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" F, which is the common vertex of the triangles ; that is, together with four right angles. 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 First Six Books: Together with the Eleventh and Twelfth - Seite 38
von Euclid - 1781 - 520 Seiten
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...Wherefore, if a side of any triangle be produced, &c. 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,...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...1.) 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 to twice as many right angles as the figure has sides. DEMONSTRATION For, any rectilineal figure ABCDE can, by drawing straight lines from a point...
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Loftus's Inland Revenue Officers' Manual: a guide to the duties and ...

William Harris JOHNSTON - 1865
...32nd prop, of Euclid, Book I., it is demonstrated that, <> all the interior angles of any rectilinear figure, together with four right angles, are equal to twice as many right angles as the figure has sides." Hence, the sum of all the angles of a rectilinear figure will be found by taking twice as many...
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Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865
...figure has sides wanting four right angles. Let ABODE be any given rectilineal figure, all its interior angles are equal to twice as many right angles as the figure has sides wanting four right angles. From F, a point within the figure, draw the straight lines AF, BF,...
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A Treatise on Surveying: In which the Theory and Practice are Fully ...

Samuel Alsop - 1865 - 428 Seiten
...and B ABC + BAC + ACB = two right angles. (32.1.) 76. The interior angles of any rectilineal figure are equal to twice as many right angles as the figure has sides, diminished by four right angles. The interior angles of a quadrilateral are therefore equal...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 Seiten
...triangles, that is, together with four right angles. [I. 15. Corollary 2. Therefore all the interior angles of the figure, together with four right angles,...equal to twice as many right angles as the figure has sides. COROLLARY 2. All the exterior angles of any rectilineal figure are together equal to four right...
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A Dictionary of Science, Literature, & Art: Comprising the ..., Band 3

William Thomas Brande, George William Cox - 1867
...polygons, the first corollary to his prop. 32, book i. (according to which all the interior angles, together with four right angles, are equal to twice as many right angles as the figure hns sides), is also true for concave polygons. His second corollary, however, according to which the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 Seiten
...Wherefore, if a side of any triangle &c. Q EB COROLLARY 1. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as thejigure has side.". For any rectilineal figure ABCDE can be divided into as many triangles as the...
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A Dictionary of Science, Literature, & Art: Comprising the ..., Band 3

William Thomas Brande, George William Cox - 1867
...polygons, the first corollary to his prop. 32, book i. (according to which all the interior angles, together with four right angles, are equal to twice as many right angles as tie figure has sides), is also true for concave polygons. His second corollary, however, according...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 Seiten
...angles of the triangles are equal to twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right...equal to twice as many right angles as the figure has sides. COB. 2. All the exterior angles of any rectilineal figure, made by producing the sides successively...
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