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... twice as many right angles as the figure has sides ; 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, containing the first six books, with a selection of ... - Σελίδα 32
των Euclides - 1874
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A Treatise on Mensuration for the Use of Schools

...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...

Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 254 σελίδες
...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...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1838 - 434 σελίδες
...which is the common vertex of the triangles : that is, (2 Cor. 15. 1.) together with four right angles. Therefore all the angles of the figure, together with...All the exterior angles of any rectilineal figure, are together equal to four right angles. Because every interior angle ABC, with its adjacent exterior...

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 σελίδες
...which is the common vertex of «2cor is i "le triangles; that is,* together with four right angles. Therefore all the angles of the figure, together with...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....

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

Euclides - 1840 - 194 σελίδες
...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...

A Treatise on Geometry and Its Application in the Arts

Dionysius Lardner - 1840 - 386 σελίδες
...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....

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

Euclides - 1841 - 378 σελίδες
...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...

Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 σελίδες
...as there are triangles (Euc. 32. 1.); that is, as there are sides in the figure BCDEF; and because all the angles of the figure, together with four right angles, are likewise equal to twice as many right angles as there are sides in the figure (Euc. 1. Cor. 32. 1.);...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 σελίδες
...angles as there are triangles (32. 1.) » that is, as there are sides in the figure BCDEF ; and because all the angles of the figure, together with four right angles, are likewise equal to twice as many right angles as there are sides in the figure(l cr. 32. 1 .^therefore...

Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - 1844 - 96 σελίδες
...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...