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" F, which is the common vertex of the triangles ; that is, together with four right angles. 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 First Six Books: Together with the Eleventh and Twelfth - Σελίδα 38
των Euclid - 1781 - 520 σελίδες
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...therefore equal to B AE and EAC. Cor. 6. All the internal angles of any rectilineal figure, ABCDE, together with four right angles, are equal to twice as many right angles as the figure has sides. Take any point F within the figure and draw the right lines FA, FB, FC, FD, and FE. There are...

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...common vertex of the triangles : that is, (2. Cor. 15. 1 .) together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angit's as the figure has sides. Cor. 2. All the exterior angles of any rectilineal figure are together...

Elements of Arithmetic, Algebra, and Geometry

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...to all the angles of the figure, together with four right angles ; that is, the angles of the figure are equal to twice as many right angles, as the figure has sides wanting four. PROP. XIII. THEOREM. If two triangles, BAG, EOF, have two angles, BAG, ABC, and...

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...common vertex of the tri• 2 Cor. angles; that is * together with four right angles. There1s, 1. fore all the angles of the figure, together with four right...equal to twice as many right angles as the figure has sides. COR. 2. All the exterior angles of any rectilineal figure are together equal to four right angles....

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...has sides (XXXII) ; but the angles at the point F are equal to four right angles (83) ; and therefore the angles of the figure, together with four right...equal to twice as many right angles as the figure has sides. This is the first corollary in the Elements, and the following is the second. (135) COR. 11....

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...twice — > -fQ as many right angles as there are sides of the figure. But all the interior angles together with four right angles are equal to twice as many right angles as there are sides of the figure (Prop. L). Therefore all the interior and all the exterior angles are...

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...twice as 118 119 липу right angles as the figure has sides. Hence the interior angles of the figure are equal to twice as many right angles as the figure has sides wanting four right angles. Cor. 1. All the interior angles of a quadrilateral figure are together...

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