 | Jeremiah Day - Measurement - 1815 - 388 pages
...solids. The only plane figures which can form such solids, are' triangles, squares, and pentagons. For the plane angles which contain any solid angle, are...or 360°. (Sup. Euc. 21. 2.) And the least number s which can form a solid angle is' three. (Sup. Euc. Def. 8. 2.) If they are angles of equilateral... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...with either of them, is greater than the other. Wherefore, if a solid angle, &c. QED PROP. XXI. THEOR. The plane angles which contain any solid angle are together less than four right angles. Let A be a solid angle contained by any number of plane angles BAG, CAD, DAE, EAF, FAB ; these together... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...together greater than the third ; and any one is greater than the difference of the other two . 137 (б) The plane angles, which contain any solid angle, are together less than four right angles . . 137 (c) 11 two solid angles are each of them contained by three plane angles, and if two of these... | |
 | Jeremiah Day - Measurement - 1831 - 394 pages
...solids. The only plane figures which can form such solids, are triangles, squares, and pentagons. For the plane angles which contain any solid angle, are...The sum of three of them is 180°, of four 240°, of five 300°, and of six 360°. The latter number is too great for a solid angle. The angles of squares... | |
 | Jeremiah Day - Logarithms - 1831 - 418 pages
...solids. The only plane figures which can form such solids, are triangles, squares, and pentagons. For the plane angles which contain any solid angle, are...triangles, each is 60°. The sum of three of them is 130°, of four 240°, of five 300°, and of six 360°. The latter number is too great for a solid angle.... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...of them, is greater than the other. Wherefore, if a solid angle, &c. QED PROP. XXI. THEOR. Theplane angles which contain any solid angle are together less than four right angles. Let A be a solid angle contained by any number of plane angles BAC, CAD, DAE, EAF, FAB; these together... | |
 | Mathematics - 1835 - 684 pages
...together greater than the third; and any one is greater than the difference of the other two . 137 (&) The plane angles, which contain any solid angle, are together less than four right angles . . 137 (c) If two solid angles are each of them contained by three plane angles, and if two of these... | |
 | Jeremiah Day - Measurement - 1836 - 418 pages
...solids. The only plane figures which can form such solids, are triangles, squares, and pentagons. For the plane angles which contain any solid angle, are together less than four right angles or 3o"00. (Sup. Euc. 21. 2.) And the least number which can form a solid angle is three. (Sup. Euc. Def.... | |
 | Mathematics - 1836 - 488 pages
...angle be contained by three plane angles, any two of these angles are greater than the third. XXI. The plane angles which contain any solid angle are together less than four right angles. BOOK in. — DEFINITIONS. 1. A solid is that which has length, breadth, and thickness. 2. Similar solid... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...angles DAB, DAG ; therefore BAG, with either of them, is greater than the other. PROP. XXI. THEOR. The plane angles which contain any solid angle are together less than four right angles. Let A be a solid ang e contained by any number of plane angles BAG, CAD, DAE, EAF, FAB ; these together... | |
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Icosaedron, whose sides are four triangles ; six squares ; eight triangles ; twelve pentagons ; twenty triangles.* Besides these five, there can be no other regular solids. The only plane figures which can form such solids, are triangles, squares, and... 
