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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... "
The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ... - Side 26
av Jeremiah Day - 1824
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A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - 1815 - 388 sider
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 350 sider
...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...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 sider
...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...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ...

Jeremiah Day - 1831 - 394 sider
...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...
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A Treatise of Plane Trigonometry: To which is Prefixed a Summary View of the ...

Jeremiah Day - 1831 - 418 sider
...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....
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 358 sider
...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...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 sider
...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...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ...

Jeremiah Day - 1836 - 418 sider
...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....
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 488 sider
...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...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 332 sider
...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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