| William Mitchell Gillespie - Surveying - 1857 - 524 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. "... | |
| Adrien Marie Legendre - Geometry - 1857 - 448 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... | |
| Elias Loomis - Conic sections - 1858 - 234 pages
...that is, together with four right angles (Prop. V., Cor. 2). Therefore the angles of the polygon are **equal to twice as many right angles as the figure has sides, wanting** four right angles. Cor. 1. The sum of the angles of a quadrilateral is four right angles ; of a pentagon,... | |
| W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...and in an irregular polygon they may be all unequal. The interior angles of a polygon are together **equal to twice as many right angles as the figure has sides,** less four. On this is based the theory of the traverse, of which further explanation will be given... | |
| Euclides - 1860
...a polygon be produced to meet, the sum of the salient angles thus formed, with eight right angles, **will be equal to twice as many right angles as the figure has sides.** Let ABCDE be a polygon, and let its sides produced meet in F, G, H, T, K ; then the sum of the salient... | |
| Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...triangles is equal to two right angles, (Th. 11) ; and the sum of the angles of all the triangles must **be equal to twice as many right angles as the figure has sides.** But the sum of these angles contains the sum of four right angles about the point p ; taking these... | |
| Royal college of surgeons of England - 1860
...two right angles ; and all the angles of any rectilineal figure, together with four right angles, are **equal to twice as many right angles as the figure has sides.** 6. The opposite sides and angles of parallelograms are equal to one another, and the diameter bisects... | |
| Euclides - 1860
...of a polygon be produced to meet, the sum of the salient angles thus formed with eight right angles, **will be equal to twice as many right angles as the figure** lias sides. 16. If on two opposite sides of a rectangle semicircles be described lying on corresponding... | |
| University of Madras - 1879
...I. Prove that all the interior angles of any rectilineal figure together with four right angles, are **equal to twice as many right angles as the figure has sides.** II. Prove the proposition to which the following is a corollary : The difference of the squares on... | |
| Rolla Rouse - 1879
...40 ... ... ... ... ... 103 The exterior and interior angles of an rectilineal figure, are together **equal to twice as many right angles as the figure has sides,** 41 ... 104 „ angles are together equal to four right angles, 42 ... ... ... ... „ The interior... | |
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