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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. "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 29
by Euclides - 1860
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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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...with the angles at the point F, which is the common vertex of the triangles : that is, (2 Cor. 15. 1.) together with four right angles. Therefore all the...twice as many right angles as the figure has sides. COR. 2. All the exterior angles of any rectilineal figure, are together equal to four right angles....
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...with the angles at the point F, which is the common vertex of «2cor is i "le triangles; that is,* together with four right angles. Therefore all the...twice as many right angles as the figure has sides. COB. 2. — All the exterior angles of any rectilineal figure are together equal to four right angles....
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...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 - 386 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 - 378 pages
...angles. 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...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 - 316 pages
...the angles at the point F, which is the common vertex of the triangles ; that is (2. Cor. 13. 1.), together with four right angles. Therefore all the...twice as many right angles as the figure has sides. COR. 2. All the exterior angles of any rectilineal figure are together equal to four right angles....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 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 - 110 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 in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...angles at the point F, which is the common vertex of the triangles ; that is, IT together * *5c°r. with four right angles. Therefore all the. angles...twice as many right angles as the figure has sides, COR. 2. All the exterior angles of any rectilineal figure are together equal to four right angles....
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