 | Cambridge univ, exam. papers - 1856 - 200 páginas
...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 - 428 páginas
...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 - 1856 - 220 páginas
...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 - 548 páginas
...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... | |
 | 1857 - 1266 páginas
...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 - 1858 - 256 páginas
...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 - 1860 - 380 páginas
...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 - 332 páginas
...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 - 142 páginas
...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 - 462 páginas
...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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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. 
