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" ... 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. "
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... - Page 30
by Robert Potts - 1868 - 410 pages
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A Complete Treatise on Practical Land-surveying: In All Its Departments ...

Anthony Nesbit - Plane trigonometry - 1847 - 492 pages
...accuracy of the previous work. Moreover, since the sum of all the interior angles of any polygon is equal to twice as many right angles as the figure has sides, lessened by four ; as the given figure has five sides, the sum of all its interior angles must be 2x5...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...Hence it follows that the sum of all the inward angles of the polygon alone, A + B -f- C + D + E, is equal to twice as many right angles as the figure has sides, wanting the said four right angles. QED Corol. 1. In any quadrangle, the sum of all the four inward...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...triangle are together equal to two right angles. COR. 1. All the interior angles of any rectilineal figure together with four right angles, are equal...rectilineal figure, made by producing the sides successively hi the same direction, are together equal to four right angles. PROP. XXXIII. THEOREM. The straight...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...is the common vertex of the triangles ; that is (Cor. 2. i. 15.), together with four right angles. Therefore all the angles of the figure, together with...twice as many right angles as the figure has sides. COR. 2. All the exterior angles of any rectilineal figuro, are together equal to four right angles....
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...(Prop. XXVII., BI), that is, as there are sides of the polygon BCDEF. Also, the angles of the polygon, together with four right angles, are equal to twice as many right angles as the figure has sides (Prop. XXVIII., BI); hence all the angles of the triangles are equal to all the angles of the polygon,...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...to two right angles, taken as many times, less two, as the polygon has sides (Prop. XXVI.); that is, equal to twice as many right angles as the figure has sides, wanting four right angles. Hence, the interior angles plus four right Let the sides of the polygon...
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Minutes ...: Correspondence, Financial Statements, Etc., and ..., Volume 2

Great Britain. Committee on Education - 1850 - 942 pages
...Question is only to be answered in each Section.) Section I. 1. All the interior angles of any rectilineal figure, together with four right angles, are equal...twice as many right angles as the figure has sides. 2. If the square described upon one side of a triangle be equal to the sum of the squares described...
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Reports on Elementary schools

Her MAjesty' Inspectors of schools - 1850 - 912 pages
...Question is only to be answered in each Section.) Section I. 1. All the interior angles of any rectilineal figure, together with four right angles, are equal...twice as many right angles as the figure has sides. 2. If the square described upon one side of a triangle be equal to the sum of the squares described...
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The Church of England quarterly review, Volume 28

1850 - 524 pages
...revelation could supersede the reasoning of the proposition that all the interior angles of any rectilinear figure, together with four right angles, are equal...twice as many right angles as the figure has sides : and the dictum is equally true, too, in moral science — only in any particular case to dogmatize...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...triangles is equal to two right angles (Th. xvii) : hence, 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 P is equal to four right angles (Th. ii. Cor. 3) ; and...
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