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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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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...COR. 10. — All the internal angles of any rectilinear 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 F E. There are formed...
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Elements of the Geometry of Planes and Solids: With Four Plates

Ferdinand Rudolph Hassler - Geometry - 1828 - 180 pages
...angles, as AGD, GDE, and so on, standing in equal segments, are equal to one another; and their sum being equal to twice as many right angles as the figure has sides wanting four: that is, eight right angles, each of these angles of the hexagon is equal eight sixths...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...and the three angles of each triangle are together equal to two right angles (Prop. 32), therefore 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. But the same angles are equal to the...
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A London Encyclopaedia, Or Universal Dictionary of Science, Art ..., Volume 10

Thomas Curtis - Aeronautics - 1829 - 814 pages
...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 equal...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...is equal to two right angles (2.) ; all the interior angles, together with all the exterior angles, are equal to twice as many right angles as the figure has angles. But all the exterior angles are, by the former part of the proposition, equal to four right...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833 - 304 pages
...angle. Cor. 6. All the internal angles of any rectilineal figure, together with four right angles, are = to twice as many right angles as the figure has sides. therefore all their angles taken together are = to twice as many right angles as the figure has sides, (prop. 32,)...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...isf equal to two right angles ; all the interior together with all the exterior angles of the figure, are equal to twice as many right angles as the figure has sides. But (by Cor. 1 .) all the interior angles are together equal to twice as many right angles as the figure'...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 216 pages
...to four right angles (2); and therefore the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. Cor. 7. The external angles of any rectilineal figure are together equal to four right angles. For...
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Inductive Geometry, Or, An Analysis of the Relations of Form and Magnitude ...

Charles Bonnycastle - Geometry - 1834 - 670 pages
...expressed as the following proposition : "The interior angles of any closed plane figure are together equal to twice as many right angles as the figure has sides, minus four right angles." 206. And as a second application of the principle in question, or, which...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...&c. QED COR. 1. 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 sides. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by...
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