 137 (б) The plane angles, which contain... | |
 | Mathematics - 1835 - 684 pages
...Solid any/e, dff. (also its "edges") . 125 \\7hen said to be a right angle sch. 203 (a) If a solid angle is contained by three plane angles, any two of them are together greater than the third; and any one is greater than the difference of the other two . 137 (&) The plane angles, which contain... | |
 | John Charles Snowball - 1837 - 322 pages
...have an angle greater than two right angles, Euclid•s Proposition, xi. 20., " If a solid angle be contained by three plane angles, any two of them are together greater than the third," would not be true in all cases. For let ACB be a circle whose diameter is А0В, and let COA revolve... | |
 | Euclides - 1846 - 292 pages
...perpendicular to the third plane. Wherefore, If two planes &. QED PROP. XX. THEOR. If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of these shall... | |
 | Samuel Hunter Christie - 1847 - 172 pages
...COD is the supplement of the inclination of the faces MB, NB. PROP. XLIV. THEOR. If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A (fig. 49) be contained by the three plane angles BAC, CAD, DAB : any two of... | |
 | Queen's University of Belfast - Education, Higher - 1852 - 306 pages
...PROFESSOR WILSON. GEOMETRY AND TRIGONOMETRY. 1. Define a solid angle, and show that if a solid angle be contained by three plane angles, any two of them are together greater than the third. ^Euclid b. xi., p. 20. 2. Show that similar polygons inscribed in circles are to one another as the... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...equiangular, and have those angles equal which are opposite to homologous sides. 2. If a solid angle be contained by three plane angles, any two of them are together greater than the third. 3. Determine the perpendicular height of a hill, its angle of elevation taken at the bottom of it being... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...to the third plane. , Wherefore, if two planes &c. QEB PEOPOSITION 20. THEOREM. If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB: any two of them shall... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...perpendicular to the third plane. Wherefore, if two planes &c. QED PROPOSITION 20. THEOREM. If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall... | |
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If a solid angle be contained by three plane angles, any two of them are together greater than the third. 
