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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.
The Elements of Euclid, containing the first six books, with a selection of ... - Σελίδα 32
των Euclides - 1874
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## Elementary Course of Geometry ...

Charles William Hackley - 1847 - 248 σελίδες
...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...

## A Complete Treatise on Practical Land-surveying: In All Its Departments ...

Anthony Nesbit - 1847 - 426 σελίδες
...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...

## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 σελίδες
...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...twice as many right angles as the figure has sides. COB. 2. All the exterior angles of any rectilineal figure, made by producing the sides successively...

## The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 σελίδες
...angles. Wherefore if a D side of a triangle, &c. QED COR. 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. For any rectilineal figure ABODE can be divided into as many triangles as the figure has sides, by...

## Elements of Geometry and Conic Sections

Elias Loomis - 1849 - 252 σελίδες
...(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,...

## Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 384 σελίδες
...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...

## Reports on Elementary schools

Her MAjesty' Inspectors of schools - 1850 - 912 σελίδες
...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...

## Minutes ...: Correspondence, Financial Statements, Etc., and ..., Τόμος 2

Great Britain. Committee on Education - 1850 - 914 σελίδες
...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...

## The Church of England quarterly review, Τόμος 28

1850 - 524 σελίδες
...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...

## Elementary Geometry: With Applications in Mensuration

Charles Davies - 1850 - 218 σελίδες
...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...