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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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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 336 pages
...by -f of one right angle. PROP. XXVI. THEOR. All the interior angles of any rectilineal figure, art equal to twice as many right angles as the figure has sides, wanting four right angles. For any rectilineal figure ABCDE can be divided into as many triangles as...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 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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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...triangle are equal to two right angles. Сон. 1. All the interior angles of any rectilineal figure are equal to twice as many right angles as the figure has sides, wanting four right anglesť 2. All the exterior angles of any rectilineal figure are to. gether equal...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 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 and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 376 pages
...two right angles, taken as many times, less two, as the polygon has sides (Prop. XXVI.) ; that is, equal to twice as many right angles as the figure has sides, wanting four right angles. Hence, the interior angles plus four right angles, is equal to twice as...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 254 pages
...vertex of these triangles = 4 rt. /.s; therefore, the sum 01 the interior angles of any polygon is equal to twice as many right angles as the figure has sides less [minus] four. M.—If the number of sides be three, four, five, six, seven, &c., what is the sum...
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A Treatise on Mensuration for the Use of Schools

Commissioners of National Education in Ireland - Measurement - 1837 - 284 pages
...you go along, as also the angles. angles, A, B, C, &c. of the figure together, and their sum must be equal to twice as many right angles as the figure has sides, wanting four right angles. But when the figure has a re-enterant angle, as F, measure the external...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 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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