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... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
The elements of plane geometry; or, The first six books of Euclid, ed. by W ... - Σελίδα 21
των Euclides - 1863
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...;• add all the inward angles A, B, C, &c. together, and when the work is right, their sum will be equal to twice as many right angles, as the figure has sides, wanting four right angles. And when there is an angle, as F, that bends inward, and you measure the...

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...within the figure to leach of its angles. And, by the preceding proposition, a 2 Cor. 15.1. Book I. all the angles of these triangles are equal to twice as many right angles as there are triangles, that is, as there are sides of the figure ; and the same angles are equal to the...

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...AED, is equal to two right angles. All the exterior angles therefore, added to the interior angles, are equal to twice as many right angles as the figure has sides. Consequently the exterior angles are equal to the four right angles which, by the last Proposition,...

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...is equal to two right angles. All the exterior angles therefore, added to the interior angles, ftre equal to twice as many right angles as the figure has sides. Consequently the exterior angles are equal to the four right angles which, by the last Proposition,...

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...the figure to each of its angles. And, by the preceding Book I a 2 Cor. 15.1. b 13. 1. proposition, all the angles of these triangles are equal to twice •* as many right angles as there are triangles, that is, as there are sides of the figure; and the same angles are equal to the...

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...triangles, is equal to two right angles (th. 17); 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 P, which are so many many of the angles of the triangles,...

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...F within the figure to Boon I. each of its angles. And, by the preceding proposition, all v-""v~*"' the angles of these triangles are equal to twice as many right angles as there are triangles, that is, as there are sides of the figure : and the same angles are equal to the...