| Cambridge univ, exam. papers - 1856
...also without construction, by superposition. 3. Prove that all the internal angles of any rectilineal **figure, together with four right angles, are equal to 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... | |
| 1856
...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... | |
| Henry James Castle - Surveying - 1856 - 185 pages
...that these angles are the exterior angles of an irregular polygon ; and as the sum of all the interior **angles are equal to twice as many right angles, as the figure has** sides, wanting four ; and as the sum of all the exterior, together with all the interior angles, are... | |
| British and foreign school society - 1857
...produced to meet the alternate sides, also produced, the angles formed by these lines, together with eight **right angles, are equal to twice as many right angles as the** polygon has sides. 4. If two chords intersect in a circle, the difference of their squares is equal... | |
| Education - 1857
...produced to meet the alternate sides, also produced, the angles formed by these lines, together with eight **right angles are equal to twice as many right angles as the** polygon has sides. 4. If two chords intersect in a circle, the difference of their squares is equal... | |
| Elias Loomis - Conic sections - 1858 - 234 pages
...F, 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... | |
| Robert Potts - Geometry, Plane - 1860 - 361 pages
...sides, then n0 is the sum of all the interior angles. But 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, that is, if ir be assumed to designate two right angles, .'. »9 + 2ir = mr, and nfl = mr —... | |
| Royal college of surgeons of England - 1860
...angles of a triangle are together equal to 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... | |
| Euclides - 1860
...wherefore the salient angles F, G, H, T, K, with twice the angles m, n, «, e, w, that is, with eight **right angles, are equal to twice as many right angles as the figure has** sides. COR. — The salient angles with four right angles, are equal to the interior angles of the... | |
| 1860
...figure must be aliquot parts of the circle or of four right angles. All the angles of any such figure **are equal to twice as many right angles as the figure has** sides minus four right angles, or if « be the number of sides, the sum of all the angles is (2n —... | |
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