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" ... therefore the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles... "
Manual of Geometry and Conic Sections: With Applications to Trigonometry and ... - Page 36
by William Guy Peck - 1876 - 366 pages
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The Modern Preceptor ; Or, a General Course of Education, Volume 1

John Dougall - 1810
...be equal to twice as many right angles as there are triangles, that is, as the figure has sides, but the sum of all the angles of all the triangles is equal to the sum of all the angles of the pol ygor^ together with the angles at the central point G, which by...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1812
...three angles of each of these triangles, is equal to two right angles (th. 17) ; therefore the snm f the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles about the point *p> which are so many many of the angles...
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New Series of The Mathematical Repository, Volume 3

Thomas Leybourn - Mathematics - 1814 - 420 pages
...Hence, by adopting the notation in the question, we have But the sum of the angles of any polygon being equal to twice as many right angles as the polygon has sides, less four; the sum of all the angles of the polygon will be equal to an even number of right angles,...
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A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well ...

Charles Hutton - Mathematics - 1816
...three angles of each of these triangles, is equal to two right angles (th 17*; therefore the sum of the angles of all the triangles is equal to twice as many iig:>t angles as the figure has sides. But the sum of all the angles about the point r, which are so...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...three angles of each of these triangles, is equal to two right angles (th. 17) ; therefore the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles about the point p, which are so / many of the angles...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...to say, the sum of the angles of the polygon, together with those about the point within . it, are equal to twice as many right angles as the polygon has sides ; but those angles which are' about the point, amount to four right angles, (Prop. VI. Cor. 2.) deducting...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...figure has sides, wanting four right angles. Hence, the interior angles plus four right .. -i angles, is equal to twice as many right angles as the polygon has aides, and consequently, equal to the sum of the interior angles plus the exterior angles. Taking from...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...of each as there arc sides of the polygon ; hence, the sum of all the interior and exterior angles is equal to twice as many right angles as the polygon has sides. Again, the sum of all the interior angles is equal to two right angles, taken as many times, less two,...
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Plane Trigonometry and Mensuration for the Use of the Royal Military College

William Scott - Measurement - 1845 - 290 pages
...end ought to coincide. Also, the sum of all the angles, together with four right angles, ought to be equal to twice as many right angles as the polygon has sides (Eue. i. 32. cor.). To find the angle contained by two straight lines conceived to be drawn from a...
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An Introduction to Geometry and the Science of Form: Prepared from the Most ...

Anna Cabot Lowell - Geometry - 1846 - 161 pages
...into as many triangles as it has sides. The sum of all the angles of each triangle = 2 RA, therefore the sum of all the angles of all the triangles is equal to 2 RA multiplied by the number of sides in the figure. But the angles (equal to 4 RA) about the point...
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