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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. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 376
by Rev. John Allen - 1822 - 494 pages
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 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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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...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 First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 390 pages
...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 Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...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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Lessons on form; or, Introduction to geometry as given in a Pestalozzian ...

Charles Reiner - 1837
...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

Measurement - 1837 - 262 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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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 329 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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...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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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...two right angles. All the angles, therefore, of the triangles into which the AE figure is divided, are equal to twice as many right angles as the figure has sides. But of these, the angles round the point F are equal to four right angles (Prop. 13, cor.) : if these...
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A Treatise on Geometry and Its Application in the Arts

Dionysius Lardner - Curves, Plane - 1840 - 314 pages
...supplement of its adjacent external angle, the internal and external angles, taken together, will be equal to twice as many right angles as the figure has sides ; but, from what has been already shown, the external angles alone are equal to four right angles....
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