 | Ferdinand Rudolph Hassler - Geometry - 1828 - 180 pages
...angles, as AGD, GDE, and so on, standing in equal segments, are equal to one another; and their sum being equal to twice as many right angles as the figure has sides wanting four: that is, eight right angles, each of these angles of the hexagon is equal eight sixths... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...right angles as the figure has sides ; but the internal angles, together with four right angles, are equal to twice as many right angles as the figure has sides (134). Take from both, the internal angles and the external remain equal to four right angles. %* This... | |
 | John Playfair - Geometry - 1829 - 210 pages
...2rxn— 4r = (2n — 4) xr = (n— 2) x 2r, that is, all the interior angles of any convex rectilineal figure are together equal to twice as many right angles as the figure has sides less two sides. " Es. PROPOSITION M. THEOREM. All the exterior angles of any convex rectilineal figure,... | |
 | Thomas Curtis - Aeronautics - 1829 - 814 pages
...BE. THEOREM XX. — All the interior angles of any rectilineal figure, А В С DE (fig. 43, p. I.), are together equal to twice as many right angles as the figure has sides wanting four right angles. For from any point, as F, within the figure, let lines be drawn to its angular... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...equal to four right angles ; and the sum of its interior angles, together with four right angles, is equal to twice as many right angles as the figure has sides . . • 15 (¿•) The area of a rectilineal figure may be obtained by dividing it into triangles,... | |
 | Euclides - 1833 - 304 pages
...= to two right angles, (prop. 13.) Therefore, all the external angles, with all the internal, are = to twice as many right angles as the figure has sides ; but the internal angles, with four right angles, are = to twice as many right angles as the figure has sides;... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...formed as many triangles as the figure has sides, and therefore all their angles taken together are equal to twice as many right angles as the figure has sides (1): but the angles at the point F are equal to four right angles (2); and therefore the angles of... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...Therefore the other angles of the triangles, (which are together equal to all the interior •INIERC. 1. angles of the figure), are together* equal to twice as many right or> '' angles as the figure has sides, diminished by four right angles. Secondly; if the figure be... | |
 | Charles Bonnycastle - Geometry - 1834 - 670 pages
...a result usually expressed as the following proposition : "The interior angles of any closed plane figure are together equal to twice as many right angles as the figure has sides, minus four right angles." 206. And as a second application of the principle in question, or, which... | |
 | Mathematics - 1835 - 684 pages
...has as many angles as sides : therefore all the interior angles together with four right angles are equal to twice as many right angles as the figure has sides. Therefore, &c. Cor. The four angles of a quadrilateral are together equal to four right angles. SECTION... | |
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Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. 
