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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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...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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...required. 15. It appears, from Euc. I. 32, Cor. 1, that ' 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.' Hence if n be the number of sides of any rectilineal figure, we have the sum of its n angles +4 x 90°=...

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...Cor. Theor. V., (page 12,) it is stated and proved, " that 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" or in other words that — In any rectilineal figure, the sum of all the interior angles, is equal...

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...being the two angles made by cne line meeting another. The sum of all the outward and inward angles, is equal to twice as many right angles as the figure has sides; but the sum of all the inward angles is equal to twice as man1 right angles as the figure has sides,...

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...polygon may be found from the property of such figures, that the sum of the angles of any polygon is equal to twice as many right angles as the figure has sides, less four. The following technical terms require explanation : — A Salient Angle is one directed...

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...end of the produced line to the end of the base. COB. 3. 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. 4. All the exterior angles of any rectilineal figure are together equal to four right angles....

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...that is a , together with four right angles. . 2 Cor Therefore all the angles of the figure, XT - *• together with four right angles, are equal to twice as many right angles as the figure has sides. [The triangle furnishes an instance of this, for all its angles are together equal to two right angles;...

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...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. 4) ; and...

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...triangles in the figure ; that is, as many times as there are sides, less two. But this product is equal to twice as many right angles as the figure has sides, less four right angles. Cor. 1. The sum of the interior angles in a quadrilateral, is equal to two...

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...which is the common vertex of the triangles : that is (i. 15, cor. 2), together with four right angles. Therefore all the angles of the figure, together with...twice as many right angles as the figure has sides. Сод. 2. All the exterior angles of any rectilineal figure are together equal to four right ,ingles....