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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 Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 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 geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...lines from a point F within the figure to each of its angles. And, by the present 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 - Euclid's Elements - 1842 - 317 pages
...as the figure has sides ; but the exterior are equal to four right angles ; therefore the interior are equal to twice as many right angles as the figure has sides, wanting four. PROP. II. Two straight lines, which make with a third line the interior angles on the...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...two regular polygons, having the same number of sides. The sum of all the angles in each figure is equal to twice as many right angles as the figure has sides, less four right angles (BI A{ Prop. 13), and as the number of sides is the same in each figure, the...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...equal to two right angles, and there are as many triangles as the figure has sides, therefore all the angles of these triangles are equal to twice as many right angles as the figure has sides ; but the same angles of these triangles are equal to the interior angles of the figure together with...
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The first six and the eleventh and twelfth books of Euclid's Elements; with ...

James Thomson - Geometry - 1845 - 358 pages
...from ii 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 in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...together with four right angles, are equal to twice as many right angles as the figure has sides. 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 (solid) geometry (Higher geometry) and trigonometry (and ...

1845
...two right angles, taken as many times, less two, as the polygon has sides (Prop. XXVIII.) ; 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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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...from any point F within the figure to each of its angles. Now, 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 : But all the angles of the triangles...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...(c) p. 13. (e)p.29; Cor. 1. All the interior angles of any rectilineal figure and four right angles, are equal to twice as many right angles as the figure has sides. For, about a point within the figure, as many triangles may be formed as the figure has sides, each...
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