| Popular educator - 1854 - 940 pages
...tiungles are equal to twice as many right anales as the figure has sides. Therefore all the angles of the **figure together with four right angles are equal to twice as many right** ung'es as the figure has sides. Corollary 2. All the exterior angles of any rectilineal figure, made... | |
| Charles Davies - Geometry - 1854 - 436 pages
...triangles in the figure ; that is, as many times as there are sides, less two. But this product is **equal to twice as many right angles as the figure has sides,** less four right angles. Cor. 1. The sum of the interior angles in a quadrilateral is equal to two right... | |
| E. W. Beans - Surveying - 1854 - 114 pages
...taken. If the entire survey has been made as above directed, the sum of all the internal angles will be **equal to twice as many right angles as the figure has sides,** diminished by four right angles. If this sum, as in practice will be likely to be the case, should... | |
| Euclides - 1855 - 262 pages
...triangles are equal to twice as many right angles as the figure has sides. Therefore all the angles of the **figure together with four right angles are equal to...twice as many right angles as the figure has sides.** СOR. 2. — All the exterior angles of any rectilineal figure, made by producing the sides successively... | |
| William Mitchell Gillespie - Surveying - 1855 - 436 pages
...proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is **equal to twice as many right angles, as the figure has sides** less two ; since the figure can be divided into that number of triangles. Hence this common rule. "... | |
| Cambridge univ, exam. papers - 1856 - 200 pages
...also be equal. Prove this also without construction, by superposition. 3. Prove that all the internal **angles of any rectilineal figure, together with four...twice as many right angles as the figure has sides;** and that all the external angles are together equal to four right angles. In what sense are these propositions... | |
| Euclides - 1856 - 168 pages
...vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the **figure, together with four right angles, are equal...twice as many right angles as the figure has sides.** XVI. If two triangles have two sides of the one equal to two sides of the other, each to each, and... | |
| 1856 - 428 pages
...triangles thus formed are equal to all the angles of the figure (Const.) ; therefore all the angles of the **figure, together with four right angles, are equal to twice as many right angles as the figure** nas sides (Лх. 1). QED The demonstration of Euclid's Cor. II. viz. "that all the pxterior angles... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...But ACD+ACB = 2R; BAC+ABC+ACB = 2R. Corollary 1.—All the interior angles of a polygon are together **equal to' twice as many right angles as the figure has sides,** minus four right angles. Let ABODE be a polygon, and let n represent the number of its sides. Draw... | |
| John Henry Robson - 1880 - 118 pages
...problem is the sth Proposition of Euclid's Fourth Book. 12. By Euc. I. 32, Cor. 1, it is proved that " **All the Interior angles of any Rectilineal figure,..."twice as many right angles as the figure has " sides."** If, therefore, we suppose the polygon to have n sides, All its interior angles + 4.90 .= 272.90 . -.... | |
| |