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" ... therefore the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles... "
Manual of Geometry and Conic Sections: With Applications to Trigonometry and ... - Page 36
by William Guy Peck - 1876 - 366 pages
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...three angles of each of these triangles is equal to two right angles (th. 18); therefore the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles about the point F, which are so many of the angles...
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Elements of Geometry and Trigonometry

C. Davies - 1867 - 342 pages
...three angles of each of these triangle* is equal to two right angles (Th- xvii) : hence, the sum of th angles of all the triangles is equal to twice as many right ax gles as the figure has sidesBut the sum of all the angles about, the point P is equal U» four right...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 432 pages
...among the equal parts. SUM OF THE ANGLES. 433. Theorem. — The gum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two. For the polygon may be divided into as many triangles as it has sides, less two (417); and...
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Nature, Volume 63

Sir Norman Lockyer - Science - 1901 - 1076 pages
...(Grynaeus-Bale, 1533 AD ) these two corollaries are given : — (1) The sum of the interior angles of any polygon is equal to twice as many right angles as the polygon has sides less two. (2) The sum of the exterior angles of any polygon is equal to four right angles. STAM. EUMORFOPOULOS....
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 394 pages
...each of these triangles is equal to two right angles (Th. xvii) : hence, the sum of the angles of «11 the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles about the point P is equal to four right angles (Th....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...a, is two right angles (11) ; therefore, the sum of all the angles, both interior and exterior, is twice as many right angles as the polygon has sides. But the sum of the interior angles alone is twice as many right angles as the polygon has sides, less four right angles...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...angles of each of these triangles, is equal to two right angles (Prop. XXVII.) ; therefore the sum of the angles of all the triangles is equal to twice as many right n.ngles as the polygon has sides. But the same angles are equal to the angles of the polygon, together...
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On Intelligence

Hippolyte Taine - Knowledge - 1871 - 600 pages
...the polygon ; so that the angles of the polygon, if we add to them the angles at the vertices, are equal to twice as many right angles as the polygon has sides. Now we know independently that the angles at the vertices are together equal to four right angles ;...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...-f- a, is two right angles (11); therefore, the sum of all the angles, both interior and exterior, is twice as many right angles as the polygon has sides. But the sum of the interior angles alone is twice as many right angles as the polygon has sides, less four right angles...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...the sum of the angles of all the triangles, that is, the sum of the interior angles of the polygon, is equal to twice as many right angles as the polygon has sides minus two. PRACTICAL QUESTIONS. 1. Do two lines that do not meet form an angle with each other ? Two...
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