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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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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...straight lines from a point F within the figure to each of its angles. And, by the preceding 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...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. COR. 2. All the exterior angles of any rectilineal figure are tegether equal to four...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...at A are greater than twice as many right angles, except four, as the figure has sides ; and all thc angles of these triangles are equal to twice as many right angles as the figure has sides (32. 1 &'.), therefore the angles of these triangles which are at their common vertex A, being those...
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The First Six Books with Notes

Euclid - 1822 - 222 pages
...equal (i)Prop. 13. to two right angles (1), therefore all the external angles, with all the internal, are equal to twice as many right angles as the figure has sides ; but the internal angles, together with four right angles, are equal to twice as many rightangles...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 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 of the angles of the triangles,...
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...twice as many right angles as the figure has sides ; or the interior angles of the figure, themselves, are equal to twice as many right angles as the figure has sides, wanting four right angles. QED Cor. 1. All the interior angles of any quadrilateral figure are together...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...straight lines from a point F within the figure to each of its angles. And, by the preceding 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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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...straight lines from a point F within the figure to each of its angles. And, by the preceding theorem, 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 ...

Robert Simson - Trigonometry - 1827 - 546 pages
...straight lines from a point F, within the figure to each of its angles. And, by the preceding 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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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 246 pages
...in each triangle amounts to two right angles, therefore the angles of all the triangles are together equal to twice as many right angles as the figure has sides, that is to say, the sum of the angles of the polygon, together with those about the point within it,...
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