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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. "
New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ... - Page 29
by Benjamin Greenleaf - 1873 - 176 pages
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...zi. 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: With Notes

John Radford Young - Euclid's Elements - 1827 - 246 pages
...in each triangle amounts to two right angles, therefore the angles of all the triangles are together equal to twice as many right angles as the figure has sides, that is to say, the sum of the angles of the polygon, together with those about the point within it,...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...excess of every reentrant angle above two right angles. But (134) the sum of the internal angles alone is equal to twice as many right angles as the figure has sides, deducting four ; hence the sum of the external angles must be equal to those four right angles, together...
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Elements of the Geometry of Planes and Solids: With Four Plates

Ferdinand Rudolph Hassler - Electronic book - 1828 - 180 pages
...two right angles. 28. THEOREM. In any rectilineal figure the sum of all the inner angles together is equal to twice as many right angles as the figure has sides, wanting four right angles. APPLIC. In the rectilineal figure ABDEFG, (fig. 34,) the sum of all the...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 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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A London Encyclopaedia, Or Universal Dictionary of Science, Art ..., Volume 10

Thomas Curtis - Aeronautics - 1829 - 814 pages
...118 119 липу right angles as the figure has sides. Hence the interior angles of the figure are equal to twice as many right angles as the figure has sides wanting four right angles. Cor. 1. All the interior angles of a quadrilateral figure are together equal...
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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 - 183 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

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 - 150 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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