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" 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. "
Elements of Plane Geometry - Page 46
by Thomas Hunter - 1878 - 132 pages
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...diagonals &c. QED PROPOSITION L. THEOREM. All the interior angles of any rectilineal figure arc together equal to twice as many right angles as the figure has sides, wanting four right angles'. Let ABCDE be any rectilineal figure; all its interior angles A, B, C, D,...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...together equal to four right angles ; and the sum of its interior angles, together with four right angles, is equal to twice as many right angles as the figure has sides . . • 15 (•) The area of a rectilineal figure may be obtained by dividing it into triangles,...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 216 pages
...angle EDN ; therefore the reentrant angle, with the sum of all the other internal and external angles, is equal to twice as many right angles as the figure has sides, and to its excess EDN above two right angles : but the internal angles, with four right angles, are...
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Elements of Geometry with Notes

John Radford Young - Geometry, Modern - 1833 - 240 pages
...interior opposite angle CDE. A•B PROPOSITION XVII. THEOREM. In any polygon the sum of all the angles is equal to twice as many right angles as the figure has sides, all but four right angles. For if from the vertices of the several angles, lines be drawn to any point...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...severally capable of being so divided. And because the interior angles of each of such smaller figures are equal to twice as many right angles as the figure has sides, diminished by four right angles, (or, which is the same thing, to twice as many right angles as the...
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Inductive Geometry, Or, An Analysis of the Relations of Form and Magnitude ...

Charles Bonnycastle - Geometry - 1834 - 670 pages
...expressed as the following proposition : "The interior angles of any closed plane figure are together equal to twice as many right angles as the figure has sides, minus four right angles." 206. And as a second application of the principle in question, or, which amounts to the same, of the...
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Inductive Geometry, Or, An Analysis of the Relations of Form and Magnitude ...

Charles Bonnycastle - Geometry - 1834 - 678 pages
...we may refer to the proposition which asserts the interior angles of a plane figure to be equivalent to twice as many right angles as the figure has sides, minus two, art. 205. And as conditions exist involving merely the directions of the points, so also we have...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...together equal to four right angles ; and the sum of its interior angles, together with four right angles, is equal to twice as many right angles as the figure has sides . . . 15 (c) The area of a rectilineal figure may be obtained by dividing it into triangles, having...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...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 and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...equal to the angle B, and the other part DAE is equal to the angle C. i PROPOSITION XXVI. THEORKM. The sum of all the interior angles 'of a polygon, is equal to two right angles, taken as many times less two, as the Jigure has sides. Let ABCDEFG be the proposed...
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