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" Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 30
by Euclides - 1814
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...a side of a triangle, &c. o. E. i,. COn. 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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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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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...Wherefore, if a side of a triangle, &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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...each of them is a right angle (10. Def.). 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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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 Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 317 pages
...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 together equal to four right angles. ABC, with its adjacent exterior Because every interior angle ABD, is equal (13. 1.) to two right angles...
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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 ...

Euclides - 1845
...then «6 is the sum of all the interior angles. But all the interior angles of any rectilinear figure together with four right angles, are equal to twice as many right angles as the figure has sides, that is, if we agree to assume IT to designate two right angles, .-. nS + 27T = ntr, and «6 = »ir...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...Wherefore, if a side of a triangle, &c. QED COB. 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. the angles of these triangles are equal to twice as many right angles as there are triangles, that...
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