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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, from the Sansk. text of Ayra Bhatta, ed. by ... - Page 40
by Āryabhaṭa - 1878
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 2

Mathematics - 1801 - 658 pages
...;• 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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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 pages
...Q^ED . CoR. i. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has fides. For any reCtilineal figure ABCDE can be divided into as many triangles as the figure has fides,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...gether 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. CoR. 2. All the exterior angles of any rectilineal figure, are together equal to four right angles....
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A Course of Mathematics in Two Volumes for the Use of Academies as Well as ...

Charles Hutton - Mathematics - 1807 - 464 pages
...work ; add all the inward angles A, B, c, &c, together ; for when the work is right, their sum will ba equal to twice as many right angles as the figure has sides, wanting 4 right angles. But when there is an angle, as F, that bends inwards, and you measure the external...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Analytic - 1809 - 542 pages
...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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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 554 pages
...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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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811 - 406 pages
...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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...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...
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